Using a Monte Carlo approach we generate the probability distribution of points in a game of Midnight. This project started with the desire to answer the question, "What are my odds of rolling a perfect game?". Using a Monte Carlo simulation we were able to answer that question and many more.
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The odds of rolling a perfect game with 6 dice is
~5.2%
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The odds of not qualifying with 6 dice is
~8.3%
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The odds of rolling a perfect game with 5 dice is
~8.0%
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The odds of not qualifying with 5 dice is
~19.8%
.
std 4.407029
min 0.000000
25% 11.000000
50% 14.000000
75% 16.000000
max 24.000000
count 1000000.000000
mean 17.791511
std 5.943059
min 0.000000
25% 17.000000
50% 19.000000
75% 21.000000
max 24.000000
count 1000000.000000
mean 9.269614
std 4.486434
min 0.000000
25% 7.000000
50% 10.000000
75% 12.000000
max 18.000000
count 1000000.000000
mean 11.372786
std 6.075701
min 0.000000
25% 10.000000
50% 13.000000
75% 16.000000
max 18.000000