QUANTUM BRIDGE THE FULL POWER OF OUR HAND

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QUANTUM BRIDGE THE FULL POWER OF OUR HAND

To understand the true nature of the Bridge game we need to ponder on the requirements of the contract to be played. The first one is the number L of odd tricks to be won. The second one is the mode m of play. The number L is a level number from 1 to 7 expressing the true number C of contract tricks by the equation C = L + 6. The mode m of play increases 5 times the quality of any playing level L, from clubs till to NT, so that it too can be considered like a true number expressing a sub level ranking of L. As we see, mode m of play has a decisive minor impact than L being only an its quality. This aspect of predominance of L on m is ruled by the fundamental LAWS of the game, a group of almost a hundred that can be found at the website of World Bridge Federation (http://www.worldbridge.org/), entity in charge of their disclosure, updating and respect. The most important LAW among them is the fundamental law of judgment of the played contract: "LAW 77 – DUPLICATE BRIDGE SCORING TABLE". This law drives at any time the behaviour of any player since it assigns a positive "score" only if the number L, that is the number C of contract tricks is respected, otherwise the declarer’s side is punished only by the number M of missing tricks, with no regard to the mode or quality of play. The mode, instead, must be rewarded only if the number C of contract tricks is at least reached. The judgement of all played contracts is so fundamentally placed on the comparison between the number C of contract tricks to be won and the number E of the actual won tricks, that is on E - C.. This characteristic and basic aspect, framed by the LAW 77, delivers to the number E and to the number C the keystone of the whole Bridge game. All that matters can be traced and driven back to their comparison: E - C. The equation now is very simple: he wins who better knows that difference! For this purpose, all our attention must be brought to know as soon as possible and with the best precision E and C. How to arrive to that knowledge? What do we have for the purpose? A fundamental fact must be considered: at cards just received, we can never know, for sure, which number C of contract tricks will be, nor its mode m of play. Instead, we can immediately know with unparalleled precision what matters more than anything else: the number W of winnable (stochastically) tricks of our hand. This number W is the complementary part of the number Z of winnable tricks by our partner’s hand. As soon as we open, conventionally calling a number W, partner can soon count W + Z and is already a big step ahead of all contestant people in the knowledge of E. He, by pondering his actual cards and strength distribution, has all he needs for carrying out the critical task of determining our most probable number E of actual won tricks. If we opened by calling, for example, “1♦” = 5 W and partner had 5 Z with distributed strength, Game would already be around the corner, otherwise it all would depend by 1

the actual fit quality. At any rate, he would always have a great light shining, especially if a hard interference would take place. His task would be to give us, when convenient, a forecast of level L, the most probable reachable one by a mild fit. For example, if he answered: “1NT” without previous interference, he would show a reachable level 4 because having used the 3rd available bid step. The answer would also imply that we ought to stop at level 3 if there were no fit and that we could even go to level 5 or 6 with good or excellent fit. Any occurring interference before the level prediction would be of great help because it would allow to update more and more accurately the strength of the hand and so L. For example, after an interference of “2♠”, our partner could update his forecast very probably to level 5 or to level 3. All our W + Z potential tricks, and the forecasted reachable level L thus become a function of the found fit quality. From now on, all the calls will be strictly traditional and all useful ones to let update the W + Z potential tricks and the forecasted L target.

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THE POWER OF OUR HAND The power of our hand is an absolute, independent value of the hand before bidding, arising from the configuration of its suits, to be fully used if wanting to play the most possible convenient contract. Only at this stage and purpose it could be defined “weak”, “average” or “strong”. During the bid, the power could change very much, becoming soon function of the real disposition and distribution of the other cards, and, above all, of the bid contract. Owing to decide if compete or not for a convenient contract, we have only one reference point: the native fundamental LAW 77 - DUPLICATE BRIDGE SCORING TABLE, the true core of all Bridge game. There, any possible contract score is fixed, so that, automatically, one can judge the convenience of any contract. Every professional player well knows it. Knowing that, a spontaneous question arises: “why fix and impose any other senseless limit for opening a hand?”. All is already fixed by that LAW. Why should we open, or interfere, having not convenience to do it? Why to open having a “weak” hand? All is so transferred to what we mean by “weak”. At the WBF site, we find the document: WBF SYSTEMS POLICY 2016 (Adopted December 1994; amended October 1996, January 2000, August 2002, October 2007, October 2008 September 2009, October 2010, September 2013, June 2016 & June 2018) where in the Preamble we can read: “References to High Card Points in this document are Milton Work Points. …. In the following ‘Weak’ means 9 points or less and ‘Strong’ means 16 points or more”. We are astonished, and somewhat horrified by that, because with 9 MW points we could have a hand like: ♠ AKQ1098765432 ♥ 2 ♦ - ♣ -, obviously tremendously strong one! Not even “weak” it could be defined a hand like: ♠ KQJ1098765432 ♥ 2 ♦ - ♣ -, and those yet able of winning 4 tricks or more playing at their best denomination, like even for example: ♠ 8765432 ♥ 32 ♦ 32 ♣ 32. A hand is really weak only when never having a convenient contract to play or to bid. Weakness concept is so relative, because tied and function of the contract conveniences. It becomes absolute only when the hand had no convenient contracts to play or oppose. Even the ending part of the Preamble is highly disturbing, because it automatically defines as “average” any hand having a power between 10 and 15 MW points. It would be too easy to report examples of that power making Grand Slam! Perhaps something must be revised. All above already introduces and defines the power of a Bridge hand, that is all that one possible to exploit during the auction for trying to play its most convenient contract. We also have seen how inappropriate is to use a measuring gauge based on points, whereas we must bid, play and be judged only by a number of tricks. There is never a way to reconcile the HCP/MW measuring gauge to that of tricks because it was, and still (!) is based on two fundamental logic errors. Let’s see them. A trick win 4 cards. That perhaps was Milton Work’s thought when attributed the 4 points value to the Ace. That is true 95 times out of 100, and 100% for Ace of trumps. But if that was the equation, we should count 52 MW for 13 won tricks and not 37 when having: ♠ AKQJ ♥ AKQ ♦ AKQ ♣ AKQ, or any other equipollent hand such as for example: ♠ AKQJ1098765432 ♥ - ♦ - ♣ -. That means only two things: the hierarchy connection, especially consecutiveness, and suits length were and still are yet completely ignored! There is a great difference between having a hand like: ♠ AKQJ10 ♥ 98 ♦ 765 ♣ 432 and a hand like: ♠ A765 ♥ K98 ♦ Q43 ♣ J102, both counting 10 MW but valuing 5 tricks the first one and about 3 tricks the second one where its hierarchy values are everywhere scattered. Recently HCP system has been introduced to take care in some way of that ignorance, but certainly not solving the problem of: ♠ AKQJ1098765432 ♥ - ♦ - ♣ -, where is too easy to see 13 winnable tricks (13 W) and a very poor count of HCP points. 3

The truth is that any suit length has its own minimal power starting from some hundredth W of a single card suit and arriving to a superb full 13 W of a one coloured hand, where we can see that a suit length is even able of proportionally increasing any leading hierarchy power. A King accompanied by one card is certainly much weaker than a King followed by 3 or more cards. The logic error was and is to assign a fix value to the “honours”. That could also be easily seen when considering a suit like KQ where K transfers a value of 0.50 tricks to the consecutive Queen, and when considering KQJ where the transferred value is of 0.66 tricks to each consecutive card. Same speech may be applied to QJ10 and QJ109 where the transferred Queen’s value grows from 0.33 to 0.50. The more the following cards, the more the leading card value. A 5th King like K7532 would have a transferrable hierarchic value of 0.80 tricks if finding consecutive cards. If not, and if the hierarchy configuration were not prolonged by the 4th card, it must be added to that value only the minimal value of a 5th suit, which is of 1.50 W, that is 0.50 W for the 4th card and 1 W for the 5th one. If the 4th card prolonged the hierarchy configuration, its minimal value of 0.50 W would increase till to 1 W if consecutive one, or some less if not. Any card beyond the 4th one has always a value of 1 W. Hierarchy, usually, ends after the 3rd leading card, as in K7532 having a total value of 0.80 W + 1.50 W = 2.30 W. Having AJ10 we can be able to win 2 tricks every 3 times out of 4 and 1 trick once out of 4 times when finding KQ at LHO (we should make the cautious assumption to not be supported by the partner’s power till to the possible maximum, owing he too to assess his hand), so we would have an average power of 2 W x 3/4 + 1 W x 1/4 = 1.75W. Having AJ109 we would have a hand power of 2.75 W, where we should count 2.75 W x 4 = 11 MW points out of 52 instead of only 5 MW out of 37 ones. Having AJ108 we would have a hand power of 1.75 W + 0.75 W = 2.50 W. Having AJ10987 we would have 1.75 W + 3 W = 4.75 W and only always 5 MW points out of 37, a poor power ratio of 0.13, instead of a right correspondent 4.75 x 4 = 19 MW points (!) out of 52 with a power ratio of 0.37, that is nearly 3 times greater. The HCP/MW system errors could be completely wiped out only measuring hands by winnable tricks. We already said that all the hand power is always of a relativistic nature, that is relative to the contract of play. The most incredible example would be if it there were 4 one coloured hands where 3 of them would see reduced to nothing their 13 tricks power. So, where is always our hand full power? The simple answer is: “it all is by playing our most convenient contract”! that target could be reached only during the bid phase! To reach the target we must have soon a convenience to call according to the picture framed by LAW 77. Being first declarer, we should have at least more than our fair share of winnable tricks, so that to can easily reach a side’s power of 4 W, or 5 W, for convenient contracts of defensive prevention. Being our fair share a quarter of 13 tricks, that is 3.25 W, we could open having at least 3.50 W. We could go on fixing such convenient limits for every situation of bid and board according to the supreme LAW77. But there is a problem. A great one! As we have just seen, LAW77 compels us to always measure our convenience by W tricks, and usually we instead measure our hand and our side’s power by points! Doing so, we soon go away by reality of W tricks having, soon after, to come back to it because the bid duty requires to call, first of all, a number of tricks. LAW77 dictates for measuring our contract convenience a gauge based on number of won tricks. Could we have and easily use such a gauge? The answer is absolutely affirmative. Let’s see an example, historical one, played at the highest tournament level, where we can have a first look of how we could behave when rightly assessing our hand power by W winnable tricks. QUANTUM BRIDGE APPLICATION Let’s imagine have, being declarer and Not Vulnerable (NV) seating at South, the following hand: ♠ 2 ♥ J1074 ♦ 3 ♣ AJT7543. We would have the distinct feeling of having a strong hand although counting only 6 MW + 4 HCP and not even satisfying the “19 ACBL” rule. We would immediately want to know how it could be its true contract power. Let’s follow what could happen applying Quantum Bridge and let’s compare our deal result with the historical ones, truly played at:

