Is Cleverness at Craps Good, Bad, or Indifferent?

They do it for a host of reasons, but one thing's for sure. Solid citizens can't combine or sequence wagers in a negative expectation game to surmount house advantage. A few techniques trim the edge, but none obliterate or negate it. And, although it's possible to raise the return for a hit or to lock up a win after surviving the high risk phase of a multi-stage wager, these ploys invariably impose hidden costs on credulous hopefuls.

Sizing "Buy" bets illustrates how sophisticated players can, in fact, reduce the edge. Buying a number involves paying a "vigorish" or "vig" equal to 5 percent of the amount bet, rounded down to the nearest whole dollar, in advance. If the number hits, the house keeps the vigorish but players recover their bets along with winnings precisely proportioned to the odds overcome.

Because it's rounded down, the vig is $1 on bets from $20 through $39, $2 from $40 through $59, $3 from $60 through $79, and so on. Buy bets just below the level where vigorish jumps by a buck therefore minimize the house's "take" relative to the action.

Here's how being clever after paying your dues during a risky step guarantees a win or push, but lowers ultimate profit expectation in the process. Say you bet $12 Don't Pass. The come?out has three ways to win $12 (a two or three) and eight ways to lose $12 (a seven or 11) - that 8-to-3 exposure is the high-risk part; there's also one way to push (a 12) and 24 ways to get the $12 behind a number (a four, five, six, eight, nine, or 10). Whenever you do get behind a number, simultaneously place it for $12 if it's a six or eight and for $10 otherwise.

Now what happens? On a seven-out, you win the $12 behind the number and lose the Place bet. This pushes on points of six or eight and nets $2 on everything else. On a pass, you lose the $12 behind the number and pick up $18 from the Place bet when the point was four or 10 (netting $6) and $14 when it was five, six, eight, or nine (netting $2).

To appreciate the price of this prestidigitation, consider how many ways each bet can be resolved and what's won or lost. On four or 10, with Don't Pass alone, you anticipate six $12 wins (ways to roll a seven) for every three $12 losses (ways to roll the number), so expectation is to earn $12x6 minus $12x3 ($36 net) in nine statistically-correct tries. With the guarantee, profit on a four or 10 would be $2x6 plus $6x3 ($30 net). On five or nine, the figures are six ways to win $12 minus four ways to lose $12 ($24 net) playing plainly, versus six ways to win $2 on a seven and four ways to win $2 on the number ($20 net) betting Baroquely. And on six or eight, they're six ways to win $12 minus five ways to lose $12 ($12 net), versus six ways to push and five ways to win $2 ($10 net). The inventive guarantee always lowers expectation, the offset adding to the house advantage.

As a final example, think about betting $3 "any craps." There are four ways to win $21 (a two, three, or 12) and 32 to lose $3. Instead, some sharpies bet the $3 on "three-way craps." This is $1 each on the two, three, and 12. Now there are two ways to net $28 (a two or 12) and two ways to net $13 (a three), still with 32 ways to lose $3. The appeal to those who like this bet is the extra $7 on the two or 12. But dope out the expectation for 36 rolls. On $3 any craps, it's four wins at $21 minus 32 losses at $3 each - $84 minus $96 ($12 net loss). On $3 three-way craps, expectation is two wins at $28, two wins at $13, and 32 losses at $3 each - $56 plus $26 minus $96 ($14 net loss).

Admittedly, a statistically aberrant bounce or two of the dice during a game of nominal duration can abrogate gains achieved by shaving edge or quash penalties for giving the devil more than its due. So, where's the real help or harm in fancy footwork? More in the mind than the pocket. As the acclaimed author of ageless amphigory, Sumner A Ingmark, artfully articulated:

Anyone can win or lose, but those whose play is efficacious,
Merit credit for good news, and find the adverse less vexatious.