'Lay' Bets Get the Odds on Your Side at Craps

An easy way to get favorable odds of winning each and every casino bet you make is to 'lay' a number at craps. No confusing combinations of bets or hedges are crucial to the concept; in fact, multiple lay bets shift the odds back to the bosses. And while sequences of progressive wagers can enhance your chance of winning, doing so is neither required nor recommended.

Lay bets are wagers that a seven will roll before the number behind which you have your money. The dice have six ways to total seven. Compare this with five ways each for six or eight, four ways each for five or nine, and three ways each for four or 10. These figures are the basis of how much you're favored to win.
o Six or eight: odds are 6-to-5 in your favor; probabilities are 54.55 percent you'll win, 45.45 percent you'll lose.
o Five or nine: odds are 6-to-4 in your favor; probabilities are 60 percent you'll win, 40 percent you'll lose.
o Four or 10: odds are 6-to-3 in your favor; probabilities are 66.67 percent you'll win, 33.33 percent you'll lose.

Sound too good to be true? Well, it is the truth. But not the whole truth. There's a downside.

Lay bets don't pay even money. A $60 "no-four" doesn't get you 6-to-3 odds of winning $60. Payoffs are inverse to the odds. Lay $60 on four or 10 to win $30. Likewise, lay $60 to get $40 on five or nine at 6-to-4 and to get $50 on six or eight at 6-to-5.

Almost. These payoffs, precisely inverse to odds of winning, would leave the casinos no edge. There'd be no money to pay staff, investors, or creditors. No money to "comp" solid citizens to tasty meals or tasteless merchandise. So casinos collect an advance commission - the vigorish or vig - equal to 5 percent of the projected payoff, and keep this whether you win or lose.

The vig works like this. To "win" $20 by laying the six or eight, give the dealer $25 - $24 at a 5-to-6 payoff and 5 percent of $20 or $1 vig. Lose and the house keeps the $25. Win and you collect $20, getting back your $24 but not the $1 vigorish. So, winners start with $25 and end with $44 - $19 net profit. A fair bet would have paid 20/24 or 83.3 percent of the outlay, not 19/25 or 76 percent. To "win" $20 on five or nine, give the dealer $31 and end with $50 - $19 net. And to "win" $20 on four or 10, give the dealer $41 and finish with $60 - $19 profit.

Combining lay bets shifts odds toward the house. See this by comparing $62 behind the five with $31 each behind the five and the nine. With the one bet in action, each roll of the dice offers 6-to-4 odds of $38 profit versus $62 loss. With the two bets, each roll still offers six ways to pocket $38 but eight ways to lose $31. So the odds of winning favor the house by 8-to-6 rather than you by 6-to-4. In compensation, the relative sizes of the payoffs are reversed. The favorable single bet pits $62 to win $38 on each roll; the adverse dual bet risks $31 to win $38 each time.

Betting progressions can enhance the probability you'll make a profit. However, using this method with lay bets requires a large bankroll. And the higher you pump your chances, the more of a disaster you face if all goes awry.

Want an example? Consider a three-bet sequence as a "round." Start with $41 "no four." End the round if you win; you'll have $19 profit. On a loss, lay $123 "no four." End the round if you win; your net will be $16 - $57 on this roll minus the $41 lost the first time. After a second loss, lay $369 "no four." Now a win yields $7 - $171 on this round minus $123 and $41 from previous losses. For every thousand players who try this, the laws of probability say a whopping 963 will win $7, $16, or $19 while a mere 37 will lose a gut-wrenching $533. But those losers, rare as they may be, will surely wonder whether $533 was wisely spent for a shot at $7 to $19. Worse, they'll doubtless curse not heeding this verse by the immortal and terse Sumner A Ingmark:

Chasing losses, a player who'd otherwise quit'll,
Oft rue betting a bundle to win just a little.