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43TH WORLD TEAM CHAMPIONSHIPS ROUND 1 2017 FINAL Board 3. Dealer South. EW Vulnerable. .........................Nord .........................♠ A10953 (2.70 W) .........................♥ AQ953 (3.10 W) .........................♦ 9 (0.05 W) .........................♣ Q9 (0.30 W) Ovest…....................................... Est ♠ QJ ………...............................♠ K8764 ♥ 862 ………..............................♥ K ♦ QJ1072 ………........................♦ AK8654 ♣ 852 ………..............................♣ K .........................Sud* .........................♠ 2 (0.00 W) .........................♥ J1074 (0.90 W) .........................♦ 3 (0.00 W) .........................♣ AJ107643 (6.00 W) we would count for us at South: ♠ 0.00 ♥ 0.90 ♦ 0.00 ♣ 6.00 that is 6.90 W. “Vow!”, we would exclaim, “that is not a "Weak hand", as, according to the aberrant WBF definitions, it should be considered. Certainly a hand, worth of more than half a Slam, could never be told "Weak”! we so would inform our partner of having that contract power by appropriately using the bid ladder (as we we’ll see) and by calling: “1♠” because falling into the 4th trick band of useful force to can open, spanning from 6.50 W to 7.50 W. West would pass, while N having: ♠ A10953 ♥ AQ953 ♦ 9 ♣ Q9 would count: ♠ 2.70 W ♥ 3.10 W ♦ 0.05 W ♣ 0.30 W that is 6.15 W and would sum [7.00 W] + 6.15 W = 13.15 P, that is Potential Winnable tricks. Having an unbalanced hand of inferior strength than ours one, he, cautiously, would sum to our tricks only his hierarchy force of about 3W, that is making 7 + 3 = 10, and would forecast a reachable level 4 of 10W called by using the 3rd Possible Call (PC) (one bid step for each level starting from level 2 because the 1st one is already exploited): “2♦”. Let’s suppose East calling: “double!”. We would tell our hand best feature by calling: “3♣”. West let’s suppose to call: “3♦”. North looking for a better fit would call: “3♥”. East, thanks to fit, could call: “3♠” destroying 1.90 W of N’s spades force. Now we would know by the fit quality and by N’s forecast to can call: “4♥”. West would pass, while N would update the side’s power by adding 4.40 W to [7.00 W] and consider if Slam were possible: “E’s call at spades and the mild fit at clubs would suggest not, while good fit at hearts yes. It does not cost anything to try asking for 1st lap controls by using the 1st Illogical Call: “4♠”. East would pass. We would answer: “5♦” having 1 Ace. West would consider that having East as strong LHO, Slam would be dangerous. Owing necessarily to risk he could call: 6♥ otherwise would more normally close at: 5♥. The 12 historical contract were: 1 E’s unacceptable contract at 3♦ + 2; 1 E’s unacceptable contract at 3♠ x 4; 1 E’s unacceptable contract at 4♦ + 2; 3 EW’ contract at 5♦ x -2; 5 NS’ contracts at 4♥ + 0, + 1, + 2; only 1 NS’ contract at 5♥ + 0. Slam could also be possible “feeling” lonely the E’s K♥. Only a few right contracts out of 12! To be noted the poor contracts at level 3 and 4 of diamonds, and how the stronger NS side, although having a contract power greater than EW’ one, gives free run to the opponent side without even calling Game. It all happened at the maximum level of competition.

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We saw that the basic aspect of the judgment delivers to the number E of actual won tricks and to the number C (or the related L) of contract tricks the keystone of the entire Game. All that matters it is only their difference: C – E. We must take conscience that we’ll never could exactly know, more than 90 times out of 100, how many E tricks we could win. We could only approach the number E at our possible best way! that way, unique one, is trying to understand how many tricks our side could possibly win: a number W many times next to, or more rarely distant from E strictly and exclusively depending by the quality of information exchanged with partner. So, we must concentrate ourselves on the best way of measuring our W winnable tricks. LAW 77 compels us to make calculations about the number C – W when playing our contract but also about the number C’ – W’ when playing a rival contract, where W’ is always our number of winnable tricks. To note that a great difference would be there nearly always between W and W’, because we will always play C exploiting the best features of our hands, while, on the contrary, we will always play C’ according to our worst features chosen by the rival side. We would play C’ only if we were sure to have greater convenience than playing C. As we see, all that above said implies that we should know at our best possible maximum two fundamental numbers: our number W of winnable tricks playing our C contract, and our number W’ of winnable tricks playing a rival C’ contract. If it were not a bid fight, we would only know W. Only now we are able of precisely define what and when is the full power of our hand: all that arising from each suit configuration, exploitable during the bid time for trying to play the most convenient contract of W or W’ tricks. Only precisely knowing our winnable contract tricks, we could take aware decisions. All that demands that we or our partner should always tell our number W of winnable tricks when opening or interfering, otherwise we’ll never be aware anymore of our precise convenient contract chances. RESPONDENT PARTNER’S KNOWLEDGE AND WORKING PATH The partner’s knowledge after our tricks opening would be soon the side’s number P = [W] + Z of total potential winnable tricks. We set the number W of winnable tricks in brackets because, for our partner, its value is corresponding to the central point of one trick interval placed between – 0.50 W and + 0.50 W. If we opened calling 5 W, we could have any power between 4.50 W and 5.50 W. That number P could be often very far or very next to E, depending only on the quality of integration of the two hands of our side. The number P tricks, at any rate, will soon tell partner if we could compete or not for a convenient contract. If P were less than 7 tricks, and second declarer had already intervened, our partner would pass without giving a forecast of play level to can be reached. If P, instead, showed a greater reachable level than that of intervention, our partner should decide, according to the risk of integration of his hand, if to give a forecast of play level and of which entity. As usual an example of historical deal would be better than any other word.

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LOOKING FOR THE BEST CONTRACT 44th World Teams Championships. Bermuda Bowl Final. Round 1. Norway vs USA 1. Board 14. Dealer East. None Vulnerable.

.........................North .........................♠ 42 .........................♥ J85 .........................♦ A10873 .........................♣ AJ9 West........................................ East* ♠ AK86....................................♠ J10753 ♥ A9743…..............................♥ KQ6 ♦ J54…....................................♦ Q92 ♣ 5….......................................♣ 43 ..........................South ......................... ♠ Q9 ......................... ♥ 102 ......................... ♦ K6 ......................... ♣ KQ108762 "Quantum Bridge" is totally applied (https://www.facebook.com/groups/QuantumBridge/): E: has an unbalanced hand of ♠ 1.90 ♥ 1.50 ♦ 0.45 ♣ 0.00 = 3.85 W, so falls into the 1st band of permissible force to can open and must so use the 1st PC: “1♣” showing a medium force of [4.00 W]. S: has an unbalanced hand of: ♠ 0.30 ♥ 0.10 ♦ 0.55 ♣ 5.75 = 6.70 W where the minimum requirement to intervene is equal to 3.75 W (N vs N) + 0 (partner not yet passed) + 0.00 (no steps of distance from 1♣) = 3.75w, falling into the 3rd trick band of permissible force to can interfere must use the 3rd PC: “1♥” showing a minimum force of 5.75 W till to 6.70 W. W: has an unbalanced hand of ♠ 2.50 ♥ 2.55 ♦ 0.25 ♣ 0.00 = 5.30 W so can sum [4.00] + 5.30 = 9.30 P and can apply, by his hand distribution, a fit factor of 70% on E’s one, and give a reachable forecast of level 2 by using the 2nd PC: “1♠”. N: has an unbalanced hand of ♠ 0.00 ♥ 0.25 ♦ 2.60 ♣ 1.35 = 4.20 W, so can sum [6.25] + 4.20 = 10.45 P and having a fit factor of 70% can forecast a level 3 by using the 2nd PC: “1NT”. E: “2♠” best proposal of unbalanced hand. S: “3♣” best proposal of unbalanced hand. W: the summed contract Power of 9.30 P is well reached by the great fit but is yet not enough for level 4 if East had less than 4 full winnable tricks, so must call: “3♠” inviting East to Game if having full 4w at least. N: fit is quite good, but the loser cards seem too many, at any rate must prepare the defense: “4♣”. E: hand force is too low to go for Game: “pass”. Final best contract: 4♣ of S. The 4 historical contracts were: 2 NS’ contract at 4♣ -1. 1 EW’ contract at 4♠-1. 1 NS’ contract at 5♣ x -2. To note how the NS’ contract Power is greater than EW’ one because could develop 12 actual tricks if leader went wrong, but a symmetric loser cards distribution penalizes them. Again, the full 100% of reached best contract is not realized by the teams. The valuation systems, reaching only a rating of 50%, seemed not at the height of the needed bid precision.

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We see from the discussed deal how much importance is now tied to the partner’s role, called to decide on the side’s contract target, basing his decision on the dimension of the number P and on the distributive features of his hand. But that would be always easy when P were greater than 9 tricks because it would always intervene the rule of not giving a forecast implying a number of controls greater than that possessed. That is, we could not, for example, give a forecast of level 5 having only one 1st lap control, or of level 4 having none of them. The number L of reachable level is the new point of reference for our side. We should never trespass it without ascertaining, directly or indirectly, an acceptable quality of fit. This integration quality is now our new star, the only light to exploit for deciding how much far from L we could stay or go. We must remember that the E number of actual won tricks can only be supposed and best approached by the exact knowledge of our number P = [W] + Z of total potential winnable tricks. We could best appropinquate E only by updating P by checking after each table declaration our real fit chances to reach level L. The number P is soon obtained by our partner as soon as we opened. From that, partner will communicate L acting on the minor number of tricks power. If it were ours, he would apply to it the integration risk of his hand, reducing it to [W’] = [W] x F% where F% is the risk percentage of his hand distribution, like we just saw in the last example. If, instead, the minor number were his Z tricks, he could add to [W] only his hierarchic strength if having an unbalanced hand, or all his strength if it balanced one. All that would lead him to a trustworthy number L of safe, most probable, level to can reach and forecast as side’s target. P is the side’s full contract power. In any case, even if P would be much bigger than 13, P would always be a great incomparable information about our side contract power. Each time P were next to or greater than 13 tricks, we could soon think of slam! When it would be lower than 10 tricks, hardly instead we could think of that, but instead we could think enough trusty of it. When much greater than 13 tricks, we should soon consider a great risk of misfit. Fortunately, the normal course of events builds up a number P almost always less than 13 tricks. The number P could be then as much real as much balanced the 2 hands would be. That would mean that our partner could soon have a real P very next to L + 6 and then to E whenever having a very balanced hand for cards number and for scatterd hierarchy. The more P would be less than 13 P, the more it would be equal to W + Z and so to E. This situation is well depicted by the following deal where 4 balanced hands are at work with all strength values scattered and minimized as much as possible among the suits:

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BOARD “MINIMUM”: ....................North ....................♠ A102 (1.15 W) ....................♥ K87 (0.70 W) ....................♦ Q93 (0.40 W) ....................♣ J654 (0.70 W) West........................................ East ♠ Q93…....................................♠ K87 ♥ J654.......................................♥ Q93 ♦ A102......................................♦ J654 ♣ K87………...........................♣ A102 .....................South .................... ♠ J654 .................... ♥ A102 .................... ♦ K87 .................... ♣ Q93 All cards are present from 2 to Ace in each hand, with the possible maximum dispersion of hierarchy among the suits, and where the total number of all players’ winnable tricks is only of 2.95 W x 4 = 11.80 W, and where the missing number of 1.20 W is in a quantic overlapping, impossibly to can be attributed to some hand. This hand tells us that P will be as much true as much the 2 side’s hand will be balanced, and vice versa.

