What's the Best Bet on the Table?

It's been a dark and stormy ... wait, that was last time. This time you tried your hand at craps, and the dice have been a whole lot friendlier than the cards were. In fact, you're showing a profit of just over $600! Say, wasn't that new, big flat screen TV you wanted Santa to bring you going for around $800? If only you could rake in a couple more C-notes, but alas you just heard the announcement that the fun bus, your ride home, was leaving in 15 minutes. If you're going to upgrade your entertainment center at the casino's expense you'll have to go for the gusto. But how?

Your eyes drift to the center of the table where the stickperson books the bets officially known as propositions (or props, for short). For a mere $7, chump change given your current financial position, you could have a chance at $210 by betting on 2 or 12. There's also the Any 7 bet, which, for an investment of only $50, would pay the desired $200. Isn't 7 the number most frequently thrown? Although these are one-roll bets and therefore meet the time constraint, the props are also called crazy crapper bets because of their high house advantage, so maybe they are not the way to go.

Your eyes next drift to the Field, another one-roll bet. You've seen players go all in on that bet trying to recover losses in one fell swoop -- and look at all of those numbers that are winners. Why not take the plunge for $200? If you lose you can always say you went down swinging, but the Field has a bad reputation, especially if it doesn't pay double on 2 and triple on 12. Next.

So what is the best bet at the craps table? Ask any knowledgeable player or dealer and I will be amazed if you get an answer other than "the odds bet because the house has no advantage on it," or something to that effect. Of course you must put up a bet on which the house does have an advantage in order to make the odds bet. At a table offering 3x/4x/5x odds the minimum bet to get the desired payoff of $200 would be $29 on Pass or Come with the maximum odds. The house advantage on this bet combination is a paltry 0.374%. But just what does that mean?

In a recent article Al Krigman reported that his preferred poet, Sumner A Ingmark mused:

What statistics say you should expect May well be technically correct, But the figures offer little grace Applied to any single case.

Put less poetically, individual bets win or lose in their entirety, but after many, many resolutions the bosses expect to win very close to a calculable percentage of the total amount wagered. This percentage is the house advantage. It is a long-term parameter. If you put $29 on Pass and take $145 (5x) odds on a point of 8, the bean counters figure the house has made $0.65076 ((29+145)*.00374) even though you will either win $203 (and the TV of your dreams) or lose $174.

Is Pass/Come with maximum odds really the best bet on a 3x/4x/5x odds craps table? As a strategy for a session of reasonable duration (e.g., a couple hours), yes. You are expected to lose, of course, but the house advantage is so low that you need only a little bit of good luck (officially known as positive variance) to come out ahead. But you are not going to play for another two hours; you are making only one more bet. Consequently, a low house advantage is not what you seek; a high probability of winning is.

It should come as no surprise that a bet's probability of winning is inversely proportional to its payoff. (English translation: bets with better chances to win have lower payoffs than bets with lesser chances to win.) A prop bet on 2 or 12 has a 2.78% chance of winning and pays 30:1 in most places. An Any 7 bet has a 16.7% chance of winning and pays 4:1. A Field bet has a 44.4% chance of winning and pays a little better than even money on average. Pass/Come bets have about a 49.3% chance of winning and pay even money. A lay bet against 4 or 10 has a 66.7% chance of winning and pays 1:2.

Hold it! What was that last one? A bet that wins twice as often as it loses?

That's right, a no-4 or no-10 lay (a bet that a 7 will be rolled before the number laid is rolled) offers the best chance to win a single bet. The catch is that you must risk losing twice as much as you will win. In addition, because the bet pays the true odds of winning (1:2 payoff for a 2:1 chance to win) the house charges a fee, known as vigorish, of 5% of the win. Some houses charge this fee up front and keep it whether the bet wins or loses for a house advantage of 2.44%; others charge it only if the bet wins for a house advantage of 1.67%. Both of these figures, while not exorbitant, are greater than the 0.374% house advantage on Pass/Come with 3x/4x/5x odds, which means that lays are expected to lose more than Pass/Come with odds during a session of reasonable duration. You, however, are looking to win $200 with a single bet. Consequently, in this atypical situation the best bet on the table is to lay $400 (plus vigorish) no-4 or no-10. Oh, and by the way, you'll still be a winner for the trip even if Santa forgets your TV.