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Why don't more craps players make Lay bets? Or, do they?

2 January 2012

Lay bets are wagers having greater probability of winning than losing, but payoffs less than the amount at risk. Craps has two major classes of these propositions.

One class, available to players who bet Don’t Pass or Don’t Come, comprises the Odds they can lay after the point is established. The Odds are auxiliary wagers giving neither bettors nor bosses an edge. This, because payoffs are exactly inverse to the likelihood of winning – with no offset.

Don’t Pass and Don’t Come bets win on sevens and lose when their points appear. Points of four or 10 can succeed six ways and fail on three, so players have favorable 6-to-3 (2-to-1) shots with Odds paying $1 for every $2 at risk. Similarly, Odds behind a Don’t Pass or Don’t Come five or nine can soar six ways and plummet four, giving dice doyens 6-to-4 (3-to-2) prospects of winning and paying $2 for every $3 at risk. Don’t Pass or Don’t Come bets with points of six or eight have six paths to joy and five to sorrow so the Odds fork over $5 for every $6 up for grabs.

When laying Odds behind Don’t Pass or Don’t Come bets, the multiple offered at the table applies to the payoff rather than the amount wagered. As examples, say you bet $10 Don’t Pass at a table with 3-times Odds. The maximum you can lay as Odds is the amount that pays 3x$10 = $30. On a point of four or 10, this is $60 since the payoff is 1-to-2. On a five or nine, you can lay $45 because a win pays at 2-to-3. And on a six or eight, you can lay $36 to collect $30 at 5-to-6.

The other class of craps Lay bets comprises wagers made directly against the numbers. They are sometimes called “No” bets, as in “$40 No 10," and are the opposites of Buy bets. Payoffs, like those on Odds behind Don’t Pass and Don’t Come wagers, are inverse to the chances of winning. Moreover, they must be at least enough to pay $20 – that is, $40 on four or $10, $30 on five or nine, and $24 on six or eight – even if the nominal table minimum is less.

While the house doesn’t have an edge on the Odds against Don’t Pass and Don’t Come wagers, it does has an advantage on direct bets. For this purpose, the casino charges a “vigorish” or “vig” when the bet is made, and keeps this juice whether you swim or sink. The vig equals 5 percent the projected payoff, rounded down to the nearest whole dollar.

To picture how the vig works, make believe you want to make a Lay bet against the five to win $30. The bet would be $45. You drop the dealer $46, the excess being 5 percent of $30 ($1.50) rounded down to $1. The dealer locks up the $1 and positions your $45 on the layout. A loss puts you down by $46. On a win, your $45 is returned along with a $30 payoff – $75 total. You started with $46 and finished with $75. Your net profit on the $46 outlay is $75 - $46 = $29.

Neither of these two types of craps wagers is especially common. The primary reason is that solid citizens typically don’t conceptualize frequencies of wins and losses very well, but clearly perceive the shortfalls of betting more than they’re positioned to gain in any particular situation. Further, in the case of “No” bets, individuals accustomed to a $5 or $10 exposure on a single proposition are often uncomfortable having to plunk down a minimum of $24, $30, or $40.

Most craps aficionados, however, don’t realize that the popular practice of covering several numbers with Pass and Place wagers is a form of Lay betting. An extreme case might be a bet on “$32 Across.” This is an amalgam of six separate Place bets – $5 each on the four, five, nine, and 10 along with $6 each on the six and eight. Players have six ways to win $9 (four or 10 hit) and 18 ways to win $7 (five, six, eight, or nine show). They have six ways to lose $32 (seven pops). Chances are accordingly 24-to-6 (4-to-1) they’ll win either $9 or $7 for $32 at risk.

As regards house advantage, for a $41 outlay including the vig, the edge on a No Four or No 10 is ((6/9)x19 - (3/9)x41)/41 = -2.439 percent. For a $31 outlay on a No Five or No Nine, it’s ((6/10)x19 - (4/10)x31)/31 = -3.226 percent. And for a $25 outlay on No Six or No Eight, it’s ((6/11)x19 - (5/11)x25)/25 = -4.000 percent. In contrast, edge on $32 Across is ((6/30)x9 + (18/30)x7 - (6/30)x32)/32 = -1.25 percent. The $32 Across looks better than any of the No bets.

But wait, there’s more. Enquiring minds want to know how house advantage translates into moolah moved from their racks to the casino coffers when decision rate is taken into account. Consider 36 statistically correct throws. No Four or No 10 will pick up 6x$19 and give up 3x$41 for $9 net loss, No Five or No Nine will reap 6x$19 and forfeit 4x$31 for $10 setback, and No Six or No Eight will win 6x$19 and lose 5x$25 for an $11 reversal. The $32 Across bet will win 6x$9 + 18x$7 and lose 6x$32 for $12 net loss. On this basis, the No bets are all more attractive than $32 Across. The punters’ poet, Sumner A Ingmark, may have had it right when he wrote:

The math may help you understand,
But money’s what the shops demand.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.