[WhiteWolf]

[ QUOTE ]
Am I calculating this correctly? If there are 4 other players in, and I estimate my chances of beating them individually as:
70%
90%
80%
95%

then my chance to beat ALL of them is about 48%

If I'm 80% against each player, I'm just under 41% to beat them all.

Correct?

Thanks
LL

[/ QUOTE ]

Your calculations are correct, *IF* your matchup against each player is independent (ie your chance that you beat the first player does not affect the chance that you beat the second). However, you cannot always assume the matchups will be independent.

To use poker to illustrate this, hands in 7-card stud are mostly independent, so the above assumptions (mostly) apply. However, hold'em hands, which all share the same 5-card board, tend to run closer together. As a result, the independence assumption does not apply. For example, AA all-in preflop against 1 random hand is usually around 80% to win. Using an independent model, you would expect the chance of winning against 9 random hands would be close to 13% (barely +EV). However, since the final hand values of your opponents are somewhat dependent on eachother (ie if there are not 3 to a flush on the board, no one beats you with a flush), your true chances in practice are around 30% (hugely +EV).

HTH,

The Wolf