Making Line Bets with Odds after the Come-out Roll

Occasionally, casinos let players make line bets with odds after points are established. Some casinos book comparable wagers in lieu of come bets on any boxes players want. Payouts are the same as on true line and come bets. A difference is that flat as well as odds money isn't on "contract" and can be taken down at will.

How do these wagers fare, relative to regular place bets?

Conventional Conrad places $12 to collect $14 on six or eight, $10 to collect $14 on five or nine, and $10 to collect $18 on four or 10. Unorthodox Undine makes line-type bets on the same numbers. Her wins and losses exactly match Conrad's when she bets $2 flat with $10 odds to collect $2+$12=$14 on six or eight, $2 flat with $8 odds to collect $2+$12=$14 on five or nine, and $2 flat with $8 odds to collect $2+$16=$18 on four or 10.

For equivalent totals, if Undine put proportionately less than the indicated amounts on the flat part of the wager with more on the odds, she'd do better than Conrad. Conversely, with more flat and less odds, she'd do worse. So, for post-point line betting to outperform placing, the odds must exceed quintuple the flat wager on six or eight and be over quadruple it on other numbers.

Here's an example of how greater or lesser odds multiples help or hurt. Say Conrad places the nine for $25 to collect $35; in 36 statistically-correct hands he'd win $35 four times - $140, and lose $25 six times - $150, a net $10 loss. If Undine bets $1 flat and takes 24-times odds, she's up to collect $1+$36=$37; in 36 statistically-correct hands she'd win $37 four times - $148, and lose $25 six times - $150, net loss therefore drops to $2. If, however, Undine bets $7 flat and $18 in back, less than triple odds, she's up to collect $7+$27=$34; in 36 statistically-correct hands, she'd win $34 four times - $136, and lose $25 six times - $150, a net $14 loss.

Dedicated dice doyens know they give the casinos less edge betting line and come, even without odds, than placing numbers. So why are quintuple odds on the six and eight and quadruple odds on everything else determining factors for this wager?

The answer lies in the discrepancies between the payouts and the likelihood of scoring on each number. The chances are 6-to-5 against winning on six or eight, 6-to-4 on five or nine, and 6-to-3 on four or 10. Place bets compensate for the stretch by paying 7-to-6, 7-to-5, and 9-to-5, respectively. With true line and come bets, the adverse chances are offset by solid citizens' being favored during the come-out roll, having eight ways to win even money versus four to lose. Bypassing the come-out and making a flat bet with odds directly on a number sacrifices this 8-to-4 one-shot advantage. The high odds multiple, with a payout which exactly counterbalances the chances against winning, is then necessary to overcome the 1-to-1 return on the flat bet.

So, who's snookering whom with line-type bets after the come-out? Take over five-times odds on the six or eight or over four-times odds on the other boxes, and you'll do better than you would with place bets. Take less and you'll do worse.

Before trying these bets, consider two other factors. 1) If minimum edge is your main concern, you'll do best going through the come-out roll at any level of odds. 2) If amount at risk is your limitation, post-point line and come betting may require too much money to get lower edge than placing the same numbers.

One of the fascinating things about craps is the variety of ways you can bet on how two little dice will land. Yet, with all the options, there's no way to totally eliminate the house edge. It's as Sumner A Ingmark, the shooter's Shakespeare, once warned:

Many a gambler's taken a bath,
Learned how to bear numerical wrath,
Betting against the tenets of math.