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YOU NEED MORE THAN RULES OF
THUMB TO SIZE YOUR BANKROLL
By Alan Krigman
Alan Krigman, and his poetic sidekick Sumner A Ingmark, have been illuminating the dark recesses of casino gambling for more than a dozen years. Mr. Krigman is especially well known for sharing his insights into the mathematics underlying the various games (including blackjack), the influence of volatility and skewness as well as edge on bankroll during the course of a session, and the impact of betting as well as decision strategies on expected performance. A searchable archive of Mr. Krigman's prose and Mr. Ingmark's muse is online at
http://www.iconworldwide.com/winningways/search.php.
Winning in a repetitive bet milieu like a casino game, often requires a big enough bankroll to weather the cold streaks. It's a matter of probabilities, not absolutes. The question isn't what multiple of your average bet is needed to play a certain game. Rather, how big a bankroll will yield some percentage confidence of surviving the normal downswings of the game with a given betting strategy.
Few solid citizens appreciate and understand the influence of bankroll size. Fewer, yet, realize how funding-needs are altered with considerations such as: average bet, edge, volatility, and the number of coups they hope to experience during a session or visit.
Each game, in some cases each way of playing, is unique. But the general effects of the various elements can be broadly applied qualitatively, if not quantitatively. Blackjack affords a useful paradigm for examining the diverse implications.
To start, picture three ways to play following Basic Strategy.
Option #1.
You bet exactly or an average of $10 per round, giving the casino a 0.5 percent edge. Your "expectation" is a theoretical loss of $0.05 per coup. A risk of ruin analysis shows what stake yields 90 percent confidence you won't go bust in some number of rounds.
For example, if you bet a flat $10 on a single spot you'd need at least the following bankrolls for the indicated number of rounds of play to be 90 percent confident you won't go broke .
|
Bankroll |
# Rounds |
|
$304 |
250 |
|
$436 |
500 |
|
$628 |
1,000 |
Option #2
Pretend you vary your bets from...
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