Understanding Basic Craps Odds: Pass Line, Don't Pass, Come, Don't Come

Craps begins with a simple set of probabilities based on two six-sided dice. There are 36 possible combinations (6 × 6). The most common sums and their frequencies determine the foundation of all odds calculations: 7 appears 6 ways, 6 and 8 appear 5 ways each, 5 and 9 appear 4 ways each, 4 and 10 appear 3 ways each, 3 and 11 appear 2 ways each, and 2 and 12 appear once each. For Pass Line and Don’t Pass bets, understanding these frequencies is key because the point numbers (4, 5, 6, 8, 9, 10) have different probabilities of being rolled before a 7, which affects the true odds and house edge.

For a Pass Line bet after a point is established, you win if the shooter rolls that point before rolling a 7. The probability the shooter rolls, for example, a 6 before a 7 is 5/(5+6) = 5/11, because there are 5 combinations for 6 and 6 for 7. That gives a true payoff odds of 6:5 for 6 and 8; similarly, for a 5 or 9 it’s 4/(4+6)=4/10=2/5, so true odds are 3:2; for a 4 or 10 it’s 3/(3+6)=3/9=1/3, so true odds are 2:1. The house-offered Pass Line payout is even money, but players can take or lay odds behind the Pass Line (free odds) which paid at true odds and have no house edge. The Don’t Pass mirror probabilities apply to betting against the shooter: Don’t Pass wins if a 2 or 3 is rolled on the come-out (12 is a push), or if a 7 is rolled before the point after it’s established. Appreciating these basic odds numbers and their relationship to 36 combinations is essential for all subsequent calculations.

Calculating True Odds for Place and Buy Bets

Place and Buy bets are common side bets where payouts differ from true odds because the house often takes a commission or adjusts the payout ratio. Place bets pay fixed odds based on house rules (commonly: 4/9 for 4 or 10, 7/10 for 6 or 8, 5/9 for 5 or 9 in some casinos expressed in money terms like 9:5, 7:6 depending on table). To calculate the true expected return, convert the number of winning combinations to probabilities, multiply by the payout, and subtract the losing probability times the stake.

Example: A place bet on 6. There are 5 winning combinations for a 6 and 6 losing combinations for a 7; the probability of hitting 6 before 7 is 5/11 ≈ 0.4545. If the table pays 7:6 (i.e., you win $7 on a $6 wager), the effective payout ratio per unit bet is 7/6 ≈ 1.1667. Expected value per $1 wager = P(win) × payout – P(lose) × stake = (5/11 × 1.1667) – (6/11 × 1) = (0.4545 × 1.1667) – 0.5455 = 0.5303 – 0.5455 = –0.0152, or about –1.52%. That’s the house edge on that place bet. If instead you use a Buy bet for 4 or 10, you pay a 5% commission on the bet to gain true odds (i.e., you pay the vig to get the correct 2:1 payout on a 4). For a $100 buy on 4, you might pay $5 commission but get paid 2:1 on wins; your long-run expectation will then reflect the commission cost but the payout aligns with true probability, often giving slightly better edges for high-volume bettors compared to unattractive place payouts.

The general method: convert combinations → probability of winning before 7; determine casino payout structure and commissions; compute EV = P(win)×(payout) − P(lose)×(stake). For multi-roll bets such as Hardways or Any Seven, list the winning combinations and losing combinations explicitly (e.g., hard 6 has 1 winning combo, but any 6 has 5 combos, and a 7 still has 6 combos). Accurate EV calculations require counting combinations precisely, then converting to per-unit returns.

Using Probabilities to Optimize Betting Strategy

Once you can compute true odds and expected value, you can optimize betting strategy by balancing house edge, variance, and bankroll constraints. The key concept is expected value: favor wagers with the smallest house edge and manage bet sizing to control variance. For craps, the best bets by house edge are Pass Line + full odds (because odds have zero house edge) and Don’t Pass + odds. Place bets on 6 and 8 often outperform place bets on other numbers, but buying 4 or 10 at true odds after paying commission can be better than placing them for worse payouts.

Bankroll management matters too: the volatility of certain bets—like hardways or proposition bets—can devastate a small bankroll despite occasional large payouts. Use Kelly-like fraction reasoning: bet a fraction of your bankroll proportional to your edge (which for most craps bets is negative, so Kelly suggests betting minimally). In practice, adopt unit sizing that withstands common losing streak lengths: for example, if you plan to play many rounds, keep unit sizes small relative to bankroll to avoid ruin from variance.

Another optimization is synergy of bets: combining Pass Line with odds, and small Come bets with odds, spreads the action across favorable numbers and increases the portion of your wager exposed to free odds. Avoid sucker bets: high house-edge single-roll props (like any 7 or certain hardways) should be limited or avoided unless you accept the entertainment value as part of your cost. Tracking your sessions and computing realized EV versus theoretical EV will refine your choices: if a given table offers nonstandard place payouts or commission structures, run the simple combos-to-EV calculation to see how it compares and play accordingly.

Quick Mental Methods and Tools from CrapsCentral

CrapsCentral’s practical approach emphasizes quick mental conversions and simple charts you can memorize to speed decision-making at the table. The foundational shortcut: memorize combinations for sums (7=6, 6/8=5, 5/9=4, 4/10=3, 3/11=2, 2/12=1) and the derived win probabilities for point bets (for a point x with w combos, P(hit before 7) = w/(w+6)). From that, you can quickly recall true odds: 6/8 → 6:5 against; 5/9 → 3:2 against; 4/10 → 2:1 against. This lets you judge any offered payout against the true payout instantly: if a table pays less than these ratios (adjusted for unit sizes), the bet carries a house edge.

Another useful mental method is percentage approximations. For critical numbers: 6/8 chance of hitting before 7 ≈ 45.45%; 5/9 ≈ 40%; 4/10 ≈ 33.33%. Multiply by offered payout to get a rough EV numerator, subtract the losing probability to get approximate edge. For everyday play, round: 45%, 40%, 33% and 55%, 60%, 67% losing probabilities respectively. These approximations are sufficient for quick calls on whether buying odds, placing numbers, or taking certain side bets is sensible.

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CrapsCentral also recommends simple tools: a small laminated odds cheat card for personal use showing combinations, true odds, and common casino payouts; a pocket calculator or phone app for more complex commission scenarios; and practice drills—counting combos mentally and converting them into probabilities under time pressure—to build comfort. Finally, keep a short list of safe plays: Pass/Don’t Pass with max reasonable odds, place 6/8 when payouts are fair, avoid most short-term proposition bets. With these mental methods and tools you can rapidly evaluate table offers and focus on bets that minimize long-term losses while enjoying the game.