Abstract
Dice problems contributed the initial impetus to the development of probability theory. Cardano, Pascal, and Fermat enunciated the concept of equally likely outcomes for the six faces of a die so the probability that any one side will face upward is 1/6. One of the questions concerning biased dice relates to the number of throws of a die necessary to ascertain the existence of a bias. In one of the oldest formal dice games, a single die is thrown until a particular number appears. If p is the single-trial probability of that event, and n is the number of throws until it occurs for the rth time. A dice game popular among military personnel consists of throwing five dice simultaneously, declaring one or more to be “frozen,” then repeating the process with the remaining dice until all five are frozen. It is aimed at maximizing the sum of the points on the five frozen dice. The game is highly favorable to the player rolling the dice since 25 is the most probable sum achieved by optimal play. A game similar in its mechanics consists of rolling n (usually five) dice, attempting to achieve the outcome 6 on all n.
Published Version
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