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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Why you'll probably bite the dust if your gambling budget is $100

14 September 2009

The majority of casino patrons who gamble with modest budgets go belly-up. Stakes under $100, especially, court disaster. Matters improve, albeit slowly, as bankrolls increase. House advantage plays a role, but has less impact than is commonly believed. The same phenomenon would occur even if the house had no edge.

Picture a "fair" game, one in which neither bettors nor bosses have a statistical advantage. Something like flipping coins for a 1-to-1 payout, or a variation of roulette involving only bets on individual numbers, each a 37-to-1 longshot paying 37-to-1.

When edge is zero, an easy formula gives the prospect of success. It's the loss limit divided by the sum of loss limit plus win goal. The chance of failure is 100 percent minus this quotient.

As an example, assume you'll risk $100 on a shot at winning $100 in a fair game. The chance of a victory is $100/$200 or 50 percent; that of a rout is 100 - 50, also 50 percent. Instead, pretend you won't quit until you're $400 ahead or broke. Now, the outlook for ecstasy is $100/$500 or 20 percent; that of agony is 80 percent. Maybe your fair game is a machine with a $24,900 jackpot. You preload $100, intent on trucking until it's gone or the meter gets to $25,000. Your chance of soaring is $100/$25,000 or 0.4 percent; that of crashing is 99.6 percent. The bosses make nothing in any such cases. Players win or lose to each other.

Conversely, if a bettor starting with $100 opts to quit as soon as a $25 profit is in, chance of attainment is $100/$125, or 80 percent. With a $10 win goal the chance becomes $100/$110 or 90.9 percent. The formula shows that fair games can work both ways.

So, why do folks with $100 stakes bust out in droves? You know the answer. Hardly anybody who starts with $100 is ready to stop as soon as that profit point hits $10 or $25. A $10 or $25 discount coupon may seem meaningful at Home Depot. But few folks feel it's worthwhile to go to a casino for this puny a return. Likewise, players starting with $100, who find themselves down $60 or $70, rarely cut their losses and run. Rather than admit defeat and sacrifice $60 or $70, they tend to blow the other $30 or $40 attempting to recover or go over the top.

Cynics might attribute such thinking to greed. But cynics, as Oscar Wilde noted, know the price of everything and the value of nothing. Nobel prize economists, however, recognize that the value of money varies among people and circumstances, and is not necessarily equal to its price. This phenomenon is an instance of principle of utility which holds, among other things, that the whole is frequently worth more than the sum of its parts.

Say a solid citizen can always dig up $100 but realizes that a $10,000 or $100,000 wad is normally out of reach. Such a person's aim in gambling might well be to invest $100 on a remote shot at a bundle he or she otherwise has no hope of amassing. Folks like this won't be much happier with $125 than $100. Nor much sadder losing $100 than $70. They're exalting what seems to be the high 100 or 1,000 times $100 value, while deriding the low $100 price.

It doesn't simply scale-up for high rollers. A $100,000 tycoon is apt to quit a with $25,000 profit, although the percentages are the same as for a $100 plebeian with a $25 gain.

When the house has an edge, win goals become more elusive than in fair games. And other factors enter the fray. Imagine risking $100 for a $100 profit on Player at baccarat. Ignoring ties, edge is 1.36 percent. At $25 per coup, the 50 percent fair game likelihood of success drops to 47.28 percent. At $10 per coup, it's 43.24 percent. The lower the bet, the larger the effect of edge. This, because more rounds up and down will be played, increasing the gross wager on which the edge takes its toll.

Players' personal exit strategies affect their session prospects. Often much more so than the joints' juice. The inimitable inkster, Sumner A Ingmark, said it like this:

While edge and luck may figure prominently,
They need not always do so dominantly.

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.