Making a Fair Deal
This came up in a tournament home game I was playing in recently. For the sake of simplicity, I am going to round out the numbers.
Anyways...Two players go heads up late in a tournament. The next person to be knocked out does not make the final table and is OUT of the money.
Player #1, who is short stacked ($20) gets dealt pocket Queens. Player #2, who is the chip leader, gets dealt pocket Kings.
Player #1 acts first and goes all-in.
Player #2 calls.
Everyone else folds.
Before the board is dealt, player #2 offers a deal to P1. He says to P1, "I am an 8-2 favorite to win this hand. You only have a 20% chance to double up and win $40, but you also have an 80% chance to bust out. Give me $12 right now, keep $8 for yourself, and we will move on to the next hand."
There was some argument from among the other players on whether this was a good deal on a mathematical level. P2 argued that since P1 only had a 20% chance to win $, that means his equity, or break even point was only $8. Someone else argued that since P1 was only a 4:1 underdog, his share of the $40 pot was $10.
At this point, everyone was confused.
Who is right? What would have been a "fair deal" for P1?
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