Craps: Practical Probabilities and Sensible Bets for the Curious Tinkerer
A clear, math‑grounded look at craps: how common bets work, what house edge means, how hit frequency and variance differ, and practical choices for smarter play.
Craps is a noisy, social table game that looks chaotic until you strip it down to dice math. For a curious, tinkering player, the fun is in understanding which bets are merely flashy and which give you the cleanest relationship between risk and reward. This article explains the key probabilities and mechanics in plain English, separates concepts that often get conflated (house edge, hit frequency, variance, expected value), and points out practical bets to favor or avoid.
The basic mechanics and simple probabilities
On the come-out roll (the first roll of a round), a 7 or 11 is an immediate win for a Pass Line bet, while 2, 3, or 12 are craps (immediate losses for Pass Line). Two dice have 36 equally likely combinations. A 7 shows up 6 ways and an 11 two ways, so the come-out immediate win probability is 8/36 (about 22.22%). If a 4, 5, 6, 8, 9, or 10 is rolled, that number becomes the “point” and the shooter continues rolling until the point or a 7 appears.
If the point is 4, the dice will produce a 4 in 3 combinations and a 7 in 6 combinations. So once a 4 is the point, the chance of making it before a 7 is 3/(3+6) = 1/3 (about 33%). For points 5 and 9 it’s 4/(4+6) = 40%, for 6 and 8 it’s 5/(5+6) ≈ 45.45%, and for 10 it’s 33% again. These conditional probabilities are what determine how likely you are to win a Pass Line bet once a given point is established.
House edge vs. hit frequency vs. variance vs. expected value
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House edge: The casino’s long-run advantage, expressed as a percentage of your initial wager you should expect to lose on average. For a straight Pass Line bet with no odds, that edge is about 1.41%. That means on average the house keeps $1.41 for every $100 wagered on that bet over the long run.
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Hit frequency: How often a bet pays out. Pass Line wins occur slightly less than half the time (roughly 49.3% when you count all outcomes). A higher hit frequency just means you see wins more often; it doesn’t mean the bet is profitable.
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Variance (or volatility): How bumpy the ride is — frequent small wins and losses have low variance; rare big wins and long losing stretches have high variance. Proposition bets (one-roll bets, hardways, etc.) tend to be high variance.
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Expected value (EV): The average amount you’d win or lose per bet if you repeated the bet many times. EV is calculated from the probabilities and payouts; for the Pass Line that EV corresponds to the house edge (e.g., −$0.01414 per $1 bet, or −$0.1414 for a $10 bet).
These four concepts are connected but distinct: a bet can win often (high hit frequency) yet have negative EV (because payouts are too small), or it can pay infrequently but still be a reasonable EV if the payout matches the true odds.
Odds bets: the one thing that isn’t rigged
After a point is established you can take odds behind your Pass Line bet. Odds bets pay true odds (they have zero house edge) because they’re paid at the mathematically correct ratio for the point. That doesn’t change the probabilities, but it changes the composition of your money at risk: the portion on odds has no house edge, so the overall house edge across your combined wager is reduced.
Example: $10 on Pass Line (1.41% house edge) and $20 in odds (zero edge). Expected loss comes only from the $10 portion: 0.01414 × $10 = $0.1414. Against a total of $30 wagered, that’s an overall edge of $0.1414/$30 ≈ 0.47%. That’s why many sensible players use the Pass Line with odds: you’re still a favorite to lose in the long run, but the rate at which you lose per dollar wagered drops.
Practical bets to favor and avoid
- Favor: Pass Line / Don’t Pass (simple, low edge) with as much odds as the table allows. Come / Don’t Come are the same math, just later in the round.
- Favor: Place 6 and 8 are reasonable side choices if you prefer more frequent hits; they tend to have lower variance than prop bets and decent hit frequency.
- Avoid or limit: One-roll proposition bets (Any 7, hardways, Horn) and many vendor-side bets. They often have high payouts but much higher house edges and much greater variance. They’re entertainment bets, not efficient plays.
Simple session tactics for tinkerers
- Use small base bets so you can stake decent odds; this tilts your total dollar exposure toward the zero-edge portion.
- Decide a session bankroll and a loss limit before you sit; treat the table like an experiment, not a paycheck.
- Track outcomes and returns. Tink’s Toolchest can help you reference strategy choices, compare bets on edge and volatility, or review a session afterward without pretending to predict dice.
Final thoughts and reality check
Craps rewards knowing the math: some bets are plainly better value than others. But no combination of bets removes the house edge — odds reduce your edge, proposition bets increase it. Play for the social energy and the interesting probabilities, not because you expect to beat the game.
Responsible-play reality check: set limits, stick to them, and never wager money you can’t afford to lose.