Craps: Practical Play for the Compulsive Tinkerer
A clear, math‑smart guide to craps: learn how the dice distribute, what hit frequency, house edge, variance, and expected value mean—and which bets matter.
Craps feels complicated until you stop treating every square on the table like a magical short cut. The table is really just a few sensible bets wrapped around the simple physics of two dice. This post peels back the noise: what the dice actually do, how often bets win (hit frequency), what the house edge and expected value mean in plain English, and how variance changes your ride.
Two dice, one distribution
Two six‑sided dice don’t produce every total equally. Seven is the most common total (6 combinations out of 36), while 2 and 12 are the rarest (1 combination each). That distribution is the foundation: it determines how often a given total appears and therefore how often particular bets win.
Practical takeaway: if a bet depends on a specific number (like rolling a 4), it’s much less likely to hit than a bet that benefits from 7s appearing frequently.
The basic bets and hit frequency
- Pass Line (shooter’s side): On the come‑out roll you win on 7 or 11 and lose on 2, 3, or 12; otherwise a point is set and you need that point rolled again before a 7. The overall win probability for a Pass Line bet is just under 50% (about 49.3%).
- Don’t Pass: the mirror image of Pass Line; it wins slightly more often in a vacuum because ties on 12 push in many rulesets. Its win frequency is just over 50% against the shooter, but the practical difference is tiny.
Hit frequency is simply how often a bet wins. Pass Line wins roughly 49% of the time; propositions that rely on a single roll can win far less frequently (or more frequently) depending on the payout.
House edge vs expected value
House edge is the long‑run average percentage of each wager the casino expects to keep. For example, a Pass Line bet carries about a 1.41% house edge — that means, on average and over a very large number of bets, you lose about $1.41 for every $100 bet. That’s the long‑run expected value (EV) expressed as a percentage.
Expected value is the numeric average outcome of a bet. If you bet $100 repeatedly on something with a 1.41% house edge, your expected loss per bet is $100 × 0.0141 = $1.41. Expected value is about averages; it does not tell you what will happen in the next roll.
Odds bets: what they do for EV and variance
Craps is unusual because it offers “odds” bets behind a Pass Line or Don’t Pass bet that pay true odds — the house takes no edge on the odds portion. If you bet $10 on the Pass Line (1.41% edge) and then put $30 behind it as odds (0% edge), the combined house edge falls because only the original $10 carries the 1.41% charge. Numerically: the effective house edge becomes 1.41% × (10 / (10 + 30)) ≈ 0.35% for the combined $40 exposure.
That’s why most mathematically minded players take odds: it reduces the house edge on the money you have working at the table. But remember: adding odds increases variance — your wins and losses will be larger because more money is changing hands when you win or lose.
Variance: why session length and stake size matter
Variance measures how wild your ride will be. High variance means big swings (large wins and losses); low variance means smaller, more predictable swings. Single‑roll props and large odds produce high variance. Small, repeated Pass Line bets without huge odds produce lower variance.
If you have a limited bankroll and want to play longer, lower variance and smaller bets help. If you want shot‑at a bigger payoff and can absorb swings, higher variance with bigger odds may be fine — just know the house edge and expected value don’t change in your favor.
Which bets actually matter in practice
- Stick to Pass Line/Don’t Pass and take reasonable odds. That combination gives you low house edge and a simple plan.
- Avoid most one‑roll proposition bets and complicated multi‑number wagers. They typically carry much larger house edges — that kills EV even if they feel exciting.
- Manage bet sizes relative to your bankroll to control variance and session length.
A simple example to keep your head straight
You place a $10 Pass Line bet. Expected loss long term: about $0.14 per $10 (1.41% house edge). Add $30 odds behind it. Your total money at risk is $40, but only the $10 carries the house edge, so your expected long‑run loss on that $40 is still about $0.14 — roughly 0.35% of your $40 exposure. You’ve lowered the percentage cost, but your swings (wins and losses) are larger because you now have $40 in action.
Tink’s Toolchest can help you reference strategy, compare bet EVs, or review a session to see how variance affected your bankroll without pretending to predict rolls.
Quick behavioral pointers
- Decide your budget and stick to bet sizes that let you play for as long as you want. Small, consistent bets limit variance.
- Don’t treat streaks as magical; each roll is independent. Strategies that depend on predicting the next roll’s direction are gambling, not math.
Responsible‑play reality check: the house edge is real and unavoidable in the long run; use smart bet choice and bankroll controls to enjoy the game without expecting to beat the math.