Craps Odds: The Cheapest Bets and the Sucker Bets

By · author of the MIT-licensed teachersbettextbook library ·

Same table, same dice: one bet costs 1.4 cents on the dollar, another nearly 17. The craps house edge is a menu, and most players order badly. Read the odds and a designed-to-lose game becomes one of the slowest bleeds on the floor.

How to read this game

Every craps bet is priced by its expected value: multiply each outcome by its probability, add them up. The craps house edge is the negative of that number.

House edge=− EV=− ⁣∑ipi⋅(payouti)\text{House edge} = -\,\text{EV} = -\!\sum_i p_i \cdot (\text{payout}_i)

Unlike roulette or slots, where every bet carries the same tax, craps offers dozens of bets with edges from about 1.41%1.41\% to 16.67%16.67\%. Picking the cheap ones decides whether you lose slowly or get fleeced. Ten times the difference. Bet selection is the whole game.

The cheapest bet on the table: the pass line

The pass line: win on a come-out 7 or 11, lose on 2, 3, or 12, otherwise a “point” is set that must repeat before a 7 shows. Enumerate every way the dice can fall and the pass line wins 244244 times out of every 495495.[1]

Worked example: the pass line house edge
P(win)=244495≈49.29%,P(lose)=251495P(\text{win}) = \frac{244}{495} \approx 49.29\%, \qquad P(\text{lose}) = \frac{251}{495}
EV=244495(+1)+251495(−1)=244−251495=−7495\text{EV} = \frac{244}{495}(+1) + \frac{251}{495}(-1) = \frac{244 - 251}{495} = -\frac{7}{495}
−7495≈−0.0141  ⇒  1.41% house edge-\frac{7}{495} \approx -0.0141 \;\Rightarrow\; \textbf{1.41\% house edge}
Even money on a bet you win 49.29% of the time: the missing 0.71% is the whole tax. Its mirror, don’t pass, is a hair cheaper at about 1.36%1.36\% (the tie on 12 keeps the house ahead).

The secret weapon: free odds

Once a point is set, you can put an extra bet behind your pass line: free odds, paid at true mathematical odds. House edge: exactly zero.

Free odds: payout=true odds  ⇒  EV=0,house edge=0%\text{Free odds: payout} = \text{true odds} \;\Rightarrow\; \text{EV} = 0,\quad \text{house edge} = 0\%

A 0% bet doesn’t lower your pass-line edge in dollars. That 7/4957/495 stays. It grows the total in action at fair odds, dragging the blended edge toward zero. The more odds allowed, the closer to fair.

Worked example: 3-4-5x odds crush the blended edge
Flat bet $10: expected loss=$10×1.41%=$0.141\text{Flat bet } \$10:\ \text{expected loss} = \$10 \times 1.41\% = \$0.141
Add ∼ ⁣$40 of free odds (0% edge): expected loss unchanged=$0.141\text{Add } \sim\!\$40\text{ of free odds (0\% edge)}:\ \text{expected loss unchanged} = \$0.141
Blended edge=$0.141$10+$40≈0.28%  ≪  1.41%\text{Blended edge} = \frac{\$0.141}{\$10 + \$40} \approx 0.28\% \;\ll\; 1.41\%
Same expected loss, spread over five times the money at risk. A pass line with full 3-4-5x odds runs an effective edge well under 1%1\%, the cheapest sustained action in the casino.

The traps in the middle of the table

The center-of-the-layout props (exciting names, big payouts) exist to pay for the free drinks. The star: “Any 7”, a one-roll bet that the next toss is a seven, paying 44 to 11. Sounds generous. It isn’t.

Worked example: why “Any 7” is a 16.67% robbery
P(7)=636,true odds=5 to 1,it pays only 4 to 1P(7) = \frac{6}{36},\qquad \text{true odds} = 5\text{ to }1,\qquad \text{it pays only } 4\text{ to }1
EV=636(+4)+3036(−1)=24−3036=−636\text{EV} = \frac{6}{36}(+4) + \frac{30}{36}(-1) = \frac{24 - 30}{36} = -\frac{6}{36}
−636≈−0.1667  ⇒  16.67% house edge-\frac{6}{36} \approx -0.1667 \;\Rightarrow\; \textbf{16.67\% house edge}
The dice are fair: a 7 comes up 6 times in 36. The robbery is the payout: true odds 5 to 1, table pays 4 to 1, and that one-unit shortfall is the entire 16.67%. More than ten times the cost of the pass line, on the same felt.

“Any 7” is the worst, but any craps, the hardways, and the field are built the same way: a true probability paid at less than true odds. The thrill is priced in.

Why you still can’t beat craps long-term

The honest ceiling: going from “Any 7” to a pass line with full odds cuts your cost by more than 90%, but every craps bet has a negative expected value. No memory, no shrinking deck, no shifting edge the way blackjack has. Each roll is independent; each bet is a fixed tax.

Best available: pass line+full odds≈−0.3%  <  0\text{Best available: pass line} + \text{full odds} \approx -0.3\% \;<\; 0

Play long enough and the law of large numbers collects. No system (not the Martingale, not the Iron Cross, not pressing after wins) turns a bag of negative-EV bets positive; a sum of taxes is still a tax. Same math as the classic betting mistakes. Where a provable edge does exist is the sports side: +EV betting means finding a payout better than the true probability, the exact opposite of what “Any 7” does to you.

The summary

Craps is designed to lose, but how much is up to you. Pass line or don’t pass with full free odds: effective edge under 1%, about as fair as a casino gets. “Any 7” and the hardways: 10 to 16 times as much for the same dice.

The math doesn’t care how a bet feels, only what it pays versus what it should. Even the cheapest bet is a tax you can’t out-run. None of this is advice. It’s arithmetic on the paytable.

Learn +EV betting →Where a real, provable edge actually lives: against a mispriced line, not a fixed house paytable.

Price a sports line the same way with the expected value calculator, or open it in the live app.

Even the cheapest bet still bleeds

The pass line at −1.41%. Six players, flat $25, 1,000 rolls. The decline is gentle. It ends in the same place anyway. Now picture the “Any 7.”

Want more math?the Nerd Corner

Nerd Corner

Advanced material. Nothing above depends on it.

Where these numbers come from

Every edge here is exact. The 244/495, the 7/495, and the 6/36 are counts, not estimates. Re-derive each from two dice and patience, or see the standard reference.[1]

  1. Ethier, S. N. (2010). The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer. A full craps chapter: the game’s exact probabilities and house advantages, worked from first principles.

Check your understanding

Frequently asked questions

What is the house edge on the craps pass line?

The pass line wins with probability 244/495 (about 49.29%) and pays even money, giving a house edge of 7/495, or about 1.41%. That is among the lowest house edges on the casino floor.

Which craps bets have the lowest house edge?

The pass line (1.41% house edge), don’t pass (about 1.36%), and their come/don’t-come equivalents carry the lowest house edges. Backing them with free odds (paid at true odds, zero house edge) pulls the effective edge well under 1%.

Why is the free odds bet in craps so good?

Free odds behind the pass line are paid at true mathematical odds, a 0% house edge. It doesn’t change the pass-line loss in dollars, but it grows the total wagered at fair odds, dragging the blended edge toward zero.

Is “Any 7” a good bet in craps?

No. It is one of the worst bets in the casino. Any 7 pays 4 to 1 but the true odds are 5 to 1, giving an expected value of −6/36, or a 16.67% house edge. That is more than ten times the cost of the pass line on the very same table.