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Jonas Martinsson's Blog
Suspended by eBay By Jonas Martinsson (Jonas Martinsson - Blog) Submitted at 12:00 Oct 10, 2007
Bankroll-Breaking Even Money Bets By Jonas Martinsson (Jonas Martinsson - Blog) Submitted at 11:45 Dec 16, 2007
Some ten years ago I ran Gambol, a short-lived gambling fund that invested money in statistical sports betting. I even managed to convince gullible friends to invest. Eventually, the fund lost all its money to the online bookmakers, and I tried to figure out what went wrong. I ran lots of simulations to better understand what had happened, and in one of them I encountered something remarkable. Recently, I was indirectly reminded about the paradox I had discovered, which I still have a hard time to understand intuitively. Here's the story of our gambling hero Andrew, who despite being an intelligent gambler, here takes a tumble and loses his entire bankroll. When Bob offers Andrew to flip coins for even money, Andrew wrongly assumes that this couldn't possibly be a losing proposition. The catch is that Andrew needs to bet x% of his bankroll on each coin flip. He is free to choose the value of x himself, provided that x stays the same throughout the game. Theoretically, the expected value of each betting round is +-0 for Andrew. His chances of winning each coin flip is 50%. When he loses a flip, his bankroll decreases by x% and if he wins he gains the same amount. Andrew decides to bet 10% of his
bankroll, which is $100. Let's take a look at possible scenarios for the outcome of the first rounds. After the first betting round Andrew's new bankroll will be either $90 or $110. If he ends up losing the first bet, his bet for the second round will be $9 (10% of his new bankroll of $90), and if he wins the first bet, his second bet will be $11. After round two he will end up in one out of the following four scenarios: • 1st round lost + 2nd round lost: $81 • 1st round lost + 2nd round won: $99 • 1st round won + 2nd round lost: $99 • 1st round won + 2nd round won: $121
It is important to note that in 3 out of 4 cases Andrew is a loser after round #2. Theoretically, each bet is even money, and the average bankroll in the four scenarios remains $100 - but still Andrew is likely to be a loser in the long run. The more betting rounds there are, the more likely Andrew is to eventually lose his entire bankroll. There is also a chance that he will win a lot of money, but that chance is getting slimmer and slimmer for each betting rounds he participates in. After the third round Andrew happens to be back at a 50% chance of being a winner, but this is just a temporary fluctuation as he is again a
likely loser after the fourth round. Below is a graph showing how Andrew's bankroll develops in 50 simulations of 2,500 betting rounds, betting 10% of an initial $100 bankroll. After 2,500 bets the best case out of the 50 simulations has Andrew's bankroll at less than $60. The blue line in graph below shows how many of the 50 initial scenarios are in the black (with a bankroll not smaller than the initial $100). The red lines displays the average bankroll over the 50 scenarios. The average bankroll should have stayed around the initial bankroll, since the expected value of the bet is +-0, but due to the limited number of simulations (50 in this case), we eventually run out of winning scenarios. No matter how many scenarios I choose to run, I can always make the average bankroll go down towards 0 by running enough betting rounds. This bet, which theoretically is even money, makes you lose your money in real life - a fascinating paradox! Note that the final outcome where the bankroll dwindles towards 0 does not change, no matter which value is chosen for x (the ratio of your bankroll wagered on each round).Technorati Tags: game theory, gambling, martingale, kelly betting
FeedJournal for Facebook and Bebo By Jonas Martinsson (Jonas Martinsson - Blog) Submitted at 14:02 Jan 17, 2008
Are you on Facebook or Bebo? With the help of FeedJournal you can now use those platforms to widen the reach of your blog. Share a
newspaper edition of your feed on any of the major social networks for free! To get started, simply visit FeedJournal Publisher, fill in your feed URL and follow the instructions on how to add the application to your Facebook or Bebo page.
As previously announced, FeedJournal already has installers for iGoogle, Netvibes, Pageflakes, Piczo, Orkut, Hi5, Ning, plus a generic JavaScript snippet.Technorati Tags: facebook, bebo
eBay suspended my account after being a member for less than a week. I never bought or sold anything, just browsed their listings. eBay refuses to give an explanation for suspending me, but claim that they "can understand [my] frustration". On Sep 30 I created a user account in order to buy a docking station for my laptop - an item which costs around $10 on eBay. I contacted about five sellers about shipping costs to Israel. Then I get the suspension e-mail from eBay. At first, I was convinced the email was a phishing attempt and marked it as spam, but when I logged on to my eBay account it was obvious that they had really suspended me. The only clue they gave as to why they suspended me is this: "Your account was suspended under the 'Abusing eBay' section of the eBay User Agreement. This section states that eBay may suspend a user's account if we think that the user is creating problems (legal or otherwise) or acting inconsistently with the letter or spirit of our policies. [...] In addition, your account was found to be in violation of our Spam Policy" Needless to say, I never sent any spam or in any other way misused eBay's services. The representative who I got in touch with in order to understand the reason behind their action says: "For security reasons we are unable to be more specific about the details that led to this action. [...] eBay is taking a tougher stand to prevent fraud". He goes on to say that "honest members may be required to take one or two extra steps before they are allowed to participate on eBay". These extra steps involves faxing them a copy of a "credit card statement, a recent bank statement or a recent utility bill". I also tried to connect with their live chat support but they can't do anything as long as I did not fax them the statements they want. I am not going to fax them this or any other personal information to get my membership back, and I will definitely never use their services again (I'm not allowed to, but that's beside the point). Development of eBay ranking according to Alexa Which other major web site are abusing new customers like this? It is amazing to consider that eBay is the #20 most popular web site in the world according to Alexa's ratings. Their rating peaked at #5 a few years ago, but has steadily been dropping since then. If they are treating me like this, a typical new user exhibiting typical user behavior - it is not being bold to assume that their rankings and popularity will continue to decline. eBay is still the #1 online auction but that has to change soon, unless they radically change their customer services and implementation of their policies.Technorati Tags: eBay