Pass Line and Don't Pass Odds
The Pass Line bet is the most fundamental wager in craps and also among the easiest to analyze. On the come-out roll, a 7 or 11 wins immediately; a 2, 3, or 12 is an immediate loss (2 and 3 are losses on Don't Pass; 12 is a push on Don't Pass in most casinos). If a point (4, 5, 6, 8, 9, or 10) is established, the shooter keeps rolling until the point or a 7 appears. The Pass Line wins if the point is rolled before a 7; it loses if a 7 appears first. The base probability of winning a Pass Line bet, including all come-out and point scenarios, is roughly 244/495 ≈ 49.29%, giving a house edge of about 1.41% when no odds are taken. The complementary Don't Pass bet has a slightly lower house edge at about 1.36% because ties on 12 are push instead of a loss (casino rules vary), and the Don't Pass wins if a 7 occurs before the point.
"Free odds" behind Pass/Don't Pass: Most casinos allow players to take additional "odds" bets behind their Pass or Don't Pass wagers, which pay at true odds with no house edge (e.g., 2:1 on point 4/10, 3:2 on 5/9, 6:5 on 6/8 depending on bet type). Adding odds reduces the overall house edge of the combined bet; for example, taking full double odds can cut the effective house edge on a Pass Line+odds bet to under 0.5%, and large multi-layered odds (e.g., 10x odds) bring the edge arbitrarily close to 0% on that portion. Calculating the combined EV requires weighting the base bet with the fixed house edge and treating the odds portion as zero-edge (expected value = 0), so the more you bet on odds relative to the base, the lower your total house advantage.
Practical takeaway: use the Pass Line (or Don't Pass) as your foundation and take the maximum odds allowed by the house. This strategy yields the best long-term return among standard craps bets while keeping volatility moderate.
Come and Don't Come Bets Explained
Come and Don't Come bets function just like Pass and Don't Pass but are made after a point has been established and apply to the next roll sequence as if you're creating a fresh come-out for that bet. A Come bet wins immediately on 7 or 11, loses on 2, 3, or 12, and moves to a point (4, 5, 6, 8, 9, 10) if rolled—then it wins if that number is rolled again before a 7. A Don't Come is the mirror: it wins if 2 or 3 appears on the next roll, pushes on 12, and otherwise moves to a number where it wins if a 7 comes before that number. The underlying probabilities for Come and Don't Come mirror the Pass and Don't Pass probabilities (around 49.3% win rate for Come, with similar house edges), because each Come bet creates its own local come-out sequence.
Odds behind Come and Don't Come bets: Like Pass/Don't Pass, you can usually back these bets with true odds once a number is established for the Come bet. For example, if your Come bet moves to point 8, you may place odds behind it that pay the true 6:5 (or the inverse for Don't Come) depending on how you bet. Since these odds pay true odds, they carry no house edge; they serve to dilute the house edge of your initial flat bet. A common strategy is to make a Come bet when you already have a Pass Line and to take odds on both; this builds multiple independent, low-edge wagers that resolve separately.
Variance and table tactics: Come bets add variance because they create multiple concurrent point races; you can have a Pass Line plus several Come numbers all seeking hits. That increases action and the chance of a big win or a string of small losses. From a bankroll perspective, manage your flat bets conservatively when you accumulate multiple Come numbers, and maintain sufficient bankroll to support the variance introduced by taking odds on several numbers.
Place, Buy, and Lay Bets: House Edge and Probability
Place bets let you bet that a specific number (4, 5, 6, 8, 9, or 10) will be rolled before a 7. Payouts for Place bets depend on the number: typically 9:5 (1.8x) for 5 and 9, 7:5 (1.4x) for 4 and 10, and 7:6 (about 1.1667x) for 6 and 8 in many casinos (payouts and house edge can vary by casino). The house edge on Place bets also varies: roughly 4.00% on 4/10 (when paid 9:5 vs true odds 2:1), 4.00% on 5/9 (when paid 7:5 vs true odds 3:2), and about 1.52% on 6/8 (often the best Place bet). Because payout tables differ by house, always check the exact payout (e.g., 7:6 vs 6:5 differences matter).
Buy bets are similar to Place bets but typically pay true odds minus a commission (commonly 5% of the bet, sometimes only charged on wins). Buying 4 or 10 pays 2:1 true odds less the commission; buying 5 or 9 pays 3:2; buying 6 or 8 pays 6:5. If the casino charges commission only on winning Buy bets, that can make Buy bets slightly better than Place bets for certain numbers because the effective cost can be lower across many outcomes. Lay bets are the inverse of Buy bets: you bet against a number (that a 7 will occur before the number), and payouts are quoted in inverse true odds minus commission. For example, laying 4 (i.e., betting it will lose before a 7 appears) pays 1:2 (you must risk more to win less) adjusted for commission.
Probability math: The raw probabilities of a number rolling before a 7 are derived from combinations of dice faces. For instance, the probability a 4 appears before a 7 is 3/(3+6) = 1/3 ≈ 33.33% on any given roll sequence because there are 3 ways to roll a 4 and 6 ways to roll a 7. For a 6 versus a 7, it's 5/(5+6) = 5/11 ≈ 45.45%. Multiply this by the payout structure to compute expected value per dollar placed. Because house edges on Place/Buy/Lay vary, the best among them for minimizing edge are Place on 6/8 or Buy 4/10 with low commission rules.
Proposition Bets: High Risk, High House Edge
Proposition (prop) bets are one-roll or short-term bets located in the center of the craps layout: Hardways (e.g., hard 4 or hard 10), Any Seven, Any Craps (2, 3, or 12), and specific one-roll doubles or totals. These bets offer very attractive-looking payouts but heavy house edges. For example, the Any Seven bet typically pays 4:1 on a single roll where the true odds are 5:1 (6 ways to roll a 7 out of 36 possible), producing a house edge around 16.67%. Any Craps (2, 3, or 12) may pay 7:1 against true odds of 8:1, giving a house edge around 11.11%. Hardways pay well if a hard pair appears before that number or a 7, but the house edge on many Hardway bets ranges from about 9% to 11% because multiple "lose" outcomes can appear before your hardway.
Why the house edge is so large: Prop bets pay less than the true odds because casinos set payouts to ensure a positive expected margin in their favor. The rare, immediate nature of these bets gives players the allure of big, fast payouts, but over time the negative EV compounds quickly. Some prop bets are worse than slot machines in expectation. The only reason to play them should be entertainment or very rare strategic purposes (covering side bets in certain matchups), not to reduce house disadvantage.
If you want to minimize disadvantage, avoid prop bets or treat them as single-spin entertainment with a small fixed bankroll. The mathematically rational strategy for preserving bankroll is to stick to Pass/Come with odds and selective Place bets on 6/8; these options combine low house edge with relatively predictable variance. Use prop bets only when you accept the long-term negative expectation as the price of occasional excitement.