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Let’s have a look also at: BOARD “MEDIUM” North “3.25” ♠ A1098 (2.00) ♥ K32 (0.65) ♦ Q54 (0.35) ♣ J76 (0.25) ♠ J76 West ♥ A1098 “3.25” ♦ K32 ♣ Q54

♠ K32 ♥ Q54 ♦ J76 ♣ A1098

East “3.25”

♠ Q54 ♥ J76 ♦ A1098 ♣ K32 South “3.25” Where, even here, all cards are present from 2 to Ace in each hand, with great dispersion of hierarchy among the suits, and where the total number of all players’ winnable tricks is of 3.25 W x 4 = 13.00 W, all due to the configuration of A1098 originating more connection tricks value for the suit. Grouping all the honours from Ace to J in one suit, we already had a contract power of just more than 4W for each hand and a total table W of 17W. It’s now time for another historical deal.

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LOOKING FOR THE BEST CONTRACT 44th World Teams Championships Round 1 Bermuda Bowl Final Board 13. Dealer North. All Vulnerable.

.........................North* .........................♠ A10853 .........................♥ .........................♦ KQ8 .........................♣ AKJ87 West........................................ East ♠ J……....................................♠ KQ742 ♥ 10742...................................♥ KJ9853 ♦ 1094......................................♦ J ♣ 96542...…............................♣ 3 ..........................South ......................... ♠ 96 ......................... ♥ AQ6 ......................... ♦ A76532 ......................... ♣ Q10 "Quantum Bridge" is totally applied (https://www.facebook.com/groups/QuantumBridge/): N: has an unbalanced hand of ♠ 2.60 ♥ 0.00 ♦ 1.50 ♣ 4.10 = 8.20 W (from 2 W to 4 W if defending), so falls into the 5th band of permissible force to can open and must so use the 5th PC: “1NT” showing [8.00 W]. E: has an unbalanced hand of ♠ 3.00 ♥ 4.00 ♦ 0.15 ♣ 0.00 = 7.15 W (from 1 W to 2 W if defending), where the minimum requirement to intervene is equal to 3.75 W (V vs V) + 0.00 (partner not already passed) + 1.00 (4 steps of distance from 1♣) = 4.75 W, falling into the 3rd trick step from that must use the 3rd PC: “2♦” showing a medium force of [7.25 W]. S: has an unbalanced hand of ♠ 0.05 ♥ 1.60 ♦ 3.90 ♣ 0.40 = 5.95 W so can sum [8.00 W] + 5.95 W] = 13.95 P and having 2 Aces and chances out of 4 to can fit must apply a risk factor of 60% on his W tricks giving a forecast of level 5 by using the 3rd PC (count start from 9 W): “2NT”. W: has an unbalanced hand of ♠ 0.15 ♥ 0.60 ♦ 0.15 ♣ 1.55 = 2.45 W so can sum [7.25 W] + 2.45 W] = 9.70 P and having 3 chances of fit can boldly forecast a reachable level 3 by using the 1 st PC: “X”, because impossible to be actual as intention of play. N: “3♣” strongest and most economic suit of unbalanced hand. E: “3♥” strongest and most economic suit of unbalanced hand. S: “4♦” looking for better fit. W: “pass” waiting for events. N: S showed 2 Aces and a strong unbalanced hand of 5W at least by giving a level 5 forecast, so must only check for level 7 by using an appropriate call, that is: “6♣”, by that assuring good fit at diamonds, 1st lap controls and a strong clubs suit needing only a bit of help for Grand Slam. E: must pass. S: N’s jump assures no need to ask for controls, fit at diamonds, a very strong clubs suit and also Ace of spades; by all that the side Potential force can be really updated to 8 W + 5 W, so: “7NT” is sure enough. W: wanted to defend against 7♦ calling: “7♥”, but now that’s impossible! Final best contract: 7NT of N. The 4 historical contracts were: 2 timid contracts of NS at 6♦ + 1 (1370). 1 NS contract at 7♦ (2140). 1 EW contract at 7♥ - 5 (-1400). To note how no team was able to call the best contract, and how timid 2 of them were. After N’s calls, South can update his hand force to: ♠ 0.00 ♥ 1.00 ♦ 4.00 ♣ 0.40 = 5.50 W giving 13 W even if N had only 7.50 W. To note, at last, how unable 3 teams were, out of 4, of trying to apply a very convenient defense at hearts, clear evidence of their poor valuation systems. 11

THE PATH TOWARDS OUR NUMBER W We, thank to LAW 77, have seen the supreme importance of counting our hand strength by a number W of winnable tricks. W is an integer followed by two decimal digits because any trick has, in mathematical representation, a chance to be won spanning from 0% to 100%, that is from 0.00 to 1. We humans are able of appreciate only a minimum difference of 0.05 W, that means that we can divide each integer trick into 20 little fragments with a width of 0.05 W, that is of a 20th of trick, all summing up its one trick interval. Being 13 the possible winnable tricks, our hand strength could fall into one of the 13 intervals of winnable tricks, each one wide twenty 20ths of trick. Graphically we could picture one of these intervals, for example that spanning from 3.50 W to 4.45 W, like that: … 3 . 5 0

3 . 5 5

3 . 6 0

TRICKS INTERVAL FROM 3.50 W TILL TO 4.45 W 3 3 3 3 3 3 3 4 4 4 4 4 4 4 . . . . . . . . . . . . . . 6 7 7 8 8 9 9 0 0 1 1 2 2 3 5 0 5 0 5 0 5 0 5 0 5 0 5 0

4 . 3 5

4 . 4 0

4 . 4 5

4 . 5 0

The actual stripe of all intervals of strength extends from 0.65 W till to 13 W, shaping the gauge for measuring any hand strength. This gauge holds up a superior power of precision given by the ratio of 253 possible W values divided by 37 HCP/MW points, that is 7 times more precise. Being North, to inform our partner of 4.15 WN, we should properly use the bid steps, losing during the operation an info precision at maximum of 0.50 W since partner, receiving our opening Quantum Call, should always assume as reference measure the central point of the called strength interval. Wanting to fix always an integer number as reference point of an opening strength, we should always make it as central point of its belonging interval. The first strength interval would be the unique exception since would span from 0.65W, possible minimum strength till to 1.50W, having 1W as its central point. Doing so, the medium loss of information, due to the transmission, would be of an average of 0.25 W. If our hand power fell into the 1st opening strength interval, we should use the 1st Possible Call (PC), that is 1♣, to show it. In the specific case of having 4.15 W, we would lose 0.15 W of precision when informing the partner. The 1st opening strength interval would so span from 3.50 W till to 4.50 W, because all its values are the next greater than 3.25 W which is the fairest tricks share for a player. All opening strength intervals are so fixed around an integer number spanning from 4 W till to 12 W. The bid ladder is instead not fixed when interfering, and could start from any W value, as we will see. Having 8.90 WN of strength opening, and being NV, we would walk on the tricks gauge taking 5 full steps beyond the minimum limit of 3.50 W till to reach 8.50 W and then another shorter one to reach and stop on 8.90 W. To signal to the partner such a strength, we should so use the 6th PC and call: “2♣”, showing a medium contract power of 9.00 W, central point of the 6th trick interval spanning from 8.50 W till to 9.45 W.

12

ALL THE POWER OF OUR HAND Measuring hand by tricks, we soon take conscience of its stochastic nature. Indeed, only an Ace of trumps would have a 100% certainty of winning the trick. Otherwise, any other card would have chances varying from 0% (0.00) till to 95% (0.95), depending by many factors, such as its hierarchy ranking, its suit quality, its role of hierarchy extension, its suit length and distribution among the other hands. If it were a single card of a suit, we should concentrate our attention only on its hierarchy ranking. If the suit had instead more cards, we should consider the chances of the whole group to can win its tricks, certainly never equal to the sum of the chances of each single card, unpardonable and incorrigible mathematical error of any possible valuation system based on points. We must sum, before bidding, all our suits strengths because we could not know at which denomination we could play, and which could be the play and suits development. Summing up all our suits tricks power, we would have all our hand contract power before bidding. Every bid call will update it, introducing also all the other aspects such as suit quality, and overall cards distribution and position. After each declaration our number of W tricks becomes ever and ever more refined a picture of our actual contract power and of the true reachable level L. THE TECHNICAL PATH OF MEASURING BY TRICKS Every trick measure should be at maximum independent by the partner’s trick values as much as possible. Let’s start from the hierarchy trick values of a suit. Ace is always worth 1.00 W. King is 0.50 W if single card, Queen 0.25 W if single card, and so on halving the W value at every successive ranking position, till to 0.00 W for the single card 8. Things would change for a 2 cards suit, where aspects of hierarchy extension can begin by which Ace transfers his full value to its contiguous cards, so that AK is worth 2.00 W. Breaking one time the hierarchy of a 2 cards chain it costs the missing card value, that is a King’s hierarchy value, and so we have 1.50 W for AQ, as stochastically can be proved. Having two chain breaks in a two cards suit, we can only sum the single hierarchy trick values, so that AJ is worth 1.15 W, K10 is worth 0.60 W, Q9 is worth 0.30 W and so on. Breaking instead two times the chain of 3 cards, as in AQ10, we lose 2 times the K’s value while in AJ2 we lose the sum of the K’s and Q’s hierarchy values, that is 0.50 W + 0.25 W, leaving a value of 1.25 W for the configuration. The HCP/MW system counts 3 points for a King, so that two Kings are worth 6 points, that is the incredible value of one Ace and a half, whereas Mathematics would tell us that having 2 Kings, averagely, we would win only 1 trick, like we had only one Ace. Having 2 Queens and summing their points, we would have 4 HCP/MW, that is the value of one Ace, whereas Mathematics, summing their chances, would instead tell us to have the trick value of only one King, able of winning 1 trick only 1 time out of 2, that is half chances of an Ace. Besides, the Queens should be protected by other 2 cards at least to be not soon a prey of AK. Q32 would value 0.35 since QJ10 is worth 1W giving to the Queen a transferrable value of 0.33 W. Q2 till to Q9 is so worth 0.30 W, Q10 like Q32; QJ, finally, 0.40 W. As we see, all is wrong using the HCP/MW system, as it would be with any other system not using the stochastic way of measuring the hand winnable tricks. Things would be worse and worse having more and more cards in a suit till to a hand like AKQJ1098765432, where we would always count 13 W while the HCP/MW system would count perhaps, at maximum, a timid 20 points or something very next to it introducing fantastic sub methods of autocorrection. Valuation errors would completely vanish measuring our hand by tricks. For two and three cards suits, the rounded winnable tricks values are: Cards AK AQ AJ A10 A9 A8 KQ

