From: Gunter Bengel Subject: Re: probabilty problem in "Run Lota, Run" Date: 28 Mar 2000 11:28:25 -0800 Newsgroups: sci.math.research Summary: [missing] deodiaus writes: > This gambling problem's approach seems to have been discussed 20 years > ago in various recreational math papers (Martin Gardnier's math puzzles in > Scientific American?). Does anyone have any references (or sites on the > web) where this dilemma is discussed. Dubins,L.E.,Savage,L.J : How to gamble if you must. McGraw-Hill 1965 Gunter ============================================================================== From: Allen Abrahamson Subject: Re: math in the casino Date: Sat, 07 Oct 2000 00:03:45 GMT Newsgroups: sci.math In article <8rldsh$rhh$1@nnrp1.deja.com>, m499 wrote: > it's been said casinos are taxes for the mathematically challenged, and > i'm inclined to agree--especially with slots and roulette. however, i > noticed that expected returns on perfect plays in select games of > blackjack and video draw poker eek out actually above 1. > > is this really true? I believe that fully optimal "zero memory" blackjack play (i.e., effectively against an infinite number of decks) with all the splitting, doubling down, etc., actually favors the player in the second decimal place. I don't recall for sure; it is discussed in detail, with strategy tables, in R. Epstein's wonderful book "Theory of Gambling and Statistical Logic" (Academic Press). As regards your dialogue with Dann Corbit vis-a-vis probability of ruin from asymmetric amounts of capital at risk, he is right with regard to fair or unfavorable games, as was concluded in the aftermath of Bernoulli's posing of the St. Petersburg Paradox. However, in the case of favorable games, it's not hard to show that a player who wagers a constant proportion of his capital at each play will enjoy an expected growth rate of capital equal to two times the difference between player's win probability and 0.50. That means, for example, a player with a single trial probability of winning of 0.505 can expect to double his capital in about ln(2)/0.01 = 70 plays. This is the origin of the adage that if the odds are with you, bet low; otherwise, put it all on the first play, and don't play a second, regardless of the outcome. The classic blackjack book, of course, is Ed Thorpe's "Beat the Dealer." Get a used copy, a seat on the red-eye to Vegas, and bring your Visa card. But make sure it's a round trip ticket. Sent via Deja.com http://www.deja.com/ Before you buy. ============================================================================== From: jmb184@frontiernet.net (John Bailey) Subject: Re: math in the casino Date: Sat, 07 Oct 2000 01:48:41 GMT Newsgroups: sci.math On Fri, 06 Oct 2000 20:49:24 GMT, m499 wrote: >it's been said casinos are taxes for the mathematically challenged, and >i'm inclined to agree--especially with slots and roulette. however, i >noticed that expected returns on perfect plays in select games of >blackjack and video draw poker eek out actually above 1. > >is this really true? An eyeopener is the article: Card counting 101 at http://www.bjmath.com/bjmath/novice/counting.htm The general math for a casino's winning edge is prettiy dismal. Even if the house had no house edge, the player's probability of being wiped out is: P = i/c where i is the players stake and c is the sum of the house's stake and the players stake. If the house has a fractional edge, t its even worse: P = (1- w^i)/(1-w^c) Where w = (0.5 +t)/(0.5 -t) BUT For Blackjack and Poker, the player faces varying odds on any given play and if they know these odds, they can choose their bets in ways that can be shown to result in a long term growth of their own stake. http://www.bjmath.com/bjmath/thorp/ch3.pdf http://freeweb.pdq.net/tomt/gambling/kellybetting.html John