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Best of Alan Krigman

Gaming Guru

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You Can Control Your Chances, But You Can't Have it Both Ways

21 June 2000

You have more control over your chances in the casino than you might imagine. I don't mean you can drive a session inexorably to triumph. I mean, you can tailor your play to enhance your shot at achieving practical goals, realizing that control is a matter of compromise. By aiming at one target, you may have to sacrifice other desirable results -- mainly trading proceeds versus prospects for success, and vice-versa. Not having the best of everything simultaneously is as basic to managing probability in the casino as it is to force, mass, and energy in the real world.

Everyone knows you can choose your game and table or machine. Whether and how much such choices affect your chances depend on available options. You can also pick your playing and betting strategies. These factors generally influence your expectation and the bankroll swings you're apt to undergo. They're important, and ultimately separate proficient gamblers from solid citizens who only bring what they can afford to lose, and later claim they had a good time losing it because they got comps for the buffet.

On an individual session or casino visit, however, these niceties tend to affect chance of success far less than properly balancing bankroll, bet size, and win target. The fraction of your starting stake you risk per round often has stronger impact on both the probability you'll be in action after some duration of play and the likelihood you'll reach some desired profit level.

Here's a simplified example. Suppose you're playing craps, making only a single bet -- buying the four. You start with $1,000.

The following list shows your chances of surviving -- maybe ahead, maybe behind, but not having hit the $1,000 bye-bye barrier -- within 100 decisions. The first column gives the figures for conventional buys, where the house takes a commission of $1 on top of every $20 bet whether you win or lose. The second column shows data for lower-edge bargain buys, on which the casino takes the commission only when you win. Note that at any betting level, owing to the significantly reduced edge, bargain buys offer greater chance of survival. However, for the same bankroll, the improvement is small compared with the changes encountered raising or lowering bets by typical increments.

nominal
bet 

 conventional
buy 

bargain
buy
$ 20 

       99.9%

99.9%
40 86.2 91.1
60 65.1 73.5
80 50.0  59.1
100 40.0 48.7

Assume you control your chances by sizing your bets to achieve a reasonable chance at survival on your bankroll. You can't then choose a win goal independently. This is the trade-off. What you can do, instead, is set a win goal consistent with your survival choice. This signals when you've had a good session and helps you quit when you're ahead by a sensible amount.

Perhaps you're willing to accept 80 to 90 percent chance of surviving 100 decisions on a $1,000 stake making conventional buy bets. You therefore jump in at the $40 level. The next list shows the chance you'll earn various profits before depleting your bankroll. Here you see the effect of setting the point at which you're ready to quit. Try to double a $1,000 bankroll with $40 and you can anticipate victory less than once every four times. Shoot for a $200 profit and you can expect nearly three fourths of your sessions to be successful.

win
goal
chance
of success
$200 71.5%
400 52.4
600  39.0
800 29.4
1000 22.3

  You can control your chances the other way too. What if you won't be happy without doubling your $1,000? Bet higher. Chance of ever getting there is 38 percent with $100 bets -- up from the indicated 22 percent at $40. But you'll only survive four out of 10 100-round sessions at $100, compared with nearly nine at $40.

It's as the poet, Sumner A Ingmark, so rhymingy remarked:

Gamblers wise must compromise,
Else their tries will yield no prize.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.