W 2.00 1.50 1.25 1.15 1.10 1.05 1.00

Cards AKQ AKJ AK10 AK9 AKx AQJ AQ10

W 3.00 2.60 2.25 2.10 2.05 2.50 2.00

Cards KJx K109 K10x K98 K9x Kxx QJ10

W 0.90 0.85 0.80 0.75 0.70 0.65 1.00 13

KJ K10 K9 K8 QJ Q10 Q9 Q8 J10 J9 J8 109 108 98 87

0.75 0.60 0.55 0.50 0.40 0.35 0.30 0.25 0.20 0.15 0.15 0.10 0.10 0.05 0.00

AQ9 AQx AJ10 AJ9 AJx A109 A10x A9x Axx KQJ KQ10 KQ9 KQx KJ10 KJ9

1.60 1.55 1.75 1.35 1.25 1.15 1.10 1.10 1.05 2.00 1.70 1.55 1.50 1.50 0.90

QJ9 QJx Q109 Q10x Q9x J109 J10x Jxx 1098 10xx 9xx xxx -

0.80 0.75 0.60 0.50 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 -

The hierarchy configuration of a suit is usually all placed in its first 3 greatest cards. For example, having AQ1032 we would soon count 2.00 W for AQ10 and then we could add the minimal stochastic length value of a 5 cards suit. Having KQ54 we would count 1.50 W for KQ5 and then add the minimal stochastic length value of 4 cards suit. Having AJ1098 we would have to consider 1.75 W for AJ10 and then add 2.00 W for 98 extending the heading hierarchy totalizing 3.75 W for all the group. It is so clear that would suffice only a bit of practice for assessing the hierarchy trick values and then adding or not the minimal stochastic trick value of the suit length, if not already overcoming its possible maximum group value, as it would happen for AKQ6543 where the 3.00 W value of hierarchy could not be fully integrated by the minimal 4.20 W value of a 7 cards suit since we would overcome 7.00 W, its maximum possible value. Hierarchy trick values have the most important role when playing at NT, and for establishing fit at some denomination. THE SUITS LENGTH AS CONTRACT POWER Every suit length has its own specific minimal contract power, giving so a typical minimal contract power also to the suit distribution type such as 4-4-3-2 or 6-3-4-0 or other ones with no regard to which is any suit. For it (stochastically valued) we have:

Length W tricks 1 0.00 2 0.00 3 0.05 4 0.50 5 1.50 6 2.90 7 4.25 8 5.50 9 7.00 10 8.50 11 10.15 12 11.35 13 13 If we had, for example, a suit like 8765432, having no MW points and no ranked hierarchy, we would feel that it had some strength, but how much of it? The stochastic length value is 4.25 W, as above shown by the table. The 0.25 W value, beyond

14

4 W, means that 1 time out of 4 the G7 group would win 5 tricks instead of only 4 ones. More exceptionally would win only 3 tricks. Letâ&#x20AC;&#x2122;s see every distribution type minimal strength:

DISTRIBUTION TYPES AND THEIR MINIMAL CONTRACT POWER NÂ° cards s1 cards s2 cards s3 cards s4

W strength

FREQUENCY TOTAL FREQ.

1 2

4 5

4 3

3 3

2 2

0.50 + 0.50 = 1.00 1.50 + 0.05 + 0.05 = 1.60

21,55% 15,52%

21,55% 37,07%

3 4

5 5

4 4

3 2

1 2

2.05 2.00

12,93% 10,58%

50,00% 60,58%

5 6

4 6

3 3

3 2

3 2

0.65 3.05

10,54% 5,65%

71,12% 76,77%

7 8

6 6

4 3

2 3

1 1

3.50 3.10

4,70% 3,45%

81,47% 84,92%

9 10

5 4

5 4

2 4

1 1

3.00 1.50

3,17% 2,99%

88,09% 91,08%

11 12

7 6

3 4

2 3

1 0

4.30 3.55

1,88% 1,33%

92,96% 94,29%

13 14

5 5

4 5

4 3

0 0

2.50 3.05

1,24% 0,89%

95,53% 96,42%

15 16

6 6

5 5

1 2

1 0

4.50 4.50

0,71% 0,65%

97,13% 97,78%

17 18

7 7

2 4

2 1

2 1

4.25 4.75

0,51% 0,39%

98,29% 98,68%

19 20

7 7

4 3

2 3

0 0

4.75 4.35

0,36% 0,27%

99,04% 99,31%

21 22

8 8

2 3

2 1

1 1

5.50 5.55

0,19% 0,12%

99,50% 99,62%

23 24

8 7

3 5

2 1

0 0

5.55 5.75

0,11% 0,11%

99,73% 99,84%

25 26

6 8

6 4

1 1

0 0

6.00 6.90

0,07% 0,05%

99,91% 99,96%

27 28

9 9

2 3

1 1

1 0

7.00 7.05

0,02% 0,01%

99,98% 99,99%

29 30

9 7

2 6

2 0

0 0

7.00 7.25

0,01% 0,00%

99,99% 99,99%

31 32

8 10

5 2

0 1

0 0

7.00 8.50

0,00% 0,00%

99,99% 99,99%

33 34

9 10

4 1

0 1

0 1

8.50 8.50

0,00% 0,00%

99,99% 99,99%

35 36

10 11

3 1

0 1

0 0

8.55 10.00

0,00% 0,00%

99,99% 99,99%

37 38

11 12

2 1

0 0

0 0

10.00 11.35

0,00% 0,00%

99,99% 99,99%

39

13

0

0

0

13.00

0,00%

100,00%

Referring to the most balanced 4-3-3-3 distribution, we must consider that to produce there a void in a suit means to shift at least 3 cards elsewhere creating at least a 5-4-4-0 distribution type triplicating the hand strength, or a 7-3-3-0 distribution with a strength 7 times greater than that. This is the real meaning of a void, and similarly of a singleton or a doubleton, that is that of increasing the other suits length and so the hand strength. We must always measure the full part of the glass.

15

A FAST METHOD OF HAND VALUATION Any suit group having less than 4 cards must always be considered a hierarchy group and their trick values have been already before shown in the appropriate table. Having more than 3 cards in a suit group, we must soon look for the break point of hierarchy at the 4th card. Having the hand: ♠ K ♥ A10643 ♦ QJ52 ♣ 432 the break points are at 4♥ and at 2♦, giving: ♠ 0.50WH ♥ 1.15WH + 1.50WL ♦ 0.75WH + 0.50WL ♣ 0.05WH that is 4.45 WH+L. Having: ♠ K6 ♥ A10987 ♦ Q52 ♣ 5432 one break point is only at 2♣ because at hearts 87 prosecute the trick value of A109 so we have: ♠ 0.55WH ♥ 2.90WH ♦ 0.35WH ♣ 0.00WH + 0.50WL that is 4.30 W. Having: ♠ AJ8765 ♥ KJ ♦ K875 ♣ 3 the trick values would be: ♠ 1.25WH + 2.90WL ♥ 0.75WH ♦ 0.65WH + 0.50WL ♣ 0.00WH + 0.00WL that is 6.05 W, a value greater than half a Slam, where its 12 HCP/MW points would tell nothing at all of it!

LIMITS TO CAN OPEN Every possible limit must necessarily derive from the limits of convenience dictated by the LAW 77. Let’s see them. FREQUENCY OF CONTRACT TYPES IN RECENT WTC CHAMPIONSHIPS RIVAL PARTSCORE CONTRACT Quality Points Premium Score 1♣ 20 50 70 1♦ 20 50 70 1♥ 30 50 80 1♠ 30 50 80 1NT 40 50 90 2♣ 40 50 90 2♦ 40 50 90 2♥ 60 50 110 2♠ 60 50 110 2NT 70 50 120 3♣ 60 50 110 3♦ 60 50 110 3♥ 90 50 140 3♠ 90 50 140 4♣ 80 50 130 4♦ 80 50 130

OUR CONVENIENT TRICKS FALL NV NN VV VN -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -

RIVAL GAME CONTRACT Quality Points Premium 3NT 100 300 4♥ 120 300 4♠ 120 300 4NT 130 300 5♣ 100 300 5♦ 100 300 5♥ 150 300 5♠ 150 300 5NT 160 400 3NT 100 500 4♥ 120 500 4♠ 120 500 4NT 130 500

OUR CONVENIENT TRICKS FALL NV NN VV VN -2 -2 -1 -1 -2 -2 -1 -1 -2 -2 -1 -1 -2 -2 -1 -1 -2 -2 -1 -1 -2 -2 -1 -1 -2 -2 -1 -1 -2 -2 -1 -1 -2 -2 -1 -1 -3 -3 -2 -2 -3 -3 -2 -2 -3 -3 -2 -2 -3 -3 -2 -2

Score 400 420 420 430 400 400 450 450 460 600 620 620 630

16

RECORDED FREQUENCY 0% 0% 1% 1% 6% 1% 2% 5% 5% 2% 3% 3% 3% 3% 2% 2% 39% RECORDED Frequency 10.00% 7.00% 7.00% 0.1% 1.5% 0.7% 0.8% 0.3% 0.1% 10.00% 7.00% 7.00% 0.1%

5♣ 5♦ 5♥ 5♠ 5NT

100 100 150 150 160

500 500 500 500 500

RIVAL SLAM CONTRACT Quality Points Premium 6♣ 120 300 + 500 6♦ 120 300 + 500 6♥ 180 300 + 500 6♠ 180 300 + 500 6NT 190 300 + 500 7♣ 140 300 + 1000 7♦ 140 300 + 1000 7♥ 210 300 + 1000 7♠ 210 300 + 1000 7NT 220 300 + 1000 6♣ 120 500 + 750 6♦ 120 500 + 750 6♥ 180 500 + 750 6♠ 180 500 + 750 6NT 190 500 + 750 7♣ 140 500 + 1500 7♦ 140 500 + 1500 7♥ 210 500 + 1500 7♠ 210 500 + 1500 7NT 220 500 + 1500

600 600 650 650 660

Score 920 920 980 980 990 1440 1440 1510 1510 1520 1370 1370 1430 1430 1440 2140 2140 2210 2210 2220

-3 -3 -3 -3 -3

-3 -3 -3 -3 -3

-2 -2 -2 -2 -2

-2 -2 -2 -2 -2

OUR CONVENIENT TRICKS FALL NV NN VV VN -4 -4 -3 -3 -4 -4 -3 -3 -4 -4 -3 -3 -4 -4 -3 -3 -4 -4 -3 -3 -6 -6 -5 -5 -6 -6 -5 -5 -6 -6 -5 -5 -6 -6 -5 -5 -6 -6 -5 -5 -5 -5 -4 -4 -5 -5 -4 -4 -6 -6 -5 -5 -6 -6 -5 -5 -6 -6 -5 -5 -7 -7 -6 -6 -7 -7 -6 -6 -8 -8 -7 -7 -8 -8 -7 -7 -

1.5% 0.7% 0.8% 0.3% 0.1% 56% RECORDED Frequency 0.4% 0.4% 0.4% 0.4% 0.4% 0.1% 0.1% 0.1% 0.1% 0.1% 0.4% 0.4% 0.4% 0.4% 0.4% 0.1% 0.1% 0.1% 0.1% 0.1% 5%

N.B. frequencies have been derived from the contracts played at 44th World Team Championships.

