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Best of Alan Krigman

Gaming Guru

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Look at Strategic Trade-Offs Before You Leap into a Game

11 August 2000

Most casino gambling involves strategic decisions. You can start with different size bankrolls, wager various amounts, pick propositions with assorted chances of winning and contrastingly inverse payoffs, look for long sessions or plan to make it or break it quickly, and aim at a modest profit with a good prospect for success or a big score with lower likelihood of victory.

Trade-offs are inherent in all such options, and offer solid citizens means to adapt their play to personal proclivities. Yet few players give any of this a second thought. And, of those who do, a majority misunderstand the situation. Rather than a trade-off, they fantasize they've found a secret of beating the house that the casino bosses have been trying to keep under wraps.

I'll illustrate the diversity of the choices and their implications in terms of two basic bets at double-zero roulette. The idea holds, in one way or another, at any table or machine.

Say you bet $10 per spin -- all on the numbers 1 through 12, or $5 each on 1 through 12 and 13 through 24. House edge is 5.26 percent of $10 either way, so the casino doesn't care which you choose, and rates you the same for comps in both cases.

The most obvious difference between the bets involves the results of individual spins. The whole $10 on a dozen numbers gives you 31.6 percent probability to pick up $20. Spreading $5 on each of two such groups gives you 63.2 percent chance to net $5.

Less evident but more important is what's expected to happen during a session. For instance, how do these alternatives affect the likelihood your bankroll will carry you through the normal downswings of a game? Assume you buy in with $125 and hope to play for two hours -- call it 100 spins. The single $10 wager yields almost 50 percent chance of staying alive this long. The split $5 wagers raise the probability of survival to over 75 percent. Conversely, if you wish to play until you've either doubled or lost your money, the balance reverses. With $10 on the twelve numbers, you'll succeed about 33 percent of the time. Splitting the bet yields only 7.5 percent chance of reaching your target. Do you see the trade-off? Distributing the bets gives you a better shot at longer play, but less chance to win big bucks.

What if, instead of $125 or bust, you'll walk when you earn $50 or blow your poke? With the single wager, chance of success rises from 33 to 61 percent. The dual bets jump it from 7.5 to 35 percent. You're swapping amount versus chance of attainment.

Maybe you're willing to risk $250, still wagering $10 in one of the two modes. Betting on one dozen, you now have 86 percent chance of surviving the 100 rounds, compared to 50 percent with a $125 stake. The two-dozen approach affords over 99% chance of being in contention this long, up from 75 percent with exposure of $125. Again the trade-off -- you'll lose more when your luck goes kablooie, but it won't happen as often.

Similarly for profits with a bigger bankroll, although for these particular cases the effect is tempered by high edge. Shooting for $50 from a $250 start will bring joy in 70 percent of your single-dozen games, a modest gain over the 61 percent with a $125 buy-in. And you'll succeed 36 percent of the time with double-dozen bets -- an improvement, albeit meager, over the 35 percent with the $125 stake. In these cases, the trade-off is a greater chance for a specific profit versus a heavier loss when you fail.

Details differ among games, but the principles are universal. Whether you prefer tables or machines, think about constraints and goals. What are you comfortable risking? What would you be happy earning? How badly do you want to come out ahead? How long would you like to play? Then consider the opportunities for give-and-take. You don't need the specific numbers to tweak your game and see whether the direction in which you've headed suits your estate and aspirations. The trade-off troubadour, Sumner A Ingmark, set it so to song:

Push a little here, pull a little there,
Compromises fair, get most folks their share.

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.