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Re: Re: Rolling a biased dieby tomazos (Deacon) |
on Apr 13, 2002 at 13:56 UTC ( [id://158773]=note: print w/replies, xml ) | Need Help?? |
Cool algorithm. It's like a king of the hill match.
1 starts as king of the hill. ($rand = 1) 2 comes along and challanges it. Whoever wins stays on top (is assigned to $rand). Just like 2, everyone else (3, 4, 5 and 6) gets a chance. Whoever is left on top ($rand) is declared the winner. :)
To understand why the probabilities work you have to step through the algorithm backwards. ie. What is the chance that 6 (the final iteration) is going to win it's match against the king of the hill? $bias{6} / sum(values %bias), which is obvious. Now - consider the second last iteration (5). Given that 6 is going to have it's chance in a minute, and hence does not need to be included, what is the chance that 5 will win it's match? $bias{5} / (sum(values %bias) - $bias{6}). We remove 6 from the running by excluding it's weighting from the total. Update: This explanation is awful. :)
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