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
Just rolling the 3 will result in a 1/6 chance of a large straight (obviously)
Rolling the 1 and 3 together will give you your straight if you roll a (1,5),(5.6),(6,5), or (5.1).
Out of 36 possible outcomes only those 4 work. That is a 1/9
Your wife is correct. What you aren’t considering is that if one of your dice land on the right spot you are now in the same exact position as your wife started in: needing a single 1/6 throw to get the one leftover number. However you had to throw the other die to get to that point with some probability of failing, while your wife started there with no luck needed
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