The best craps strategy, mathematically

The answer is short: bet the don't pass or the pass line, take maximum free odds behind it, and make no other bets. Below is why that's correct, what it costs in dollars, and how fast it stops being correct when you add anything to it.

What “best” can and can't mean

No craps strategy has a positive expectation. Every bet on the layout except the free odds pays less than the true chance of winning, so the expected value of any combination of them is negative. No bet order, bet size, or progression turns a stack of negative numbers into a positive one.

So “best” means something narrower. The best strategy is the one that loses the least per dollar you wager, and by extension the least per hour you play. That is measurable, and the gap is large: about 27 cents per $100 of action at the top of the list, $16.67 at the bottom. Sixty times the cost, same game, same dice.

It also cannot mean “most likely to end the night up.” One $100 bet on any seven has a better chance of doubling your money in a single roll than a careful night of line bets does. If a short shot at a big number is the goal, none of this describes what you want.

The ranked answer, with real numbers

These are edges per bet resolved — expected loss each time the bet wins or loses. Keep comparisons on one basis or the numbers stop meaning anything. Full list: house edge on every craps bet.

Notice how fast it degrades. The top two entries are in a different category from everything under them, and the reason is one bet.

Why odds are the whole trick

The free odds bet is the only wager in the casino that pays exactly what it should. A 4 hits 3 ways against the 7's 6 ways, so true odds are 2 to 1, and odds behind the 4 pay 2 to 1. A 6 hits 5 ways against 6, and odds pay 6 to 5. Zero edge. Not small — zero.

You cannot bet it alone. It only exists behind a pass, come, don't pass, or don't come bet, and it is capped. Here and at most Las Vegas tables the cap is 3-4-5x: 3x behind the 4 or 10, 4x behind the 5 or 9, 5x behind the 6 or 8 — arranged so maximum odds always win 6x your flat bet.

That creates the most useful lever in the game. The 1.41% edge on the pass line is charged on the flat bet only; the odds ride along free. So the way to lower your average cost is not to bet less — it is to move money out of the flat bet and into the odds.

The $60 comparison

Say you're willing to risk $60 on a hand. Two ways to deploy it.

Version A: $60 on the pass line, no odds. Every time that bet resolves you expect to lose $60 × 1.41% = 84.6 cents.

Version B: $10 on the pass line, then up to $50 in odds behind the point. With 3-4-5x on a $10 line that's $30 behind a 4 or 10, $40 behind a 5 or 9, $50 behind a 6 or 8 — about $41.67 in odds on average whenever a point is set, and roughly $37.78 of total action per decision once you count comeouts that resolve before odds go up. Expected loss per decision: $10 × 1.41% = 14.1 cents. The odds add nothing to it, because their edge is zero.

Same $60 of exposure, same game, one sixth of the cost. The ratio is exactly 6 because you cut the flat bet from $60 to $10, and the flat bet is the only part the house charges for.

The same move on the other side is cheaper still: a $10 don't pass with full lay odds costs $10 × 1.36% = 13.6 cents per decision, blending to about 0.27% of total action. That is the cheapest complete strategy in the casino, full stop.

This is the highest-leverage change most players can make, and it costs nothing to make. If you bet $25 on the line with no odds, you pay 35 cents a hand. Drop to $5 flat with full odds behind it and you pay 7 cents, with more money working, not less.

What “just one more bet” actually costs

Here is the part that undoes people. You've built a 0.37% game, then you toss a dollar to the stickman every roll because it feels cheap.

A pass line decision takes about 3.4 rolls on average. A $1 any seven on every roll is about $3.40 wagered at 16.67%, or 57 cents of expected loss — on top of your 14 cents. The hand now costs 71 cents instead of 14, and against total action your 0.37% game just became about 1.7%. One dollar did that.

Softer version: a $5 field bet every roll. About $17 wagered per decision at 2.78%, or 47 cents. Your 14 cents becomes 61 cents and the blend goes from 0.37% to roughly 1.1% — tripled, by the tamest bet in the center of the layout.

The pattern is general: every bet you add raises your average edge, because nothing on the table is cheaper than the odds you're already taking. Even place bets on the 6 and 8 at 1.52% do it. Those are genuinely good bets on their own, and they still raise your blended cost when you bolt them onto a line-and-odds game.

Pace matters as much as bet selection

House edge is a rate. What you lose is that rate times the money that runs through it, so the number of decisions you face is half the equation.

Suppose your table produces 100 rolls in an hour, roughly 30 pass line decisions. At $10 flat with full odds you're paying about 30 × 14 cents = $4.20 an hour. The same player at $60 flat with no odds pays about $25 an hour. Add that $1 any seven on every roll and you've added 100 × 16.67 cents = $16.67 an hour, four times what your entire line-and-odds game costs.

Two consequences. A fast table costs more per hour than a slow one at identical bet sizes, and a solo online table is far faster than a crowded live one, so the same strategy has a different hourly price by venue. And sitting out a few comeouts is not weakness — money not wagered cannot be lost, the only genuinely free way to cut your expected loss. How much to put at risk in the first place is bankroll management.

Why no progression changes anything

Betting systems are the most persistent idea in gambling and the easiest to check. Expectation adds: a session's expected value is the sum of the expected values of its individual bets, every one of them negative. Rearranging the size or order of a list of negative numbers never produces a positive total.

Martingale — doubling after a loss — converts many small wins into rare enormous losses. Eight losses in a row starting at $10 needs a $2,560 bet to continue, which exceeds either the table maximum or your rail. The sequence ends somewhere, and where it ends you lose everything staked in it.

Pressing a winning place bet raises your average bet size, which raises your expected loss in dollars while leaving the percentage exactly where it was. Regression — $44 inside, then taking most of it down after one hit — does cut your expected loss, but not because it is clever: it cuts it because you wagered fewer dollars. Same mechanism as betting less.

What progressions genuinely change is variance: the shape of the swings, how often you finish a session up versus how badly you lose when you don't. That is a real thing to tune for. It is not an edge.

Best is not the same as most fun

The don't pass with full lay odds is the correct play and a fair number of people hate it. You spend a live session quietly rooting against the rail, and none of the noise of the game belongs to you. Pass with full odds and a come bet or two costs a whisker more and puts you on the table's side, which for most people is worth ten cents.

If you want a hardway for a dollar because you like the sweat, take it. Just price it honestly at about nine cents on the dollar, and keep it small and fixed. The failure mode isn't having fun — it's paying 3% for a game you could have had for 0.3% without noticing. For how these feel side by side, see the strategy comparison.

It all fits in one line: line bet, maximum odds, nothing else. Everything past that you're buying, not winning.