According to the tables values and to Mathematics, we should have a bit more than our fair share of 13/4 W tricks, that is just more than 3.25 W tricks so that to have good probability to meet a partner’s number W that could let us reach at least a convenient level of play. We could need only a level 1 or 2 of play if in danger of suffering a rival vulnerable Game, even less for rival vulnerable Slam. Being green as first declarer it would seem crazy to open having a hand like: ♠ J109 ♥ 1098765 ♦ 432 ♣ 2 worth of ♠ 0.35 ♥ 3.20 ♦ 0.05 ♣ 0.00 that is 3.60 W tricks, where we could soon lose 9 or 10 tricks and not be able to have any convenient contract at sight, even if green vs red. But in that case very easily the opponent side could have Slam. Supposing the partner had: ♠ A8765 ♥ J432 ♦ 5 ♣ 432 worth of ♠ 2.50 ♥ 0.70 ♦ 0.00 ♣ 0.05 that is of 3.25 W tricks and a rival hand like: ♠ - ♥ AKQ ♦ AK109876 ♣ QJ10; the rival side would always call Grand Slam at a minor suit while we always would have a convenient defence at 7♥. Only if we opened, or interfered, opening [4W], so that the partner could sum P = 7.20 and derive fit at hearts by the rival calls, we could rightly defend. Obviously, that would be an extreme case, but personally I think that it would always be useful to let our partner know about our spendable strength during the bid. It could be very important with practically no risk at all.

17

TECHNICAL PATH AND RULES FOR BIDDING Rules could be set for opening and calling our WN, if, when and how. But they could plaster the personal behaviour or make heavy the following actions. We should be free as much as possible for opening or interfering, being our freedom always and only dictated by the rules of convenience framed by the LAW 77. At this purpose, it would be not difficult to frame a table taking into consideration aspects of convenience related to each vulnerability position, such as that: CENTRAL POINTS OF OPENING TRICK BANDS Quality NV NN VV VN 1♣ 4.00 4.25 4.50 4.75 1♦ 5.00 5.25 5.50 5.75 1♥ 6.00 6.25 6.50 6.75 1♠ 7.00 7.25 7.50 7.75 1NT 8.00 8.25 8.50 8.75 2♣ 9.00 9.25 9.50 9.75 2♦ 10.00 10.25 10.50 10.75 2♥ 11.00 11.25 11.50 11.75 2♠ 12.00 12.25 -

where we should open the bid if thinking to can have an advantage from it, even if defensive one. After a double “pass”, having just more than 3.50 W of unbalanced hand, for example like that: ♠ 865432 ♥ J432 ♦ 5 ♣ 43 worth of ♠ 2.90 ♥ 0.70 ♦ 0.00 ♣ 0.05 that is of 3.60 W tricks, we should worry a lot if being NV and should always open. Same we should do if second to bid after a very strong LHO’s opening. We should open with that strength even if first declarer as prevention. The justification is all in the minimal possible strength that partner could have, that is: 0.65 W. So minimal strength that it is more probable to can have at least 1.50 W than 0.65 W. If so, surely the rival side would have Game at least, confirming the full convenience of the opening. To not exploit such opportunities would be rather crazy if not insane. We can start our path from that, calling: “1♣” if having at least 3.50 W when NV. Our partner should assume 4.00 W as reference point of our just called strength band. The following vulnerability positions would demand to increase the limits of 0.25 W for each increasing vulnerability position till to a minimum opening value of 4.25W if being VN. Being NV and first declarer, the contract convenience thresholds decree that our side, in order to sign a positive score or a convenient one, even if negative, should have at least a power of 7.00 W so that to can conveniently defend against the 95% of all possible contracts. For the same reason the requiremnt should be raised up till to 7.50 W being NN, till to 8.00 W being VV, and till to 8.50 W being VN. Halving all these numbers and mediating them, we see that in order to can conveniently fight when bidding, we should have at least 3.50 W being NV, 3.75 W when NN, 4.00 W when VV and 4.25 W when VN. Wanting not to have different opening thresholds and, above all, not 4 different trick band limits to manage, it would be better to hold fixed the 3.50 W opening limit for all the board positions, taking them anyway in mind for deciding. That would take fixed all the limits of the following trick bands, and all their central points referenced by an integer number. Picturing the 1st trick band of opening strength, we have: 3 . 5 0 N V

3 . 5 5

FIRST TRICK STEP OF USEFUL STRENGTH TO OPEN 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 . . . . . . . . . . . . . . . . 6 6 7 7 8 8 9 9 0 0 1 1 2 2 3 3 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 N V V N V N

.

18

4 . 4 0

4 . 4 5

LIMITS TO CAN INTERFERE Wanting to interfere, our thresholds will be function primarily of the actual vulnerability position, of the actual bid level and of the new implied thresholds of convenience. For each position of vulnerability, wanting to interfere we should apply the correspondent opening limit. For each bid step beyond 1♣ of the actual offer of auction, we should always increase the minimum interfering limit by 0.20 W. If partner were already passed, the so counted limit must be increased of 0.25 W if being NV, of 0.50 W if NN, of 0.75 W if VV and of 1.00 W if VN. Owing to intervene, being NV and second one to call, on a rival 2♥ call, we should at least have 3.50 W (NV) + 1.40 W (0.20 W x 7 bid steps) + 0.00 W (partner not already passed) = 4.90 W of minimum interfering strength. Partner should assume by our 1st Logical Call (LC): “2♠”, a medium strength of 5.40 W +- 0.50 W. The “double” declaration is always punishing at higher levels than 1. Owing to interfere on a rival 5♣ call with partner already passed being VV and 4th one to bid, we should at least have 4.00 W (VV) + 5.00 W (0.20 W x 25 bid steps) + 0.50 W (partner already passed) = 9.75 W and partner should assume, by our 1st LC: “5♦”, a strength of 9.75 W till to 10.70 W. Having, for example, 7.30 W being NN and 2nd one to call after: “1NT”, wanting to interfere we should have a minimum of: 3.75 W (NN) + 0.80 W (0.20 W x 4 bid steps) = 4.55 W; falling, instead, into the 3rd trick band ahead, we should call: “2♥” by using the 3rd LC and showing at least 6.55 W till to 7.50 W.

19

OTHER STRENGTH ASPECTS We can, now, be able also to see how powerful it could be another aspect tied to the distribution type: the eventual asymmetry of the short suits. Here an incredible example. Board “ANOMALY”. Declarer East. EW vulnerable. .........................North ........................ ♠ 863 ........................ ♥ K9754 ........................ ♦ 5 ........................ ♣ A842 West……................................... East * ♠ KQ1054................................... ♠ AJ97 ♥ J2............................................. ♥ Q10 ♦ AJ96….....................................♦ KQ1087 ♣ Q10…..................................... ♣ J3 ..........................Sud ......................... ♠ 2 ......................... ♥ A863 ......................... ♦ 432 ......................... ♣ K9765 E and W, each have a good hand of 13 HCP/MW spendable contract power, while N and S each have a "weak" hand, conventionally defined by WBF because “having 9 points HCP/MW or less”. After E’s opening, S being NV with a contract power of 3.90 W should soon interfere as the rules of convenience derived from the LAW 77 demand. Let’s follow a possible “Quantum Bridge” path and calls: E: ♠ 1.85 W ♥ 0.35 W ♦ 3.50 W ♣ 0.20 W has 5.90 W and so falls into the 3rd band of contract power to be announced by the 3rd PC: “1♥” that is 6.00 W +- 0.50 W. S: ♠ 0.00 W ♥ 1.50 W ♦ 0.05 W ♣ 2.35 W has 3.90 W and must check his requiremnt to can interfere: 3.50 W (NV) + (3 x 0.20) = 4.10 W. Being only 0.20 W less than the limit, must consider the great risk of a rival Vulnerable Game and must so decide to intervene by using the 1st PC: “X” meaning strength of 4.10 W at least. W: sums a contract power of [6.00 W] + 5.90 = 11.90 W that could warrant a fair level 4 of play to can be announced by using the 3rd PC starting from level 2: “1NT”. N: sums a contract power of [4.60 W] + 3.90 W = 8.50 W corresponding to a possible level 2 of play, to be perhaps empowered by the presence of asymmetric numbers of loser cards; a forecast of level 2 could so be announced by using the 1st PC (level 1 is not anymore exploitable): “X”. E: “2♦” most economic and best suit call. S: “2♥”, unique possible proposal of play at level 2. W: the fit quality is good, but the symmetry of loser cards is worrying; best call now is: “2♠” looking for an easier Game. N: the hearts great fit lets overcome the level 2 forecast and call: “3♥”, showing great fit and hoping for a lucky game with a double fit. E: “3♠” assuring fit. S: “4♣” trying to set up a defense at level 5. W: “4♠” compelled by the double fit. N: “5♥” also compelled by the double fit to defend and being somewhat sure of the loser cards asymmetric distribution. At this point it would not be significant to know how it could continue the whole bid, but only to consider how important it is to interfere, standing as South, having a hand where its contract power not only resides in hierarchy and length of suits, but comprehends also a relevant quantity of controls and a possible exploitation of the loser cards asymmetry. All these aspects of contract power are able of raising up till to Level 5 the poor initial potential of only 8.50 P, and to decrease to level 3 a real initial potential of 11.90 P, notwithstanding a double fit! 20

When opening a medium force hand of about 4 W or 5 W, we often could have normal rival interferences, and often would have our side total tricks spanning from 6 W till to 13 W. Let’s see a historical example: 2019 IMSA World Masters Championships – Round 5 – Open Teams Board 6. Dealer East. E-W Vulnerable. ♠J9543 ♥J87 ♦7 ♣KQT4 ♠72 ♥KQ9 ♦KQ85 ♣9853

