IJK (iconjack) has calculated the probability of rolling a Yahtzee in no more than n rolls.

begin{align*} p(n) &= 1 + frac{53}{13}left(frac{5}{6}right)^{2n+1} + frac{11cdot 5^n}{13cdot 2^{n+5}cdot3^{3n+1}} \ &phantom{=} - frac{5^n}{8cdot 3^{2n-2}} - frac{7cdot 5^{n+1}}{2^{n+5}cdot 3^{n-1}} end{align*}

The first few numerical values are
p(1) = 0.0007716
p(2) = 0.0126316
p(3) = 0.0460286

The probability is 0.95 after 23 rolls, and 0.99 after 32 rolls.

Here’s a plot.

The post Probability of rolling a Yahtzee first appeared on John D. Cook.

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