I. Origin — From Hazard to American Bank Craps
Craps descends from the medieval English game Hazard, documented as early as the 14th century in Geoffrey Chaucer's Canterbury Tales. Hazard was a two-dice game with a complex point-and-chance structure that became popular among British soldiers during the Crusades. The simplified American descendant — initially called "crapaud" (French for "toad," the slang for losing 2/3/12 rolls) — emerged in 1813 New Orleans courtesy of Bernard de Marigny, a Louisiana Creole gambler who adapted Hazard's rules for casual play.
The casino "Bank Craps" version was standardized in 1907 at Hot Springs, Arkansas, where John H. Winn introduced the Don't Pass bet and the modern table layout. World War II spread craps globally via American GIs; by 1960 it was the dominant casino dice game in the United States and the second-largest table game by handle (after blackjack). Today craps generates approximately 4% of US casino table revenue but commands disproportionate cultural mindshare.
II. The Basic Rules
- One player (the "shooter") rolls two six-sided dice. Other players bet on outcomes.
- The first roll is the come-out. Possible outcomes:
- Roll 7 or 11: Pass Line wins, Don't Pass loses
- Roll 2, 3, or 12: "Craps" — Pass loses, Don't Pass wins (12 is a push on Don't Pass)
- Roll 4, 5, 6, 8, 9, or 10: that number becomes the "point"
- Once a point is set, the shooter continues rolling until either:
- The point is rolled again → Pass Line wins, Don't Pass loses, new come-out
- A 7 is rolled (a "seven-out") → Pass Line loses, Don't Pass wins, shooter ends, dice pass to next player
- Anything else → roll again, no resolution
III. The Mathematics of the Dice
Two fair six-sided dice produce 36 equally likely outcomes. Sum probabilities:
| Sum | Combinations | Probability |
|---|---|---|
| 2 | 1 (1-1) | 1/36 = 2.78% |
| 3 | 2 (1-2, 2-1) | 2/36 = 5.56% |
| 4 | 3 | 3/36 = 8.33% |
| 5 | 4 | 4/36 = 11.11% |
| 6 | 5 | 5/36 = 13.89% |
| 7 | 6 | 6/36 = 16.67% |
| 8 | 5 | 5/36 = 13.89% |
| 9 | 4 | 4/36 = 11.11% |
| 10 | 3 | 3/36 = 8.33% |
| 11 | 2 | 2/36 = 5.56% |
| 12 | 1 | 1/36 = 2.78% |
The peak at 7 is the central fact of craps: 7 is the most likely roll. This drives every probability calculation. Pass Line wins more often than it loses on the come-out (8/36 win vs 4/36 lose = 8/12 ≈ 66.7% of resolved come-out rolls win), but the unresolved 24/36 rolls establish points, and from the point phase the house edge clamps down.
IV. The Pass Line Math — 1.41%
Pass Line calculation:
- Win immediately on come-out (7 or 11): 8/36 = 0.222
- Lose immediately on come-out (2, 3, 12): 4/36 = 0.111
- Set point and win it back (sum across all points): 0.271
- Set point and seven-out: 0.396
- Net expected value: 0.493 win, 0.507 lose → −0.0141 → −1.41%
Pass Line's 1.41% is mathematically a function of: ① the favorable come-out (7s help you), ② the unfavorable point phase (sevens hurt you), ③ the asymmetric treatment of 2/3/12 vs 7/11. The math was settled by John Scarne in his 1949 Scarne on Dice and has not changed since.
V. Free Odds — The Casino's Strangest Bet
After a point is established, you can place a "free odds" bet behind your Pass Line. This bet pays true mathematical odds:
| Point | True Odds | Pays |
|---|---|---|
| 4 or 10 | 2:1 | $2 win per $1 odds bet |
| 5 or 9 | 3:2 | $1.50 win per $1 |
| 6 or 8 | 6:5 | $1.20 win per $1 |
The odds bet carries zero house edge. The combined edge on a Pass + odds package:
| Odds Multiple | Combined House Edge |
|---|---|
| No odds | 1.41% |
| 1x odds | 0.85% |
| 2x odds | 0.61% |
| 3-4-5x odds (Vegas standard) | 0.374% |
| 10x odds | 0.184% |
| 20x odds | 0.099% |
| 100x odds (rare) | 0.021% |
Why does the casino offer this? Because at $10 line + $30 odds, you bet $40 per round instead of $10. The casino's absolute dollars-per-hour rise even though percentage edge falls. Players win on the percentage; casino wins on the volume. It's a remarkable mutual deal — the only one in the building.
