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there are 15 possible outcomes where two dice will match; and; there is one possible outcome where all three dice will match; and so; there are 125 possible outcomes where no die will match the number. At payouts of 1 to 1, 2 to 1 and 10 to 1 respectively for each of these types of outcome, the expected loss as a percentage of the stake wagered is:
These perfect dice from the Tropicana Atlantic City have been retired by drilling a hole completely through between the 1-6 faces; the four-digit serial number on the 6 face has been partially obliterated, but it started and ended with a 4. The dice used at casinos for craps and many other games are sometimes called perfect or gambling house dice.
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value .
The three-dice sum wagers either are on a range ("small" being a sum of 4 through 10, inclusive; "big" being a sum of 11 through 17, inclusive), a specific sum, or whether the sum is odd or even. All of the three-dice sum wagers lose when the three dice roll a triple. The most common wagers are "Big" and "Small".
A martingale is a class of betting strategies that originated from and were popular in 18th-century France.The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails.
Hazard is an early English game played with two dice; it was mentioned in Geoffrey Chaucer's Canterbury Tales in the 14th century.. Despite its complicated rules, hazard was very popular in the 17th and 18th centuries and was often played for money.
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The actual origins of the game are not clear; some of the earliest documentation comes from 1893, when Stewart Culin reported that Cee-lo was the most popular dice game played by Chinese-American laborers, although he also notes they preferred to play Fan-Tan and games using Chinese dominoes such as Pai Gow or Tien Gow rather than dice games.