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jt1
09-07-2005, 06:20 PM
How do you figure out the chance that someone will get 2nd or 3rd place?

If there are 4 players left, with each the exact same skill level, you can easily calculate the chance of anyone of them winning first place. (current stack size / number of chips at the table)

But how do you calculate the odds of anyone of them winning second or third or coming in fourth.

thanks in advance

AaronBrown
09-17-2005, 07:03 PM
To compute this, you would need a model for Poker hands. One formula that is consistent and seems to work reasonably well is the chance of Player 0 being the next one eliminated is the sum from i = 1 to N - 1 of:

Wi/(W0 + Wi)

divided by N*(N-1)/2 where N is the number of players remaining and Wi is the stack of the ith player.

For two players this reduces to W1/(W0 + W1), which we know is correct. It's also easy to show that the probabilities add up to 1 for any N. The predictions are plausible and correspond reasonably well to computer simulations and some tournament data.

Once you have a formula for the chance of being the next player to be eliminated, you can set all the probabilities by assuming that once someone is eliminated his chips are either uniformly or randomly distributed among the other players.

It's not a perfect solution, but it gives reasonable results.