Craps: Practical Math for the Curious Tinkerer

Craps can feel like organized chaos: two dice, one table full of people cheering, and a forest of bet options. If you like to tinker — testing small changes, comparing outcomes, and understanding why things behave the way they do — craps is a great game to examine. This post strips away the myth and focuses on the math that matters: how the dice produce outcomes, what common bets really cost you, and how to match bet choice to tolerance for swings.

How the dice work (quick and useful probabilities)

Two fair six‑sided dice produce 36 equally likely ordered outcomes. Sums have these frequencies (out of 36):

2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/36
12: 1/36

Those raw frequencies are the foundation. For example, a single roll hits a 7 with probability 6/36 ≈ 16.67%, a 6 with 5/36 ≈ 13.89%, and a 2 or 12 with 1/36 ≈ 2.78% each.

When a bet depends on which number comes before another (for instance, “6 before 7”), you can reduce the sample space to just the competing outcomes. For a bet that wins if a 6 appears before a 7, the only relevant outcomes are the five faces that make a 6 and the six faces that make a 7, so the win probability is 5/(5+6) = 5/11 ≈ 45.45%.

Common bets and their math (plain English)

Pass Line: A classic starter bet. On the come‑out roll, 7 or 11 wins; 2, 3 and 12 lose under standard rules. Do not confuse this with Don’t Pass, where a come-out 12 is commonly a push. If a point is set, the shooter must roll the point again before a 7 for the Pass Line to win. The house edge on a plain Pass Line bet is about 1.41% — meaning, on average, you lose $1.41 per $100 wagered over the long run.
Odds (backing Pass/Come): Odds bets pay true odds and carry no house edge. For Pass/Come, they are available after the relevant point is established; laying odds behind Don’t Pass/Don’t Come is a different wager. Adding odds increases the money exposed to a loss even though the odds portion has zero expected loss under fair-dice assumptions and standard payouts.
Place bets (betting that a specific number like 6 or 8 will roll before a 7): These pay different amounts and have different edges. For example, 6 and 8 are relatively efficient place bets — they win about 45.45% of the time (5/11) and typically have a low house edge (~1.52%). The 5/9 and 4/10 place bets win less often and have higher house edges.
Proposition bets (single‑roll or longshots like Any 7, hardways): These often have low hit frequency and high house edge. Any 7, for instance, wins roughly 1 in 6 rolls but usually pays only 4:1, producing a large negative expected value.

Note: payout tables vary, and variations change the house edge. When in doubt, ask for the payout on a bet and compare it to the true odds implied by the dice.

Hit frequency, variance, house edge, and expected value — what each term means

House edge: The casino’s average percentage gain on a bet over the long run (e.g., 1.41% on Pass). Multiply your bet size by the house edge to estimate expected loss over a very long time.
Expected value (EV): The average outcome per bet. EV = (probability of each outcome × payoff) summed across outcomes. For simple communication, EV often equals negative house edge × stake.
Hit frequency: How often a bet wins. Place 6/8 wins about 45% of the time (so you see winning results often). Any 7 wins only about 16.7% of single rolls (so wins are less frequent).
Variance: How wildly results swing. High‑variance bets (rare wins, big payouts) produce big short‑term swings. Low‑variance bets (frequent small wins) feel steadier.

These are separate ideas. A bet can have low variance but a worse house edge than a high‑variance bet. Hit frequency affects how ‘entertaining’ a bet feels; house edge determines long‑run cost.

Practical tinkering: small experiments that teach more than they cost

Play a modest Pass Line bet and add single‑point odds. Example: $5 Pass Line with $10 odds. The $5 Pass Line carries about 1.41% house edge (≈ $0.07 expected loss on that $5), while the $10 odds have 0% edge. Combined, your expected loss on the $15 is about $0.07, which is an effective house edge of ~0.47% on the total money at risk. The roughly seven-cent expected loss is unchanged by adding the fair odds portion; the percentage falls because more money is at risk. This does not make a session safer or guarantee a profit.
Compare place bets for feel vs math. Place a small $6 on the 6 or 8 and watch the hit frequency; you’ll win fairly often for modest payouts. Then try a few rounds of proposition bets at tiny stakes to observe the high swings and high long‑term cost.
Track outcomes, not narratives. Record the size of each bet, wins/losses, and number of rolls per decision. That data will show variance and expected loss much more clearly than memory.

Use Tink’s Toolchest as a companion for the supported games and session tools described on its product page. Keep any paper calculations separate from the app’s actual feature set; a record of past outcomes does not predict the next independent roll.

Final reality check

Craps is math you can observe at the table: probabilities are fixed, and the house edge tells you the long‑run cost of each bet. You can choose lower‑edge bets and use odds to reduce effective cost, but no betting pattern eliminates the house edge. Play with curiosity, set a budget, and treat the table as entertainment — not a way to solve financial problems.

Sources and calculation assumptions

The New Jersey Division of Gaming Enforcement rules of the games, Chapter 69F describe standard Pass and Don’t Pass rules and payouts. Check the posted rules at the actual table. The calculations above assume independent fair dice and the payouts stated in each example. They describe averages across many resolved wagers, not a forecast of your next session.

Reviewed October 21, 2026: corrected the Pass Line twelve rule, distinguished establishing a point from making it, clarified the risk added by odds, and added worked expected-value examples.

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