♠KT86 ♥A42 ♦A932 ♣J6

♠AQ ♥T653 ♦JT64 ♣A72 Let’s revise the bid applying the tricks count of Quantum Bridge. E: has ♠ 1.20 W ♥ 1.05 W ♦ 1.55 W ♣ 0.20 that is 3.95 W, falling into the 1st band of contract power required to can open, shows his strength by using the 1st Possible Call (PC): “1♣”, showing to have a force of 4.00 W +- 0.50 W. S: has ♠ 1.50 W ♥ 0.60 W ♦ 0.90 W ♣ 1.05 that is 4.05 W, and must check his requiremnt of intervention: 3.50 W (NV) + 0.00 W (no step of distance from 1 clubs); falling into the same band of contract power, can show his strength by using the 1st PC (“double” at level 1 is never actual): “X”, showing to have a force of 4.00 W +- 0.50 W. W: has ♠ 0.00 W ♥ 1.60 W ♦ 2.00 W ♣ 0.60 that is 4.20 W, and sums [4.00 W] + 4.20 W = 8.20 W; his balanced hand normally assures at least a normal fit, so can forecast a level of play, safely reachable with a mild fit, equal to 2, using the 1st PC since the vulnerable level count starts from level 2: “X X”. N: has ♠ 1.75 ♥ 0.20 ♦ 0.00 ♣ 2.25 that is 4.20 W, and sums [4.00 W] + 4.20 = 8.20 W; he considers that the table total W tricks is next to 16 W, that is a moderate balanced deal where the real cards position can do all the difference, so can forecast a level of play, safely reachable with a moderate fit, only equal to 2, using the 2nd PC: “1♥”. E: “1NT” showing to have no 5 cards suits. S: “Pass” Logical Call showing, itself too, a balanced hand. W: “Pass”; S’s bad situated strong hand, the inexistence in his hand of 5 cards suit and the rules of convenience dictated by LAW 77 for a “partscore” when Vulnerable, do not permit to risk more. N: “Pass”, level 2 at spades is a big risk with such a weak suit. The historical results were: 1 E’s contract at 1NT – 1; 1 E’s and 1 W’s contract at 3♦ - 1; 1 S’s contract at 2♠x – 1. Under this light, only the historical contract of 1NT of EW’ side was right. To note the unreality of the 2 contracts of EW’ side at 3♦ - 1 never doubled and above all their inconvenience to defend, against a possible 90 rival scoring points. at level 3 being vulnerable and so risking -500.

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ITALIAN CLUBS OPEN TEAMS CHAMPIONSHIPS - ROUND 4 Board 4. Dealer West All Vulnerable. (winnable tricks are shown after each hand suit) ..................................North ..................................♠ - (0.00) ..................................♥ 6 (0.00) ..................................♦ AQJ97643 (7.50) ..................................♣ J852 (0.80) West*......................................................... East ♠ J10982 (2.00).........................................♠ AKQ54 (4.50) ♥ A97 (1.10) ….........................................♥ KQ85 (2.00) ♦ - (0.00) ……….......................................♦ 1095 (0.15) ♣ K10973 (2.40)…....................................♣ 6 (0.00) .................................South ................................ ♠ 763 (0.05) ................................ ♥ J10832 (1.90) ................................ ♦ K2 (0.55) ................................ ♣ AQ4 (1.55) Let’s revise the bid applying the tricks count of Quantum Bridge. W: has 5.50 W trick falling at the starting point of the 3rd trick band of opening force, so must use the 3rd Possible Call (PC): “1♥”, showing to have a force between 5.50 W and 6.50 W. N: has 8.30 W tricks and must check his requiremnt for intervention: 3.50 W + 0.40 W = 3.90 W; falling into the 5th trick ahead of that, must intervene by using the 5th PC (“double” can be used as 1st PC): “2♥”, showing to have force spanning from 7.90 W to 8.90 W. E: has 6.65 W tricks, so can sum [6.00] (interval medium point) + 6.65 = 12.65 W. Having only 1 Ace he can forecast a level of play only equal to 4 by using the 2nd PC (“double” at level 2 is actual) starting the level count from level 3 since level 2 is no more useful for a bid space: “2NT”. S: has 4.05 W, he can sum [8.40] (interval medium point) + 4.05 = 12.45 W tricks at least. He can surely add all his tricks of high hierarchy, that is 2.00 W reaching so [8.40] + 2.00 = 10.40 W tricks. By all that he can forecast a level of play equal to 4 having only 1 Ace using the 2nd PC: “3♦”. Note: The actual number of the table total winnable tricks (WT) is greater than 20 W showing the presence of very long suits. The distributional calls now follow.

W: “3♠”, best chance of Game of unbalanced hand. N: can overcome the partner’s forecast having an independent fit: “4♦”. E: can adjust his W tricks count to ♠ 3.00 ♥ 1.50 ♦ 0.00 ♣ 2.00, and to level 5 or 6 his forecast, so can look for slam using the 1st Illogical Call (IC): “4NT”, asking for sure controls of 1st lap (C1). S: can terribly feel the danger and must call: “5♦” having diamonds fit and high hierarchy at clubs. W: “5NT”, that is 4th Logical Answer (LA) to signal 1.5 C1 controls (as after we’ll see), that is 1 Ace and 1 void. N: “pass”. E: much probably W has Ace of hearts and void at diamonds, so can call: “6♠”. S: “7♦”, conveniently defending because level 4 is the minimum one assured. W: “X”, since having Ace of hearts as sure trick at least. The contract would be 3 down, very conveniently. The historical contract was of 6♠ after an initial W’s pass and an opening at “5♦” by N! East incredibly and some crazily intervened! Applying and playing QB, NS side would easily have reached the right defence.

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43TH WTC - SEMIFINAL ROUND 4 – BERMUDA BOWL – VENICE CUP Board 23. Dealer South. All Vulnerable. ..................................North ..................................♠ 87 (0.00) ..................................♥ AQJ932 (5.50) ..................................♦ KQ64 (2.00) ..................................♣ 4 (0.00) West............................................................... East ♠ AKJ (2.60)..........................................♠ Q2 (0.30) ♥ K4 (0.55)............................................♥ 107 (0.10) ♦ 10972 (0.60)........................................♦ J5 (0.15) ♣ K1073 (1.30)......................................♣ AQJ9852 (6.50) .................................South* ................................ ♠ 1096543 (3.20) ................................ ♥ 865 (0.05) ................................ ♦ A83 (1.05) ................................ ♣ 6 (0.00) S: though having only 6/4 HCP/MW has instead 4.30 W tricks, that is 0.80 W more than the minimum force requested to open when NV and only 0.30 W more than that when VV, having also a superior quality sixth suit and also 2 controls, must forget the senseless and a-mathematical rule of not be able to open at level 1 because “having a K at least less than 10 HCP/MW”, and should so open calling: “1♣”, showing to have a force of 4.00 W. W: has 5.05 W tricks of a balanced (because having no 5th suits) hand, and must check his requiremnt of intervention = 3.50 W, falling into the 2nd trick band ahead of that he must use the 2nd Possible Call (PC): “1♦” (“double” would show 4W) showing to have a force of 5.00W +-0.50W. N: has 7.50 W tricks, so he can soon sum up [4.00 W] + 7.50 W = 11.50 W; having an unbalanced hand with no hierarchy at all at two suits, he must assume a risk factor for fit next to 50% to be applied on S’s weaker hand, so he should forecast a reachable level equal to 7.50 + (0.50 * 4.00) = 9.50 W, that is very next to level 4, to be called by using the 3rd PC: “1♠”. E: has 7.05 W tricks, so he can sum [5.00 W] + 7.05 W = 12.05 W; having an unbalanced hand with poor hierarchy and cards at 3 suits, he must assume a risk factor for fit of about 70% to be applied on W’s weaker hand, he should so forecast a reachable level of play equal to 7.05 + ((1-0.70) * 5.00) = 8.55 W, that is very next to level 3, to be called by using the 2nd PC: “1NT”. S: “2♠”, proposal of play of unbalanced hand. W: “2NT”, telling to have no 5th suits. N: “3♥”, looking for a better fit and updating his hand power to 8 W at least for the lucky position of W’s LHO. E: W’s balanced hand always warrants a normal fit at least, so can update the reachable contractual level to 4 L: “4♣” thanks to his strong suit, and unable to support any other hypothesis of play after the strong N’s bid, excluding the great risk of the 3NT contract, and showing one unique way of possible convenient defence. S: “4♥”, since can count now at least on a mild fit. W: cannot afford a rival Game having updated to zero his hearts power and counting only 2 or 3 sure tricks, not enough for the rival contract to fall, so must call: “5♣”, for a convenient defence of 2 tricks down, at maximum, since level 3 is assured by the forecast and by fit. N: having certainty of a not possible Slam, vanished by spades misfit, and being W’s LHO can surely double: “X”. Final contract: E’s 5♣ X. The contract would fall by 2 tricks, but conveniently since NS’ side has Game at hearts. To note how the forecasts have precisely cut down both the contractual potentials by taking count of the risk of integration. To note also how the declarations leave still the S’s forecast, while downgrade to only level 3 the EW’ one, where K♥ is now very much probably worth 0.00 W. The 4 historical contracts were: 2 EW’ contracts at 3NT+1, +2; 2 EW’ contracts at 4NT one of which -6! All of them not certainly a good 23

example of contractual conclusion, either for the EW side, which always risked “all in” playing NT, either for the NS side which never imagined of having Game, and always ran the risk of suffering the rival game at NT, only once crashed by the rational, and not imaginative N’s lead at diamonds! The NS side always left free ground to the EW’ one, never being able to correctly judge his own contractual potential, unique one able to reach game by fair correct play. It all that happened because South, probably, never opened, missing to correctly judge his own hand force, worth more than 4 full tricks, certainly not definable “weak” one, just as the actual WBF definition make believe by her “extra LAWS” document: “SYSTEMS POLICY” that compels to open at a level greater than 1 every “weak hand”, as if it were not already penalized by its same weakness. The enormous blunder is all in not considering the hand full strength during the bid phase, and in not considering all the aspects of strength like the extension of the heading hierarchy values or like the strength generated by the suits’ length. In the discussed deal S’s 4 W tricks are all real and spendable during the bid time. After that time, they would become 1 W or even zero if not winning the contract. We can never miss the chance to exploit all our hand contract power during the bid, because every unbalanced hand strength vanishes after that, or is at least violently minimized. Think always of four simultaneous 13-0-0-0 distribution types, where 3 of them would completely see their strength degrade to zero W.

