My wife and I go back and forth on this one. Assume that you already have your small straight. Lets say your 5 dice are 1,2,3,3,4. To get a large straight, should you re-roll the 3, or re-roll the 1 AND 3? My wife says just the 3, because that way you only need 1 die to go your way instead of 2. I say the 1 AND 3 because it doubles your chances of getting a 5 which you need, and you still have a 1/3 chance that the second dice is a 1 or 6.
Looking for some probability experts to help me through this one.
In: Mathematics
Assuming that you’ll take the 1 or 6 on your first roll if you don’t get the five, then your odds of getting a large straight are as follows:
1/9 to get LS on first roll
7/36 to get a 5, but no 1 or 6
[1/3 to get LS on subsequent roll]
4/9 to get 1 or 6, but no 5
[1/6 to get LS on subsequent roll]
1/4 to get no 1,5 or 6
[1/9 to get LS on subsequent roll]
So your odds are (1/9) + (7/36 x 1/3) + (4/9 x 1/6) + (1/4 x 1/9) = 10/36
Your wife needs to get a 5 on either of her rolls, which would be 1-(5/6)^2 =11/36
So your wife has the better strategy, beating yours by 1/36.
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