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Hazard

Introduction

The dice game Hazard was at its most popular during the 17th and 18th centuries in England. However, historical records show that this game has existed since at least the 14th century. The contemporary game of craps is derived from Hazard and likely contributed to its decline.

History

The subsequent details regarding Hazard's history are sourced from The Doctrine of Chances by Stuart N. Ethier, an excellent reference for the evolution and mathematical principles behind gambling games.

It is believed that Hazard was introduced to the Western world around the year 1125 during the siege of a castle named Hazart. The initial form of the game closely resembles what we now recognize as sic bo in modern times. It likely underwent a transformation into a two-dice game between the 13th and 14th centuries, which I describe further on this page. From England, its popularity spread to France and later to America, where it developed into what we currently know as craps today.

Rules

While the terminology in Hazard differs from that in craps, the mechanics of the games are largely similar. For those who are accustomed to craps, playing Hazard resembles placing a bet on the pass line; however, in Hazard, the number designated as the equivalent of 7 in craps can range from 5 to 9, as chosen by the player. If the shooter opts for a number other than 7, the results on an 11 or 12 during the come out roll will be impacted.

  1. A player selects a number between 5 and 9 to serve as the Main, which functions similarly to 7 in craps.
  2. If the initial roll, referred to as the 'come out roll' in craps, matches the Main number, the shooter emerges victorious.
  3. Conversely, if the initial roll results in 2 or 3, the shooter faces defeat.
  4. The outcome of a roll resulting in 11 or 12 is influenced by the Main number, as outlined below:
    • 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.
  5. The remaining numbers are classified as 'chances.' For instance, if the Main is designated as 5, the chances are 4, 6, 7, 8, 9, and 10. If the player rolls any of those numbers, it is termed a 'chance' (point). The shooter continues to roll the dice until either the Main or Chance appears. If Chance appears first, the shooter wins; if the Main appears first, the shooter loses.
  6. 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 table below illustrates potential results based on the chosen Main. The last row indicates a house edge of 1.52% for a Main of 5 or 9, 2.34% for 6 or 8, and 1.41% for 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

In accordance with French rules, the player does not select the Main; instead, it is established randomly by rolling the dice until a number between 5 and 9 is achieved, thus designating the Main. In this scenario, the overall house edge rises to 1.835%.

Strategy

Opt for a Main of 7 to reduce the house edge to 1.41%.

Players may have eventually discovered this optimal strategy and thus began to consistently select 7, leading to the transformation of Hazard into Craps.

Outside Links

Wikipedia page on Hazard .