Question

what is the probability of getting yahtzee in three rolls?

Answer 1

There are various possible scenarios possible to get Yahtzee in three rolls. Here is the exhaustive list of the same. The probability of:

• Four of a kind, then nothing, then matching the last die on the last roll is
• Three of a kind, then nothing, then matching with the correct pair on the last roll :
• A matching pair, then nothing, then matching with the correct three of a kind on the third roll :
• A single die, then nothing matching this, then matching with the correct four of a kind on the third roll
• Three of a kind, matching an additional die on the next roll, followed by matching the fifth die on the third roll
• Matching an additional pair on the next roll, followed by matching the fifth die on the third roll is
• Rolling a pair, matching an additional die on the next roll, followed by matching the last two dice on the third roll
• Rolling one of a kind, another die to match it on the second roll, and then a three of a kind on the third roll .
• Rolling one of a kind, a three of a kind to match on the second roll, followed by a match on the third roll is
• Rolling one of a kind, a pair to match it on the second roll, and then another pair to match on the third roll is

Summing all of the above, we get the required probability as

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