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LOOKING FOR THE BEST CONTRACT 44th World Teams Championships Round 1 Bermuda Bowl Final

.........................North .........................♠ QJ1085 .........................♥ 9 .........................♦ J .........................♣ J87652 West........................................ East ♠ 764……...............................♠ A ♥ Q1083..................................♥ A642 ♦ K87.......................................♦ 109432 ♣ Q43…..…............................♣ AK9 ..........................South* ......................... ♠ K932 ......................... ♥ KJ75 ......................... ♦ AQ65 ......................... ♣ 10 "Quantum Bridge" is totally applied (https://www.facebook.com/groups/QuantumBridge/): N: has an unbalanced hand of ♠ 2.75 ♥ 0.05 ♦ 0.15 ♣ 3.30 = 6.25 W (0.50 N if defending), so falls into the 3rd band of permissible force to can open and must use the 3rd PC: “1♥” showing a medium force of [6.00 W] E: has an unbalanced hand of ♠ 1.00 ♥ 1.50 ♦ 1.65 ♣ 2.05 = 6.20 W (4.05 N if defending), where the minimum requirement to intervene is equal to 3.50 W + 0 (partner not passed) + 0.40 (2 steps of distance from 1♣) = 3.90 W, falling into the 3rd trick band ahead of that should use the 3rd PC: “1NT” showing a minimum force of 3.90 W + 2.00 W = 5.90 W S: has a balanced hand of: ♠ 1.20 ♥ 1.50 ♦ 2.00 ♣ 0.10 = 4.80 W so can sum [6.00 W + 4.80 W] = 10.80 P and having 1 Ace can forecast a level 4 by using the 3rd PC: “2♥”. W: has a balanced hand of ♠ 0.05 ♥ 1.00 ♦ 0.70 ♣ 0.35 = 2.10 W so can sum [6.40 W + 2.10 W] = 8.50 P and must call: “2♠” because wanting to give a minimum forecast of Level 3, useful to can defend. N: “X” exploiting W’s call E: “3♦” S: “4♠” for the great fit W: “5♦” for a convenient defense N and E pass while S must double: “X”. Final best contract: 5♦ x of E. The 4 historical contracts were: 4 contracts of NS at 4♠, 2 of them doubled. Results were 4♠ +1 (?), 4♠ -1 (?), 4♠x +0 and 4♠x -1 (?). No EW side saw to have to defend. To note how the N’s hand had a strength even stronger than E’s! and how EW side did never feel the danger. N’s hand is worth 6.25 W only if playing at spades, while it would be worth much less playing at clubs, even zero W if playing at a red suit. That means that the hand contract power is a function of the final contract denomination of play. N’s hand is a “weak hand” or a “strong” one? How, then, could we define it? It is clear that we must better define the “average hand” and what it follows by that.

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43th WTC ROUND 5 BERMUDA BOWL 2017 FINAL Board 26. Dealer East. All Vulnerable. .........................North .........................♠ K109 .........................♥ 42 .........................♦ K75 .........................♣ AKQJ8 West….................................... East* ♠ A32……...............................♠ Q865 ♥ AKQ8...................................♥ J10765 ♦ QJ82……..............................♦ 96 ♣ 64..........................................♣ 97 ..........................South ......................... ♠ J74 ......................... ♥ 93 ......................... ♦ A1043 ..........................♣ 10532 "Quantum Bridge" is totally applied (https://www.facebook.com/groups/QuantumBridge/): E: ♠ 1.00 ♥ 1.90 ♦ 0.05 ♣ 0.05 has "3.00" W of contractual force, so must pass S: ♠ 0.25 ♥ 0.05 ♦ 1.60 ♣ 0.60 has "2.50" W of contractual force, so must pass W: ♠ 1.05 ♥ 3.50 ♦ 1.25 ♣ 0.00 has "5.80" W of contractual power of balanced hand, so falls into the 3rd Band of force permissible to open, so must use the 3rd PC: “1♥” indicating a medium contractual force of 6.00 W +0.50 N: ♠ 0.80 ♥ 0.00 ♦ 0.65 ♣ 5.00 has "6.45" W of contractual force of unbalanced hand; must check his requiremnt to intervene, and counts: 3.50 + 0.40 (2 steps of distance from 1♣) = 3.90, so falling into the 3rd trick of distance from that limit, must use the 3rd PC: “1NT” showing to have a medium contractual force of 5.90 W + 0.50 W E: sums a potential of [6.00 W] + 3.00 W = 9.00 P; having an unbalanced hand can only add his hierarchy tricks that is about 2.00 W, so can indicate a forecast of safe Level 2 by using the 1st PC: “X” (L2) S: sums a potential of [6.40] + 2.50 = 8.90 P; with a balanced hand only by cards number can add only his hierarchy tricks, that is about 2.00 W, so can give a forecast of safe level 2 by using the 1st PC: “X X” (L2) W: Having not a 5th suit must indicate his balanced hand saying: “pass”. N: Having hierarchy placed after W’s strong balanced hand, and having authorization to go up to L2 must say: “2♣” having an excellent fifth suit E: “2♥” for his 5th suit and exploiting the L2 forecast and W’s balanced hand S: has too many loser cards and no Game to reach or fight, better call: “pass”. W: fit is very good and deserves: “3♥” hoping for Game N: Having no sight of Game nor rival Game to fight it is useless to risk level 4: “pass”, leaving to S the last word. East is too poor to go up to L4 so passes followed by South. The 4 historical contracts were: 2 W’s contracts at 2♥ + 0 and + 1; 1 contract of N at 3♣ -1; 1 unacceptable contract of S at 3♦ -2. The number P of potential tricks of the two sides are very close.

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LOOKING FOR THE BEST CONTRACT 43th WTC - SEMIFINAL ROUND 2 Board 19. Dealer South. EW Vulnerable. .........................North .........................♠ AQ864 .........................♥ KJ2 .........................♦ J64 .........................♣ 74 West........................................ East ♠ KJ2……...............................♠ ♥ Q7........................................♥ A109854 ♦ A1073...................................♦ KQ952 ♣ 9863……….........................♣ A2 ..........................South* ......................... ♠ 109753 ......................... ♥ 63 ......................... ♦ 8 ......................... ♣ KQJ105 "Quantum Bridge" is totally applied (https://www.facebook.com/groups/QuantumBridge/): S: ♠ 1.65 ♥ 0.00 ♦ 0.00 ♣ 4.00 has 5.65 W of unbalanced hand and so falls into the 2nd band of force permissible to open, so must use the 2nd PC: “1♦” meaning force included between 5.00 W and 5.95 W. W: ♠ 0.80 ♥ 0.30 ♦ 1.60 ♣ 0.60 has 3.30 W so must call: “pass” N: ♠ 3.00 ♥ 0.80 ♦ 0.25 ♣ 0.00 has 4.05 W of contract power, sums up a potential of [5.50] + 4.05 = 9.55 W, but having a slight unbalanced hand must add only his hierarchy ricks, that is 5.50 W + 3.00 W = 8.50 W and can so indicate a safe prediction of L2 using the 2nd PC: “1♠” meaning Level 2 E: ♠ 0.00 ♥ 4.00 ♦ 3.05 ♣ 1.00 has 8.05 W of contract power, must so check his requiremnt of intervention: 3.50W + 0.50W (partner already passed) + 0.60W (3 bid steps from 1♣) = 4.60 W; falling into the 4th trick ahead, can intervene using the 4th PC: “2♦” meaning a force interval spanning from 7.60 W to 8.55 W]. S: “2♠” unique chance for Game since L5 seems too far away W: sums up a potential of [8.10] + 3.30 = 11.40 W, and having a balanced hand with only 1 Ace can indicate a safe prediction of L4 using the 2nd PC: “3♣” (“double” would be actual) N: “4♠” for the tremendous fit that compulsively raises up the forecast to L4 level E: “5♥” since W has 1 Ace at least having forecasted L4, and much probably at diamonds! S: “5♠” obviously defending W: must now call: “X” for the not so good fit at hearts, for Ace of diamonds and for power at spades. Final contract: 5♠ x of S. The 12 historical contracts: 5 EW’s unacceptable contracts at 5♦ + 0, +1. 4 W’s unacceptable contract at 4♠ x + 0. 1 W’s right contract at 5♠ x – 1. 1 E’s unacceptable contract at 5♥ + 0. 1 W’s unacceptable contracts at 6♦ + 0!!? Eleven (!) wrong contracts out of 12, all played at the maximum level of competition!

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INSIGHTS From “Bd’I Online” magazine the official comment on the last game played in the women team finals of the World Mind Games 2014 can be read: “…. The bid begins with 1♥ to your right (west), and you have at north: ♠ Q5 ♥ AK87♦ QJ97 ♣ J104. I imagine you will say pass, after which passes also East, the partner reopens with 1 ♠ and the opener says 2♣. You double – Of course, I would say – Est says 3♣, your partner 3♦ and finally it's up to you to decide the fate of the gold medal. This problem happened to Meike Wortel, who chose a conservative “pass” (I would have said 3♠: having basically denied before to have 3 cards, I should now show a good second support and support to diamonds). Bad for she, because Marion Michielsen had: ♠ AK9843 ♥ 6 ♦ K8653 ♣ Q. Who would you blame? Although Wortel had used a lot of prudence, I think it's Michielsen the major responsible, but to you to choose the percentages to be attributed. With the gained 7 IMP's, England won of 3.” Unfortunately, the commentator does not report the news about the situation of vulnerability. Let’s so suppose all vulnerable, that is VV. Let’s see who is to blame playing Quantum Bridge: Woertel (N): ♠ Q5 (0.30) ♥ AK87 (2.50) ♦ QJ97 (1.40) ♣ J104 (0.30) = “4.50 W”. Michielsen (S): ♠ AK9843 (4.95) ♥ 6 (0.00) ♦ K8653 (2.15) ♣ Q (0.25) = “7.35 W”. It needs to say that playing Quantum Bridge, having "4.50 W" of contract power, after the W’s opening of “1♥”, N should absolutely intervene (!) because satisfying the minimum requiremnt of 3.50 W + 0.40 W = 3.90W and because having also a balanced hand guarantor of fit, so should always call: “double!" showing a contract power of [3.90 W + 0.50 W]. This would already fix the "quaestio" of guiltiness by N, with the commentator’s good peace. East historically would pass. South, having "7.35 W" and summing a side potential of 7.35 W + [4.40 W] = 11.75 P, should reduce it applying to [4.40 W] his hand risk factor of unbalanced hand, next to 60%, and should so indicate a prediction of level correspondent to 7.35 W + 2.60 W = 9.95 W, that is of L4 by using the 3rd PC: “1NT”; West would probably call a historical “2♣”; North would call: “2NT” for his balanced hand; South could now easily close at: “4♠”. Playing Quantum Bridge, we would have traded information about our contract power, and there it would not have been certainly any error on the final contract, as, instead, dramatically happened to NS. Playing QB we would never have stopped at 3♦ (!), as historically happened although standing a contract potential of about 12 P and a sure fit warranted by the balanced hand!

