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Best of Alan Krigman
Betting "$32 across" in craps6 December 2010
How does this bet stack up against a similar amount on any of the numbers individually?
A qualitative comparison might involve the intensity of the action. With $32 across, you average 30 decisions in 36 throws. That's 24 chances to win $6 or $7 and six to lose $32; the other six out of 36 are pushes. In contrast, buying the four or 10 for $31 (plus $1 vig), you average three $61 net wins, six $32 losses, and 27 pushes in 36 throws. Placing the five or nine for $30, you expect four $42 payoffs, six $30 letdowns, and 26 pushes in 36 throws. And a $30 six or eight theoretically yields five $35 victories, six $30 defeats, and 25 pushes in 36 throws. Frequent small earnings on $32 may be less exciting than occasional big scores on the single Buy and Place alternatives, but the suspense associated with the money at risk is roughly the same.
A more mathematical comparison would start with the edge on the bets. For $32 across, ignoring pushes, prospects are 6/30 to win $9, 18/30 to win $7, and 6/30 to lose $32 So edge equals ((6/30) x $9 + (18/30) x $7 - (6/30) x $32)/$32 or -1.25 percent, the minus sign showing the house is favored. Nominal edge on the separate numbers is higher: -1.52, -4.00, and -3.12 percent Placing sixes or eights and fives or nines, and Buying fours or 10s at the $31 level, respectively
A second mathematical factor is the volatility of the bets. This is commonly measured by a quantity the math mavens call "standard deviation," loosely pictured as the characteristic size of bankroll jumps. The one-round standard deviation for $32 across is $15.82. It's $43.84 Buying the four or 10 for $31, $35.27 Placing the five or nine for $30, and $32.36 Placing the six or eight for $30. Typical swings in fortune are two to three times smaller but correspondingly more frequent with $32 across than with like amounts on the individual numbers.
Edge and volatility are the stock-in-trade for the gurus. Normal players typically care more about their chances of reaching levels at which they tell themselves they'll quit (but rarely do) before they exhaust their stakes. Pretend you start with $500 and are determined to double your money or go belly-up, regardless of how long it takes either way. With $32 across, you've got almost 17 percent chance of success. Betting $30 on the five, as one example, the probability you'll succeed is just over 24 percent. The better shot follows from the larger payoffs on the individual bets.
Another practical criterion is the likelihood your bankroll will buy you a satisfactory amount of playing time. Make believe you want at least three hours. That would be about 270 throws in a well-paced game. Betting $32 across, you'd average 225 win-or-lose decisions, and would have nearly 93 percent chance of being in action this long. Placing the five for $30, 270 throws would result in an average of 75 decisions and about 84 percent chance of at least three hours' action.
You needn't go whole hog with $32 across, of course. Some players bet on Pass then Place all the numbers except the point for a total of $27 or $26 as the case may be. An even more common strategy is to bet on Pass, then Place two additional numbers for another $10, $11, or $12 total depending on the choices. You can infer the tendency for these wagers to impact the probabilities associated with the game by extrapolating the data presented for $32 across.
Craps purists would argue that the "best" way to cover multiple numbers at craps is with a wager on Pass followed by a series of Come bets. This will, in fact, minimize the house advantage – a strategy which is certainly commendable. Depending on the Odds multiple taken, adverse edge can drop below half a percent. The downside of high Odds is that you can have big bucks at risk, vulnerable to being lost in one fell swoop on the appearance of a seven – $5 flat with 10X odds on three numbers puts $165 at the mercy of some bozo who doesn't know how to shoot the dice right. If this approach leads you to overbet your bankroll, you can still make out like a bandit. Or you can be relegated to the showers before you've buttered up the pit boss for a decent comp.
Another danger of Pass and Come bets with high Odds is that you can do too well too fast. Many are the solid citizens who earned what otherwise would have made them ecstatic – only to continue because they figured they were on a roll. And... well... you know the rest of the story. As that canny composer of casino cantos, Sumner A Ingmark, lyrically lamented:
It seemed like I could do no wrong,
But Lady Luck did not portend,
A hint my streak had reached its end.
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