Free odds: the only bet in the casino with no house edge

Every bet on a craps layout pays you a little less than the true chance of winning, except one. The odds bet pays exactly what the dice say it should. Here is why that's true, how much you can bet, and the one thing odds can't do.

What a fair bet looks like

Two dice land 36 ways. Three of them make a 4 (1-3, 2-2, 3-1). Six make a 7. Once a point of 4 is set, nothing but those two numbers matters, so you're looking at 3 winning combinations against 6 losing ones. You lose twice as often as you win. A perfectly fair bet on the 4 would therefore pay 2 to 1: bet $10, win $20. Over 9 hands you'd win 3 of them for $60 and lose 6 of them for $60. Net zero.

Now look at what the layout offers on that same 4. A place bet pays 9 to 5, which is $18 on a $10 bet. Over those same 9 hands you'd win $54 and lose $60. That $6 shortfall over $90 wagered is the 6.67% house edge. The hard 4 pays 7 to 1 on a bet that should pay 8 to 1. The casino makes its money by paying just under fair.

The free odds bet is the exception. It pays 2 to 1 on the 4 and 10, 3 to 2 on the 5 and 9, and 6 to 5 on the 6 and 8. Check each one against the dice:

They match exactly. The expected value of the odds bet is zero: not a small negative number, zero. That's what “no house edge” means, and it's why the bet has no printed box on the layout. There's nothing in it for the casino to advertise.

Why the casino allows it

Because you can only make the bet if you've already made one that isn't free. Odds go behind a pass line bet, a come bet, a don't pass or don't come. Those flat bets carry their 1.41% or 1.36%, and the odds bet is capped at a multiple of them. The casino already has its edge on your flat bet; the odds are a sweetener that keeps you betting the line hand after hand. It's a good deal for you as long as you understand which part is free and which part isn't.

3-4-5x explained

How much odds you can take is set by the table, always as a multiple of your flat bet. Some tables offer single odds (1x); some advertise 10x, 20x, even 100x. The Las Vegas standard, and what PointPuck uses, is 3-4-5x:

• Behind a point of 4 or 10: up to 3 times the flat bet.
• Behind a point of 5 or 9: up to 4 times the flat bet.
• Behind a point of 6 or 8: up to 5 times the flat bet.

Why the different multiples? Multiply each one by its payout. 3x at 2 to 1 wins 6x. 4x at 3 to 2 wins 6x. 5x at 6 to 5 wins 6x. Full odds win exactly six times your flat bet on every point. With $10 on the line, a winning point always pays $60 in odds plus $10 on the flat, $70 total, whether the point was 4 or 8. Dealers love it because there's one number to remember.

The rule also scales your exposure with your chances. Behind a 6 or 8 you're allowed the most money, where you're most likely to win. Behind a 4 or 10 you're allowed the least, where you're least likely to.

Odds shrink the edge, not the loss

Here's the honest part. The odds bet has no edge, but it doesn't give you an edge either, and it doesn't reduce the edge on your flat bet. What it does is dilute it. If $10 of your money faces 1.41% and $50 of your money faces 0%, the blend on that hand faces about 0.24%. Averaged over every hand, including the ones that end on the comeout before you can take odds at all, the published combined figures for the pass line are:

Read the last column. Your expected loss in dollars is the same in every row. A $10 pass line bet costs you about 14 cents per hand and nothing you stack behind it changes that. The percentage falls only because you're dividing the same 14 cents by more money. Odds don't make you a favorite. They don't make you break even. They make the game nearly free per dollar of action, which is a very different and much more honest claim.

So why take them? Because if you're going to bet $60 a hand anyway, $10 flat plus $50 odds costs 14 cents per hand while $60 flat costs 85 cents. Same action, one-sixth the price.

Less flat, more odds

That last point is the single most useful idea in craps strategy. The house edge lives in the flat bet, so make the flat bet as small as the table allows and put the rest behind it.

Compare two players who each want about $60 on a point of 6:

Player B risks the same $60, wins more when the 6 hits, and pays a sixth of the rake. The only thing Player A gets in return is a bigger comeout win on a 7 or 11, and a bigger comeout loss on a 2, 3, or 12 to go with it. The math isn't close.

At a real casino the table minimum sets your floor, so a $10 table means a $10 flat bet at least. On PointPuck the minimum is $1, so you can run $5 flat with $25 behind it and see what a low-rake game feels like.

Table maximums and how odds fit

Every table posts a minimum and a maximum flat bet, plus the odds multiple. The odds cap is a multiple of your flat bet, not a share of the table maximum, so a $10 bet at a 3-4-5x table can have $50 behind it regardless of what the table max says. Most casinos treat the two limits separately; if a big bet would push against a posted max, ask the dealer before you stack it. The same 3-4-5x cap applies behind come bets. On the don't side you lay odds instead of taking them, laying more to win less at the same true ratios, and the cap is set so you can win up to 6 times your flat bet.

Two housekeeping rules keep the payouts whole. On a 5 or 9, bet odds in even dollars, since 3 to 2 on an odd number leaves half a dollar and payouts floor to the whole dollar. On a 6 or 8, bet in multiples of $5, since 6 to 5 on $12 pays $14 and swallows the change. On a 4 or 10, anything works. A $10 flat bet with $30, $40, or $50 behind it never runs into trouble.

Odds are never a contract

Unlike the flat pass line bet, which locks once the point is set, odds can be added, cut, or pulled at any time before the point resolves. There's no penalty, because the bet has no edge either way. One rule to remember: odds behind a come bet sit OFF on a comeout roll by default. Details in working on the comeout.

What odds can't do

Every craps myth eventually arrives at the odds bet and tries to make it more than it is. Odds can't turn a losing bet into a winning one, can't beat the house, and can't recover a bad session. The flat bet loses 1.41% forever and no multiple of a zero-edge bet changes that. If someone tells you their odds system wins long-term, they're describing luck.

What odds can do is make craps the cheapest game in the casino to play well. A pass line player with full 3-4-5x odds is giving up 0.37% of the money in play. Very few games anywhere in the building come close, and none of them are as simple to play correctly. That's the real claim, and it's enough.