on the odds of rolling two successive yahtzees in two rolls ( or life in the driftless region ).

so, mister koppa ( proprietor of the heavy duty press ) and i ended an exciting evening for two middle-aged guys by playing a round of yahtzee.

it came down to the final two turns of dice rolling and neither of us had rolled an “any yahtzee” ( defined as all five dice have the same value during a player’s turn of three rolls of 5 dice).

mister koppa got a yahtzee in two rolls on his turn and i promptly responded with a yahtzee in two rolls on my turn. neither of us had ever seen anything like that happen. ever. and it made me wonder what the odds were of it happening.

most of the yahtzee probability sites seem to agree that the odds of rolling an any yahtzee after two rolls is 1.3% or about 1 in 75 turns, which means you might rightly expect to get a yahtzee on two rolls about every 6 games ( with 13 turns per game ).

but what are the odds of rolling two successive yahtzees in two rolls? isn’t it 1.3%*1.3% or 0.02% or 1 in 5,000 turns?

if so, that’s just another night of improbability in the driftless region.

and, yes, i won.

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