VI. The Proposition Bets — Where Money Goes to Die
The center of the craps table contains proposition bets. They are visually prominent, large, and reckless. House edges:
| Bet | Pays | Probability | House Edge |
|---|---|---|---|
| Any 7 | 4:1 | 16.67% | 16.67% |
| Any Craps (2/3/12) | 7:1 | 11.11% | 11.11% |
| 11 (Yo) | 15:1 | 5.56% | 11.11% |
| 2 or 12 (Aces/Boxcars) | 30:1 | 2.78% | 13.89% |
| Hard 6 / Hard 8 | 9:1 | 2.78% | 9.09% |
| Hard 4 / Hard 10 | 7:1 | 2.78% | 11.11% |
| Field (2-4, 9-12) | 1:1 (2:1 on 2 & 12) | 44.44% | 5.56% |
Proposition bets are 4-12x the house edge of Pass Line. A single $5 hop bet ($5 on a specific dice combination like 3-3) over an hour erases the entire mathematical advantage of your Pass + 3x odds play. The center of the table is the casino's profit center — by design.
VII. Place Bets, Buy Bets, Lay Bets
Beyond the main bets, craps has several "side bets" that act as one-roll-equivalents but persist across multiple rolls:
- Place Bets: directly bet a specific number (4, 5, 6, 8, 9, or 10) to roll before a 7. Pays 9:5 (4/10), 7:5 (5/9), 7:6 (6/8). House edges: 4/10 = 6.67%, 5/9 = 4.0%, 6/8 = 1.52%. Only Place 6 and Place 8 are tolerable.
- Buy Bets: same as place but pays true odds for a 5% commission. Only Buy 4 / Buy 10 are profitable (with commission only on win) — house edge ~1.67%.
- Lay Bets: opposite of buy — bet that a 7 comes before a specific number. House edge under 4% on most, but social tax of betting against the table.
- Don't Pass + Lay Odds: the mathematically optimal craps system. Combined edge: 0.014% at 5x odds. Even slightly better than Pass + free odds.
VIII. The Boxman, the Stickman, and Table Crew
A craps table requires four casino staff:
- Boxman — seated at the center, oversees the bankroll, settles disputes, watches for cheating. The senior position.
- Two dealers — one on each side, manage bets, payouts, and chip movements for their half of the table.
- Stickman — controls the dice with a hooked stick, announces results, manages the proposition bet area. Often the most performative role — good stickmen build table energy and increase betting volume.
This is the largest table-game crew in any casino — explaining why craps has high overhead and why casinos have steadily replaced 14-foot tables with 12-foot variants (one less dealer required). Online craps eliminates this entire structure but loses the social energy that drives the game.
IX. Common Misconceptions
- ❌ "The shooter affects the outcome." The dice must hit the back wall and bounce. Dice control techniques have not been verified in controlled experiments. The shooter is functionally a random number generator.
- ❌ "After many rolls without a 7, a 7 is overdue." Each roll is independent. The 7 probability remains 16.67% regardless of previous history.
- ❌ "The Field bet is fair because 2 and 12 pay 2:1." Field bet still carries 5.56% house edge — much worse than Pass.
- ❌ "More bets means more chances to win." More bets means more exposure to house edge. A single $10 Pass + odds bet has lower expected loss than ten $1 proposition bets.
X. FAQ · Sources · Responsibility
What's the difference between Pass Line and Don't Pass?
Why are 'free odds' bets the only zero-edge bet in the casino?
Why do casinos offer different 'odds multiples' (3-4-5x, 10x, 100x)?
Why are the 'proposition bets' (in the center) so bad?
What is 'dice control' and does it work?
Why is the craps table so confusing to first-timers?
Sources
- John Scarne (1949), Scarne on Dice, Military Service Publishing
- Stewart N. Ethier (2010), The Doctrine of Chances: Probabilistic Aspects of Gambling, Springer
- Frank Scoblete & Dominator (2007), Golden Touch Dice Control Revolution
- Stanford Wong (2005), Wong on Dice, Pi Yee Press
- Michael Shackleford, Craps Appendix 1 & 2 — House Edge of Every Bet, wizardofodds.com