On Fri, Aug 26, 2011 at 08:17:46PM +0200, Vincent Diepeveen wrote: > On Aug 26, 2011, at 10:43 AM, Shawn Hood wrote:
>> A betting system will not improve the negative mathematical >> expectation of a casino game. Right. > Except that this system doesn't have a negative expectation. it has a > positive expectation. > > There is no other system in roulette that has a positive expectation, > other than the doubling system. Vincent, are you shitting us? Or am I misremembering the tortured history of this thread, and by "doubling system" you do NOT mean the trivial martingale betting system that's been used (disastrously) and analyzed for over 200 years? Actually it doesn't matter; as Shawn Hood pointed out above, your assertion is still wrong even if you actually meant some other non-martingale betting system. You insisting that *martingale* betting gives you a positive expectation at roulette just makes it much funnier! There are ways to gain positive expectation in roulette (other than the obvious fraud and collusion). They involve finding a poorly installed roulette table and using a wearable computer and physics to predict where the ball will land. Look up Thorp and Shannon's research on the subject; they actually used it in casinos c. 1961. None of those ways are due to some special method of betting. The point of betting systems is to optimize your small edge, but you have to HAVE that edge in the first place. Money management is important because tells you how to properly size your risk, but it can't give you alpha. Now yes, if you have a very volatile "roulette" game and a 0% edge (no advantage to either you or the house), with some luck you could get rich by playing it for a limited period of time and quitting while you're ahead. But you still have a 0% expectation game; look up the mathematical definition of "expectation". Also, I don't remember for sure, but I believe martingale betting is (always) more aggressive than Kelly. If so, then it is inherently stupid. Kelly defines the MAXIMUM size bet that it is rational to make, assuming your goal is maximum compounded wealth AND you have a quantifiable edge (however small) in the game. It can make sense to bet less than Kelly, and if you believe you have no edge the rational bet is zero. It is never rational to bet more than Kelly. In practice, even when you are sure you have a real edge, you want to bet less than Kelly, often much less. There are several reasons for that; one is that calculating Kelly depends on your estimate of how big your edge is, and it is easy to overestimate your edge such that in truth you are massively overbetting (taking way too much risk) at 2x Kelly or even more. But optimizing the way you bet doesn't turn an inherently losing game into a winner. If the edge is with the house - as it certainly is with a fair roulette table - the rational bet is not to make one. This news article is probably more interesting: http://www.theonion.com/articles/casino-has-great-night,1506/ Casino Has Great Night; May 28, 2003 -- Andrew Piskorski <[email protected]> _______________________________________________ Beowulf mailing list, [email protected] sponsored by Penguin Computing To change your subscription (digest mode or unsubscribe) visit http://www.beowulf.org/mailman/listinfo/beowulf
