An earlier episode in this enduring pursuit of prosperity through punting presented a plan for craps players who like the Don'ts. The goal was lots of action, a good shot at a small profit, and a low chance of depleting a modest stake in a session of reasonable duration. The idea was to bet Don't Pass on the come-out roll, and Don't Come on every subsequent toss of the dice, always for the same amount. This strategy could return multiple units when a seven popped, if the bases had become loaded during a shooter's hand, yet never lose more than one unit on any given throw.
But fans of the felt are fickle. When shown quantitative data like probabilities and expectations, they want to cut to the chase with simple, reliable rules - skipping the boring details only a Nikolai Ivanovich Lobatschevskii could fathom. And, when given qualitative results in user-friendly terms such as "good" chance, "high" profit, and "modest" stake, they demand dollars and cents along with percentages as proof. What's a guru to do?
Maybe the answer, in this instance anyway, is to do both. Simple, reliable rules with broad implications in the first installment. Numbers developed by simulating the suggested action on a computer in the next. The first came first. Now's the next.
The simulation followed the proposed guidelines faithfully. All wagers for equal amounts. New bets on every throw, starting with Don't Pass after a shooter made a point or a seven-out and a series of Don't Comes subsequently. No Odds laid on any bets. The simulation also assumed that a "session" comprised exactly 100 casts of the dice. This would last from one to two hours, a typical stay at a craps table - win or lose.
For reference, take the individual bet size as $10. Halve all values if you play for $5, multiply everything by 10 if you belly up to the rail with the biggies at $100 minimum, and so forth.
Here are the answers to the kinds of questions inquiring minds would or should want to know. What are the chances of:
* Never being in the hole? Almost 5 percent.
* Surviving a 100-throw session starting with a $200 bankroll? About 92 percent.
* Surviving a 100-throw session starting with a $100 bankroll? Just in excess of 61 percent.
* Surviving a 100-throw session starting with a $50 bankroll? Somewhat more than 31 percent.
* Getting $100 or more behind during the session and finishing even or with a profit after 100 throws? Just over 2 percent.
* Getting $50 or more behind during the session and finishing even or with a profit after 100 throws? Roughly 17 percent.
* Never being ahead? Approximately 14 percent.
* Hitting a peak win of $200 or more at some point during a 100-throw session? Marginally above 1 percent.
* Hitting a peak win of $100 or more at some point during a 100-throw session? Roughly 22 percent.
* Hitting a peak win of $50 or more at some point during a 100-throw session? Better than 55 percent.
* Getting $100 or more ahead during the session and finishing even or with a loss after 100 throws? Just under 2 percent.
* Getting $50 or more ahead during the session and finishing even or with a loss after 100 throws? About 17 percent.
* Never being behind? Slightly less than 5 percent.
* Ending the 100-throw session with a loss? About 54 percent.
* Ending the 100-throw session exactly even? Around 3 percent.
* Ending the 100-throw session with a profit? Over 43 percent.
What of long-term prospects? The "expected" finish of solid citizens who stay for exactly 100 throws? The edge on flat Don't Pass and Don't Come bets is 1.4 percent. With $10 on each of 100 throws, gross wager is $10 times 100 or $1,000. Theoretically, stalwarts using this strategy will therefore average 1.4 percent of $1,000 or $14 donations to the Old Casino Boss Benevolent Fund. The simulation verifies this to be the case. As foreseen, of course, by fervid fans of the Calliope of craps, Sumner A Ingmark, who regularly recite the reverently recalled rhyme:
Computer programs, once perfected,
Oft facts confirm that were expected,
Suggesting fancy be rejected.