- #1
FallenApple
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So say that we roll three of them and assume that the fates of the roll are all decided simultaneously. I've seen the baysean network analysis for games where one player goes first and another goes second. But what I'm talking about is a roll of three dice such that they have to land simultaneously. Say we have dice A, B, and C, say with properties P(A > B) = P(B > C) = P(C > A) =5/9. where A, B , C are the sum of the numbers on a die's faces. So does the probability not work anymore if all three have to land at the same time?
The probability of die A being greater than die B is 5/9 and the probability of die B being greater than die C is also 5/9. So A is more likely than B and B is more likely than C, so it's common to assume that A is more likely than C. But it's not since C is more likely than A. So it's non transitive and we can't tell which one is the most likely to land with the largest sum out of the three.
It seems one of them have to land first before the others in order for the other two to have meaningful probabilities.
The probability of die A being greater than die B is 5/9 and the probability of die B being greater than die C is also 5/9. So A is more likely than B and B is more likely than C, so it's common to assume that A is more likely than C. But it's not since C is more likely than A. So it's non transitive and we can't tell which one is the most likely to land with the largest sum out of the three.
It seems one of them have to land first before the others in order for the other two to have meaningful probabilities.
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