Slow day on the ambulance. Perversion Tracker.
Strange dice game? Can a math geek 'splain this? (And go here?) (Better info here.) <-- I wanna go on a trip with this guy.
Strange dice game? Can a math geek 'splain this? (And go here?) (Better info here.) <-- I wanna go on a trip with this guy.
posted by dementia at 3:20 PM
4 Comments:
So this is an interesting application of conditional probabilities. The probability that die A rolls higher than die B can be expressed as:
P(A > B) = (P(A=3) * P(B=2)) + (P(A=5) * P(B=2,4)) + (P(A=7) * P(B=2,4))
This says that the probability that die A is greater than die B is conditionally determined based on the probability that A rolls a 3 and B rolls a 2, plus the probability that A rolls a 5 and B rolls a 2 or 4, plus the probability that A rolls a 7 and B rolls a 2 or 4.
The probability that A equals a 3, 5, or 7 is 1/3. The probability that B rolls a 2 is also 1/3, while the probability that B rolls a 2 or 4 is 2/3, giving us:
P(A > B) = (1/3 * 1/3) + (1/3 * 2/3) + (1/3 * 2/3) = 5/9
Determining P(B > C) and P(C > A) is left as an exercise for the reader ;] The correct answer in all cases is 5/9, however.
On a related note, I found this interesting: Schrodinger's Pawn
Ow. Both the explanation and Schrodinger's Pawn hurt my head. Although, Nightmare Schrodinger's chess on any of these boards, would take a week to figure out who should move first. Adding any of these ideas would probably be silly.
I think we should combine a bunch of weird chess rules with the possibility of physical injury. We could call it "Extreme Chess" perhaps.
Oh, wait. Looks like someone already did that.
OW!! That hurt so much that it made the baby cry. It'll probably make his kid cry it was so bad. I think it altered my DNA so that all future progeny will wake up one day saying 'OW!' for no reason.
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