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
This math seems right to me, but perhaps a different perspective will help you accept the result.
You want to lock in as many dice as possible towards you large straight. You wouldn’t want to pick up all the dice and start by rolling all of them – your strategy is a bit like going back towards rolling all the dice again.
Another way to think about this is your strategy allows two ways to achieve the large straight, but the chances for each is less than the one way your wife’s strategy has to achieve the large straight.
I hope these perspectives help.
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