While the odds are 1/21, real life doesn't follow the odds. In practice, it may take longer as an initial pair may be discarded to roll for something else, such as a straight." To put this into perspective, since 1/21 is approximately 4.74 percent, by chance alone a player should expect a Yahtzee once every 21 turns. This means that the probability of obtaining a Yahtzee in a given turn is approximately 4.74 percent. Since each of these are mutually exclusive, we add the probabilities together. "The probability of a Yahtzee in one roll is 0.08 percent, the probability of a Yahtzee in two rolls is 1.23 percent and the probability of a Yahtzee in three rolls is 3.43 percent. Probably you lean to heavily towards straights or something else. ![]() ![]() And you seem to have had extraordinary bad luck in your real life or you played with screwed dice. ![]() If you roll a Yahtzee only every 8 or 9 games, you are actually off in a way that you roll too few Yahtzees.
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