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HANDS WITH ONLY FOUR CARDS SUITS After our partner’s level L forecast, wanting to propose NT we must have a hand with balanced strength among the suit hand without a 5 cards noble suit and without some insignificant trick power at any suit. This “NT” call is extremely important because will always assure a mild fit at least with any partner’s hand, and so the reliability of his level L forecast. The development of the following dialogue will strictly depend on the available bid space left by the forecast, and on the contract convenience. It needs to underline that the first distributive call at NT implies two consequences: it permits to automatically raise up the forecast level and permits to apply a useful convention: “NOBILIA”, aimed at knowing the real distribution of cards in the noble suits. NOBILIA CONVENTION (NC) The NC convention can be applied by our partner soon after our NT proposal of play, if it there is compatible bid space. It is always triggered by using the 1st LC (Logical Call), even automatically by passing after a RHO’s interference. It aims to know the spades number of cards. Wanting to know the number of cards at hearts it must be used the 2nd LC. The table of possible Logical Answer (LA) is: LA answers LA meaning 1st LA < 3 Cards nd 2 LA 3 Cards 3rd LA 4 Cards 4th LA 4 cards at the other noble suit 5th LA 4 cards at both noble suits If partner did not trigger the NC convention and declared beyond the 2nd LC, he would signal a weak unbalanced hand, only playable at the called denomination. FIRST AND SECOND LAP CONTROLS Looking for Slam sometimes we could need to know the number of 1st and, perhaps after that, of 2nd lap controls. The request is always made by using the 1st Illogical Call (IC) for both the needs. The answer would always be: 1st LA for 0/3, 2nd LA for 1/4 and 3rd LA for 2 Controls.

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Board “GRAND SLAM” (TT = 12.75) North “6.90” ♠ AQ62 (2.10) ♥ AQ5 (1.60) ♦ AQ4 (1.60) ♣ AQ3 (1.60) West “1.00”

♠ 873 ♥ 1062 ♦ 10985 ♣ 874

♠ 1095 ♥ J84 ♦ J73 ♣ J1062

“1.50”

♠ KJ4 (0.80) ♥ K973 (1.30) ♦ K62 (0.65) ♣ K95 (0.70) South “3.45” North, being VN, counts 6.90 W and, falling into the 4th trick band of permissible strength, opens by using the 4th PC: “1♠” showing a medium force of [7.00 W]. South with 3.45 W and a balanced hand can add all his strength thanks to its optimum distribution, obtaining a potential of [7.50 W] + 3.45 W = 10.45 P, but having no Aces must answer with a forecast of 3rd level by using the 2nd PC: “2♣”. North calls: “2NT” showing a balanced hand. South must consider how N could have reached [7.00 W] not having 4 Kings, so must perforce have 4 Aces followed by some Queen or J10. His 4 Kings now are worth at least 1.25 W each so can easily update the side potential to 12 W! he must only ask for length at spades to fully understand N’s hand by using the 1st PC: “3♣”. North answers “3♠”, 3rd LA (Logical Answer) showing 4 cards of spades excluding 4 cards of hearts. South can continue asking for C1 controls by using the 1st IC (Illogical Call): “4♣”. North answers: “4♥” that is 2nd LA for 1 or 4 Aces. South asks also for C2 controls by using again the 1st IC: “4NT”. North answers: “5NT” that is 5th LA for 2 C2 (AQ is worth 1 C1 and 0.5 C2). South now “sees” 4 suits headed by AQ and can call a full: “7NT”.

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LOOKING FOR THE BEST CONTRACT 43TH WTC BERMUDA BOWL - SEMIFINAL ROUND 2 Board 27. Dealer South. None Vulnerable. .........................North .........................♠ 9542 .........................♥ K5 .........................♦ 6532 .........................♣ 1063 West........................................ East ♠ K7…….................................♠ A106 ♥ 743.......................................♥ J10862 ♦ AQ9......................................♦ 107 ♣ AKJ94..…............................♣ Q75 ..........................South* ......................... ♠ QJ83 ......................... ♥ AQ9 ......................... ♦ KJ84 ......................... ♣ 82 "Quantum Bridge" bid totally applied (https://www.facebook.com/groups/QuantumBridge/): S: ♠ 1.25 ♥ 1.60 ♦ 1.40 ♣ 0.00 has 4.25 W of contract power and falls into the 1st band of force permissible to open, so must use the 1st PC and call: “1♣” meaning a medium strength of [4.00 W]. W: ♠ 0.55 ♥ 0.05 ♦ 1.60 ♣ 4.40 has 6.60 W of contract power and must check his requiremnt of intervention: 4.00 + 0.00 (partner not yet passed) + 0.00 (no step of distance from 1 clubs) = 4.00 W, falling into the 3rd trick band of distance must intervene by using the 3rd PC: “1♥” showing a minimum force of 6.00 W till to 6.95 W. N: ♠ 0.55 ♥ 0.55 ♦ 0.50 ♣ 0.15 has 1.75 W of contract power, sums up a potential of [4.00 W] + 1.75 W = 5.75 P not enough for any level forecast, so must call: “pass”. E: ♠ 1.15 ♥ 1.80 ♦ 0.10 ♣ 0.40 has 3.45 W, sums up a potential of [6.50 W] + 3.45 W = 9.95 P, having a slight unbalanced hand and 1 Ace can indicate a safe prediction of L3, so must use the 2nd PC being level 1 not fully available: “1NT” meaning Level 3 of 9 tricks. W: “2♣” having no force at all at hearts for calling NT E: having fit assuring the forecasted 3rd level must try the unique chance of Game: “2♥” W: a bit of fit, so: “2NT” trying the shortcut to Game and also to see how much force E has at hearts E: W has a 3-5-2-3 distribution with no power at diamonds; but fit at clubs lets increase the forecast to level 3, so: “3NT” must be tried. Final contract: 3NT of W or with more risk 4♥. The 4 historical contracts were: 3 W’s contracts at 4♥ + 0. One W’s unacceptable contract at 2♥ + 2.

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LOOKING FOR THE BEST CONTRACT 43TH WORLD TEAM CHAMPIONSHIPS ROUND 8 BERMUDA BOWL 2017 FINAL FRANCIA - USA2 Board 32. Dealer West. EW Vulnerable. .........................North .........................♠ 965 .........................♥ KQJ10 .........................♦ 1032 .........................♣ 1062 West*........................................ East ♠ AJ43.....................................♠ KQ1082 ♥ A2........................................♥ 9 ♦ KQJ9....................................♦ A76 ♣ J95.......................................♣ AK87 ..........................South ......................... ♠ 7 ......................... ♥ 876543 ......................... ♦ 854 ......................... ♣ Q43 "Quantum Bridge" bid totally applied (https://www.facebook.com/groups/QuantumBridge/): W: ♠ 1.75 ♥ 1.00 ♦ 2.75 ♣ 0.25 has 5.75 W and falls into the 3rd trick band of force permissible to open, so must use the 3rd PC: 1♥ meaning a medium force of [6.00 W] +- 0.50 tricks N: ♠ 0.10 ♥ 3.00 ♦ 0.15 ♣ 0.15 has 3.40 W, whereas the minimum requirement to intervene is: 3.50 + 0.00 (partner not yet passed) + 0.40 (actual distance from 1♣) = 3.90 W and having less must pass. E: ♠ 3.50 ♥ 0.05 ♦ 1.05 ♣ 2.50 has 7.10 W of unbalanced hand, sums up a potential of [6.00 W] + 7.10 W = 13.10 P; having 2 Aces and a hierarchy force of almost 6 W must well predict a level 5 of 11 tricks by using the 4th PC: 2♦ for Level 5 reachable S: ♠ 0.00 ♥ 2.90 ♦ 0.05 ♣ 0.40 has 3.45 W and must say: “pass” W: “2NT” showing no 5th noble suits and much hierarchy force scattered among the suit E: “3♣” asking for the number of spades cards W: “3♠” that is 3rd bid step for 4 spades cards, excluding 4 hearts cards E: “4♣” checking for slam by using the 1st IC number W: answers by using the 3rd LA: “4♠” for 2 Aces of balanced hand E: there is no way of testing for Grand Slam, so being sure of 4 Aces and 12 W at least it’s useless to play at spades and it can be called: “6NT” giving a chance for Grand Slam if W were next to 6.50W. W: “pass” having only 5.75W and so being at the beginning of the showed trick band. Final contract: 6NT of W. The 2 historical contracts: E’s 7♠ -1 and W’s 6♠ + 0.

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Let's make a significant example of how easy it is to be wrong evaluating the actual contractual force of the hands, even at the maximum levels of competitive Bridge. This deal was played at: BALI World Championships 2013 Board 21 N N/S (Total W = 15.90) North “4.85” ♠ A952 (1.60) ♥ AJ83 (1.75) ♦ QJ (0.45) ♣ A86 (1.05) West “3.60”

♠ J64 (0.25) ♥ 4 (0.00) ♦ K7652 (2.15) ♣ K953 (1.20)

♠ KQ10 (1.75) ♥ KQ106 (2.25) ♦ A1043 (1.60) ♣ Q2 (0.30)

East “5.90”

♠ 873 (0.05) ♥ 9752 (0.55) ♦ 98 (0.10) ♣ J1074 (0.85) South “1.55” To shorten the speech, during the Poland-Italy match, Italy opened at North calling 1NT, and all other players passed! In other room Poland stopped at 2♥! In other room, USA played 2♥ of South! Let's see how EW’ hands should be evaluated and declared applying Quantum Bridge after “1NT” by North. NS have "4.85 W + 1.55 W” that is “6.40 W" of contract power, while EW have "5.90 W + 3.60 W" that is 9.50 W, enough for an easy “3NT” contract once dialogue were started. E: has 5.90 W of balanced hand; he must check his requirement of intervention: 3.50 W + 0.80 W (4 bid steps of distance from 1 clubs) = 4.30 W, falling into the 2nd trick band ahead should use the 2nd PC: “2♣” showing a contract power spanning from 5.30 W to 6.30 W, and would right away bribe South. West would count 5.80W (E’s interval central point) + 3.60 = 9.40 W, and with a risk only at Hearts would indicate a contract forecast of level 2 using the first PC: “2♦”. East, being authorized to use the whole second level, would show his balanced hand by calling: “2NT”, automatically increasing to level 3 the forecast. West should grasp the only chance of Game and question East about noble suits cards (see “Nobilia Convention”). East would answer 4 cards at hearts, and EW side would easily close at “3NT”. That was, perhaps, one of the historical most incredible episodes, but certainly not the rarest one. THE END

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# QUANTUM BRIDGE THEORY 2020.01.15

PLAYING BRIDGE ONLY AND ALWAYS BY TRICKS

# QUANTUM BRIDGE THEORY 2020.01.15

PLAYING BRIDGE ONLY AND ALWAYS BY TRICKS

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