Craps: Practical Probabilities and Smart Choices for the Curious Tinkerer
A clear, practical guide to craps probabilities, hit frequency, variance, and simple bet choices—useful math for curious players who like to tinker.
Craps looks chaotic: two dice clatter, chips fly, and the table erupts. Beneath the noise, the game is a compact probability lab where a few simple facts let you choose bets with your eyes open. This post walks through the dice math that matters, how house edge and variance differ, and which bets give the most reasonable tradeoffs for a curious player.
How the dice work (quick math you can hold in your head)
Two standard six‑sided dice give 36 possible ordered outcomes. Totals from 2 to 12 have these counts: 2 (1), 3 (2), 4 (3), 5 (4), 6 (5), 7 (6), 8 (5), 9 (4), 10 (3), 11 (2), 12 (1). That makes a 7 the most likely roll (6/36 ≈ 16.67%) and 2 or 12 the least likely (1/36 ≈ 2.78%).
On the come‑out roll the Pass Line wins on 7 or 11 (8/36 ≈ 22.22%) and loses on 2, 3, or 12 (4/36 ≈ 11.11%); the rest (24/36 ≈ 66.67%) establishes a point (4, 5, 6, 8, 9, or 10).
If a point is set, the shooter’s job is to roll that number again before a 7. The probability of making the point depends only on the point number: for 4 (3 combinations) the chance is 3/(3+6)=1/3 (≈33.33%), for 5 it’s 4/10 (40%), for 6 it’s 5/11 (≈45.45%), and symmetric for 10, 9, 8.
Combine the come‑out and point math and the Pass Line wins about 49.29% of decisions. Lose chance is the remainder, and the small difference between winning and losing probabilities is the source of the house edge.
House edge vs. hit frequency vs. variance vs. expected value
- House edge: the casino’s long‑run advantage expressed as a percentage of your wager. For a straight Pass Line bet (no odds) it’s about 1.41%. That means, on average over a huge number of bets, you’ll lose about $1.41 per $100 wagered on the Pass Line.
- Hit frequency: how often a bet pays off. The Pass Line pays roughly 49.3% of the time; a bet on 6 (place bet) hits about 45.45% of its resolution cycles.
- Variance: how wild results swing around the average. High‑variance bets pay infrequently but can pay big when they win (proposition bets, hardways); low‑variance bets pay more often but in smaller amounts (Pass Line with odds, place 6/8).
- Expected value (EV): the average result per unit wagered. If EV is negative, the bet loses money on average. EV combines hit frequencies, payouts, and house edge into a single number you can use to compare bets.
These are separate ideas: a high hit frequency doesn’t mean a positive EV, and a low house edge doesn’t mean low variance. You can have a low‑edge bet that still swings wildly in the short term.
The bets that matter (and why)
- Pass Line (and Come): simple, low edge, moderate hit frequency. House edge ≈1.41% on the initial bet.
- Taking Odds: once a point is set you can back the Pass Line with odds. The odds bet pays at true odds (e.g., 2:1 on a 4/10; 3:2 on a 5/9; 6:5 on a 6/8) and carries no house edge. Adding odds lowers the effective house edge across your combined wager. For example, if you bet $10 on the Pass Line and take $30 in odds (3x), your total money at risk is $40 but the expected loss still comes only from the $10 pass bet (~$0.14), so the effective edge on the $40 is ~0.35%.
- Place 6/8: close second to Pass Line for reasonable edge and steady action. Place 6/8 are hit about 45.45% of the time and commonly offer a house edge near 1.52%—a respectable tradeoff.
- Proposition bets (any 7, hardways, etc.): generally high house edge and high variance. They’re fine for short bursts of excitement, not steady value.
Don’t chase “systems” that rely on patterns of wins and losses; dice are memoryless and probabilities don’t change because of prior rolls.
Practical choices for the tinkerer
- If you like low edge and tolerable swings: play Pass/Come and take as much odds as the table allows. That reduces the effective house edge even though it increases absolute volatility because you’ve got more money at work on zero‑edge odds.
- If you want steady wins but not too tiny: consider place bets on 6 and 8. They hit with decent frequency and are easy to manage.
- If you want excitement: pick a small portion of your bankroll for higher‑variance proposition bets and accept they’re long‑term losers by design.
Keep bets proportional to your bankroll so variance doesn’t force you into poor choices.
Tools and tracking
If you like to tinker, keeping a short log of which bets you made, outcomes, and session length helps you see how variance plays out versus theory. Tink’s Toolchest can help reference strategy choices, compare bets, or review a session without claiming to predict outcomes or change the math.
Responsible-play reality check
Craps is a great mix of simple probabilities and lively hands—use the math to choose bets that match your tolerance for risk, and remember the house edge means gambling should be entertainment, not income. Play within limits and walk away when it stops being fun.