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Hazard
Introduction
The dice game Hazard reached its pinnacle of popularity in 17th and 18th century England. Evidence of the game, however, goes back to at least the 14th century. The modern game of craps is based on Hazard and is probably responsible for its demise.
History
The following information about the history of Hazard is based on The Doctrine of Chances by Stuart N. Ethier, which is an outstanding source on both the history and mathematics of gambling.
The game of Hazard likely became known to the Western world in 1125 at the siege of a castle named Hazart. The early version bears closer resemblance to what we know as sic bo today. Likely in the 13th or 14th century, the game evolved into a two-dice version, which I describe in this page. From England, the game spread to France and later to the United States, where it became what we know as craps today.
Rules
Hazard uses different terminology than craps, but the play of the game is mostly the same. For those familiar with craps, Hazard plays like the pass line bet, except in Hazard the total that serves as the 7 in craps may be anything from a 5 to a 9, according to the choice of the shooter. If the shooter chooses anything other than a 7, then what happens on an 11 and a 12 on the come out roll is affected.
- The shooter chooses a number from 5 to 9 to serve as the Main (the function of the seven in craps).
- If the first roll (what is called the "come out roll" in craps) is the Main, then the shooter wins.
- If the first roll is a 2 or 3, then the shooter loses.
- If the Come Out Roll is an 11 or 12, then what happens depends on the Main, as follows:
- Main of 5 or 9: 11 and 12 both lose.
- Main of 6 or 8: 11 loses and 12 wins.
- Main of 7: 11 wins and 12 loses.
- The remaining numbers are known as the "chances." For example, if the Main is 5, then the chances are 4,6,7,8,9, and 10. If the shooter rolls one of those numbers, it becomes known as the "chance" (point). The shooter will then keep throwing the dice until he rolls either the Main or the Chance. If the first to appear is the Chance, then the shooter wins. Otherwise, if the Main is first to appear, then the shooter loses.
- All wins pay even money.
Terminology
| Craps | Hazard |
|---|---|
| 7 | Main |
| Place numbers | Chances |
| Point | Chance |
| Come out winner | Nick |
| Come out loser | Nick out |
| Shooter | Caster |
| Dealer | Setter |
Analysis
The following table shows the possible outcomes according to the chosen Main. The bottom row shows a house edge of 1.52% on a Main of 5 or 9, 2.34% on 6 or 8, and 1.41% on 7.
Hazard Odds
| Event | Main of 5 or 9 | Main of 6 or 8 | Main of 7 |
|---|---|---|---|
| Come out win | 0.111111 | 0.166667 | 0.222222 |
| Come out loss | 0.166667 | 0.138889 | 0.111111 |
| Point win | 0.381305 | 0.321619 | 0.270707 |
| Point loss | 0.340917 | 0.372825 | 0.395960 |
| Any win | 0.492416 | 0.488286 | 0.492929 |
| Expected return | -0.015168 | -0.023429 | -0.014141 |
French Rules
Under French rules, the player does not get to choose the Main; instead, it is chosen randomly by rolling the dice until the player gets a 5 to 9, thus designating the Main. In this case, the overall house edge would be 1.835%.
Strategy
Choose a Main of 7, which minimizes the house edge at 1.41%.
Perhaps players eventually learned this, and chose 7 every time, resulting in Hazard morphing into Craps.