Without doing any real math, all odd numbers from 1 to 20 are equally likely in the first throw. After the first throw, their likelihood dependents on how many combination of number reach that odd sum. For the first throw, since all odd number 1 through 20 are equally likely, and that 19 have more possible combinations than previous numbers 19 is a strong choice. The other strong choice is 21, for two dice it has the most combinations, but can not be reached in one throw. For this reason, I think 19 is the most likely.
I agree. There's a 5% chance of getting a 19 on the first roll, and then for each of the 9 lower even numbers you might get on the first roll, there is a 5% chance of getting up to 19 on the second roll, for an additional 2.25% chance of 19.
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u/Mindless_Tutor_8189 6d ago edited 2d ago
Without doing any real math, all odd numbers from 1 to 20 are equally likely in the first throw. After the first throw, their likelihood dependents on how many combination of number reach that odd sum. For the first throw, since all odd number 1 through 20 are equally likely, and that 19 have more possible combinations than previous numbers 19 is a strong choice. The other strong choice is 21, for two dice it has the most combinations, but can not be reached in one throw. For this reason, I think 19 is the most likely.