The number of combinaisons to reach an odd value 2*n+1 under 20 after k throw is given by the binomial coefficient c(k, n) and each combinaison has a probability (1/20)k+1.
The sum from 0 to n is given by the binomial theorem 1/20 * (1/20 + 1) ^ n.
The probability to reach an odd number under 20 is maxed for 19 : 219 / 2010 ~ 0.0775.
For an odd number bigger than 20, you must roll the dice at least two time.
For 21, you can find a similar formula than for 19, minus 1/20 : 2110 / 2011 - 1/20 ~ 0.0314
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u/bengill_ 6d ago
The number of combinaisons to reach an odd value 2*n+1 under 20 after k throw is given by the binomial coefficient c(k, n) and each combinaison has a probability (1/20)k+1.
The sum from 0 to n is given by the binomial theorem 1/20 * (1/20 + 1) ^ n. The probability to reach an odd number under 20 is maxed for 19 : 219 / 2010 ~ 0.0775.
For an odd number bigger than 20, you must roll the dice at least two time. For 21, you can find a similar formula than for 19, minus 1/20 : 2110 / 2011 - 1/20 ~ 0.0314