When Do Put Bets at Craps Beat Their Place and Buy Counterparts?

Some casinos let players make "Put" bets at craps. These wagers look like Pass or Come bets, with "flat" parts returning 1-to-1 and "odds" components paying in inverse proportion to chances of winning. However, the flat money doesn't get to a number via the come-out roll with the odds added after the point is established. Players drop the entire amount on anything they want from four through six or eight through 10. Essentially, Puts are surrogate Place or Buy bets which offer benefits under some circumstances.

As far as likelihood of winning or losing on a particular number is concerned, Put bets are identical to their Place and Buy counterparts. Either way, the odds against winning are 6-to-5 on sixes and eights, 6-to-4 (3-to-2) on fives and nines, and 6-to-3 (2-to-1) on fours and 10s. The differences are in the payoffs.

To picture the idea, make believe you want to risk a total of $30 on your favorite number. Place the six or eight in the ordinary way for $30 and you're up to win $35. Place the five or nine for $30 and you're going for $42. You could Place the four or 10 for $30 trying to win $54, but any experienced dice devotee would make a $29 buy bet and pay the $1 vigorish in the hope of netting $57 (collect $58 but subtract the unreturned $1 vigorish).

Instead, say you made a Put bet of $10 flat plus 2X odds of $20. On the six or eight, you'd collect $10 on the flat portion and $24 on the odds for a total of $34. On the five or nine, your net would be $10 on the flat part and $30 on the odds for a total of $40. And on the four or 10, you'd pick up $10 on the flat segment and $40 on the odds for a total of $50. But nobody would do this. None of these is as good as the conventional Place or Buy option.

What if you were at a table with a $5 minimum and the casino offered quintuple (5X) odds? Your $30 total in Put bets could then be $5 flat and $25 odds. Now, consider what happens.

The six or eight would pay $5 on the flat plus $30 on the odds for a total of $35. Allocating $5 plus $25 wouldn't quite work on the five and nine because the casinos require odds to be exactly divisible by two, so payoffs can be in whole dollars. But pretend they have a weak moment and book this bet. The payoff would be $5 on the flat and $37.50 on the odds for a total of $42.50. And on a four or 10, the profit would be $5 plus $50 or $55 in all.

You can see the trend. On six and eight, as the odds portion of the bet relative to the flat money rose from 2X to 5X, Put bets went from worse than to the same as Place bets. On five and nine, going from 2X to 5X made the Put bets superior to Place bets. And on four and 10, the change from 2X to 5X made Putting better than Placing and closer to Buying. High odds multiples are the key.

Crossover odds multiples, above which Put bets return more than Place wagers for the same total at risk, are as follows. It's 5X on six and eight, and 4X on four, five, nine, and 10.

Comparing Puts and Buys on the four and 10 gets complicated because vigorish, unlike edge, isn't simply a fraction of the wager. It's 5 percent of the expected payoff, rounded down to the next lower whole dollar. For total outlays (the bets plus the vigorish) equal to or under $40, the crossover odds multiple is the outlay minus $3 divided by 3. This yields 12X odds for $38 bets with $1 vigorish. The equivalent Put, were it allowed, would be $3 with $36 odds. Both net $75. Betting $20 with $1 vigorish, the crossover is at (21-3)/6, which comes to 6X odds; again, were it allowed, this would be $3 flat with $18 odds. Both net $39.

In case you're thinking of Put bets as substitutes for money on Pass or Come, forgeddaboudit. You'd lose the 8-to-4 advantage on the flat wager during the come-out roll, yet end up in the same position after the point is established. And it's the 8-to-4 hammer "right bettors" at craps hold over the casino, albeit for only the first roll of the cycle, that distinguishes them from solid citizens who plunk their dough down at the carnival games earning the really big bucks for the bosses. Here's how the beloved bard, Sumner A Ingmark, regarded this type of trade-off:

Don't sacrifice the best of it,
While paying for the rest of it.