Comments on: What is the gambler’s equivalent of Amdahl’s Law? http://www.win-vector.com/blog/2009/10/what-is-the-gamblers-equivalent-of-amdahls-law/?utm_source=rss&utm_medium=rss&utm_campaign=what-is-the-gamblers-equivalent-of-amdahls-law The Applied Theorist's Point of View Thu, 15 Jul 2010 00:13:50 +0000 hourly 1 http://wordpress.org/?v=3.0.1 By: jmount http://www.win-vector.com/blog/2009/10/what-is-the-gamblers-equivalent-of-amdahls-law/comment-page-1/#comment-1038 jmount Sun, 11 Oct 2009 18:40:38 +0000 http://www.win-vector.com/blog/?p=878#comment-1038 I should have mentioned that the Kelly System is only proportional betting in very special cases. Proportional betting is not always a good strategy. In general the Kelly System is solving a constrained optimization problem to maximize expected log return- which may have a fairly complicated (and non rule-of-thumb) solution. I should have mentioned that the Kelly System is only proportional betting in very special cases. Proportional betting is not always a good strategy. In general the Kelly System is solving a constrained optimization problem to maximize expected log return- which may have a fairly complicated (and non rule-of-thumb) solution.

]]> By: jmount http://www.win-vector.com/blog/2009/10/what-is-the-gamblers-equivalent-of-amdahls-law/comment-page-1/#comment-1037 jmount Sun, 11 Oct 2009 16:53:02 +0000 http://www.win-vector.com/blog/?p=878#comment-1037 I have received some very insightful private comments to the effect that investing or gambling with the Kelly criterion is no simple or safe thing. These comments are correct. But we must remember that professional traders and gamblers work very hard- they are not known for restricting themselves to what is easy or beautiful. I certainly in no way advise carrying any simplifying assumptions out of the laboratory (where they help with the initial analysis and understanding) into the field (where the assumptions are provably false). There are two essential points of a real world gambling system. First the underlying game must be profitable to the player (no system can turn an unprofitable game to a profitable one). Systems are at best techniques for managing risk and return in a situation that is already known to be profitable to the player (i.e. the player has some knowledge or skill and the system is merely the method of maximizing the benefit of this knowledge or skill). Second the system must model reality, not model what is traditional or convenient. Even the simple alteration of allowing the player to hold some money out of the game complicates the analysis (as I said the original paper deals with the situation, but it is not as pretty as the basic solution). If there is any risk of ruin (say some bet is not-allowed so you can no longer get your probabilities to sum to 1) or if there is a minimum bet (so while the strategy can guarantee you don't lose all of your money it cannot guarantee you quickly fall to a pittance that you are no longer allowed to bet) the math gets messier and the published pay-offs re-enter the analysis. I have received some very insightful private comments to the effect that investing or gambling with the Kelly criterion is no simple or safe thing.

These comments are correct. But we must remember that professional traders and gamblers work very hard- they are not known for restricting themselves to what is easy or beautiful. I certainly in no way advise carrying any simplifying assumptions out of the laboratory (where they help with the initial analysis and understanding) into the field (where the assumptions are provably false).

There are two essential points of a real world gambling system. First the underlying game must be profitable to the player (no system can turn an unprofitable game to a profitable one). Systems are at best techniques for managing risk and return in a situation that is already known to be profitable to the player (i.e. the player has some knowledge or skill and the system is merely the method of maximizing the benefit of this knowledge or skill). Second the system must model reality, not model what is traditional or convenient.

Even the simple alteration of allowing the player to hold some money out of the game complicates the analysis (as I said the original paper deals with the situation, but it is not as pretty as the basic solution). If there is any risk of ruin (say some bet is not-allowed so you can no longer get your probabilities to sum to 1) or if there is a minimum bet (so while the strategy can guarantee you don’t lose all of your money it cannot guarantee you quickly fall to a pittance that you are no longer allowed to bet) the math gets messier and the published pay-offs re-enter the analysis.

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