Hello,Statisticians! in 3-way action...

one player has a 50% chance of beating your hand and another player has an 80% chance of beating U.

What's the odds against your winning the pot?

Just wondering

Sitting Bull

10%

You beat the second opponenent 20% of the time, but of that 20%, you lose half the time to the first opponent assuming the beats are independent, so you would only win 10% total.

The probabilites will probably not operate independently in this way. If your hand is good enough to beat the second player, it is likely to be good enough to beat the first player too. So while it depends on the hand, I'm going with something closer to 20%.