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# Is it preferable to spread or concentrate your bets at craps?

14 November 2011

Losing in the casino is bad.. A close second at craps, frustration-wise, is waiting and not winning while everyone else is racking up the chips on dice totals you haven’t covered. Which is why most titans of the tables put money on multiple, complementary propositions at the same time. Not as hedges, another kettle of fish entirely, where opposing bets having different sizes and payoffs compensate for one another – such as \$1 on Any Craps to “protect” \$5 or \$10 on Pass during come-out rolls. Rather, as wagers that win individually on alternate outcomes. Like “32-across” – \$5 each on the four, five, nine, and 10 with \$6 each on the six and eight. The appearance of a five, for instance, pays \$7 and has no influence on any of the other elements.

On the average, 32-across pays either \$9 or \$7 on 24 out of every 36 throws (66.7 percent), loses \$32 on six out of every 36 (16.7 percent), and pushes on the remaining six out of 36 (16.7 percent). Contrast this with \$32 or \$30 up for grabs on a single number. Expected frequencies on four or 10 are to win only three out of 36 (8.3 percent), lose six out of 36 (16.7 percent), and be idle otherwise – a whopping 27 out of 36 (75 percent) of all throws. On five or nine, the rates are four out of 36 (11.1 percent) to win, six out of 36 (16.7 percent) to lose, and 26 out of 36 (72.2 percent) to have no action. Likewise on six or eight, the figures are five out of 36 (13.9 percent) to win, six out of 36 (16.7 percent) to lose, and 25 out of 36 (69.4 percent) to do nothing.

You needn’t start as high as \$32 just to get action on more throws. For example, compare the figures above for \$12 on either six or eight with \$6 each on the six and eight. The latter pair is projected to win 10 tosses out of every 36 (27.8 percent) – twice as often, lose six out of 36 (16.7 percent) – the same, and push 20 out of 36 (55.6 percent) – a 13.9 percent notch downward.

If being in the fray is important to you, spreading money over multiple numbers may be apropos. Of course, you can’t take the action you relished at the casino to the bank. For this, you have to earn a profit. So it helps to know how distribution versus concentration affects monetary results.

Use 32-across as the archetype and ignore pushes. Resolutions will average 24 wins for every six losses. This represents 4-to-1 odds favoring the solid citizens. The individual numbers give three wins for every six losses on the four or 10, four wins for every six losses on five or nine, and five wins for every six losses on six or eight. The respective odds are 2-to-1, 1.5-to-1, and 1.2-to-1 – with the bosses having the best of it in all cases. The odds advantage for players with 32-across, however, must be reconciled by considering payoffs along with chances of winning and losing.

A win on a 32-across bet pays \$9 or \$7, according to which number pops. The entire \$32 loses on a seven. One win therefore can’t turn a profit on a hand if the money is kept at on the table for subsequent throws, as it usually is. You need either four or five hits in a row, again depending on the numbers scored, to break even or be ahead. The probability of breaking even is 8.6 percent – with two wins on four or 10 and two on any combinations of fives, sixes, eights. The chance of an actual profit is 22.8 percent in four or five consecutive wins with other appropriate combinations. On the individual bets, you can’t break even. The chance of winning as opposed to losing is 33.3 percent on four or 10, 40.0 percent on five or nine, and 45.4 percent on six or eight.

But wait. There’s more. Not only are probabilities of profit greater with bets on individual numbers – 33.3, 40.0, or 45.4 versus 31.4 percent – amounts are higher. The 33.3 percent chance on a four or 10 nets \$61 for a \$31 Buy bet (a \$32 outlay), the 40.0 shot on five or nine earns \$42 for \$30 at risk, and the 45.4 percent prospect on six or eight gets \$35 for \$30 wagered. The largest gains for four and five straight wins with 32-across are \$36 and \$45, respectively.

Further compounding the conundrum, bets on single numbers are all-or-nothing affairs. On a five, as an example, you can win \$42 or lose \$30. On 32-across, you can lose the whole amount. Or you could win on fewer throws than needed to break even or show a profit and, in doing so, cut your losses. Success on a four followed by a winning six then a seven-out, for instance, would bring in \$16 before it lost \$32 for a net deficit of only \$16.

As always in gambling, one size never fits all. Every strategy involves trade-offs with other alternatives. Approaches that suit your personal preferences at any given moment may seem undesirable for someone else or maybe for you under different circumstances. Then, of course, there’s the element of randomness. In one craps session, a particular number may hit repeatedly – making the concentrated approach highly profitable (if you’re on it). In the next, sevens may be few and far between a long and jumbled string of other numbers, such that spreading money around the table would be most rewarding. And, nobody knows, in advance, how long a shooter will hold those captivating cubes. As the wise wordster, Sumner A Ingmark, adroitly advised:
A gambler’s wise to weigh suggestions,
‘Cause no one answer fits all questions.