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Best of Alan Krigman

Gaming Guru

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If You Think One Bet is as Good as Another, Think Again

7 September 2005

Say you take a $100 to a casino. You have lots of options about how to bet. Many of the choices you make are more subtle than what you choose to play, or things like "do" or "don't" at craps or colors at roulette. And you can utilize these subtleties to shape the characteristics of your session. Solid citizens who think gambling is gambling and one bet's like any another -- except, of course, for differences in edge they don't quite understand -- are missing a whole phase of casino fun and games.

Before you rush to an empty spot and start acting like a hotshot without really knowing what you're doing, there are a few things you'd be wise to consider. Chief among these are how much you're comfortable risking on any coup, the profit level at which you'll be happy to quit, and the amount of time you consider adequate for what you'll have spent if you deplete your fanny pack. You may need to make compromises because some of these factors are incompatible with or work against others.

Take roulette as an example. Similar reasoning would apply to other games. A $100 buy-in might get you a long session with $5 per spin on an "outside" 1-to-1 proposition such as Odd or Even; but you're unlikely to bag big bucks this way. In contrast, $10 or more on a single number can yield a handsome return, but is apt to sap that $100 stake in short order.

Changing the amount you bet without switching propositions may also have a major impact. Assume your primary criterion is to stay in the game for three hours. You decide to bet strictly on Red, at a table that returns half your wager if a spin yields 0 or 00. The chance your $100 stake will suffice for three hours is 89.5 percent. You try this for a few outings but find you're not content with the profit even when Red hits regularly. Small wonder, since the chance you'll double your money within three hours is only about 3.5 percent. On your next trip, you bet $10 on Red, keeping your bankroll at $100. The chance you'll double your money leaps up to 26.1 percent. But the likelihood you'll still be in the fray after three hours falls to 54.7 percent.

Incidentally, when outside propositions lose altogether on 0 or 00, $5 bets give players 82.8 percent chance of surviving for three hours on $100 bankrolls, with 2.1 percent shots at doubling their dough. Betting $10, prospects of lasting three hours drop to 43 percent while those of winning $100 rise to 19.6 percent.

Other bets show similar tendencies. Make believe you want to aim for bigger bucks and bet $1 on each of 10 numbers. The chance you'll double your money within three hours isn't bad -- 55.3 percent. However, you've only 32.0 percent chance of enduring for the three hours. Cut the bet to $1 on each of five numbers. Now there's 46.5 percent chance you'll survive for three hours, but the likelihood you'll see $100 profit is cut to 37.5 percent.

Maybe you're not interested in playing time -- just in striking it rich. If you're not afraid to see it all go at once, you could toss your whole $100 on one spot. The chance you'll be in the clover with $3,500 is one out of 38. That's about 2.6 percent.

Perhaps you like longshots but aren't prepared to go for broke. You could put $10 on one or another single spot for each of 10 spins. The chance all 10 will miss, taking your $100 in about a quarter of an hour, is 76.6 percent. Alternately, the chance you'll hit at least once is the complementary 23.4 percent.

The likelihood you'll have exactly one win and net $260 is a respectable 20.7 percent; that of two wins, a $620 profit, is 2.5 percent. From there, you've got hopes but they're dim -- 0.18 percent for $980, 0.008 percent for $1,340, and so on. You could even finish the series of 10 $10 bets with $3,500 by winning every one. The chance of this is under one in six quadrillion so you may not want to rely too heavily on being lucky that day. For, as the songster of steep odds, Sumner A Ingmark, asserted:

Though some may this dispute, When chances are minute, A quest is vain pursuit.

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.