Making a Fair Deal

[Macedon]

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?

[LetYouDown]

4 to 1 = 1/5, not 1/4...I believe therein lies the confusion. With a $40 pot, a $30/$10 split is 3:1.

[Macedon]

Actually, there wasn't that much confusion with the 4:1 comment. Most of us knew right off the spot that 4:1 isn't the same as 1/4. All his comment did was muddle everyone's head with more numbers.

But is the deal that P2 proposed correct? Did it make mathematical sense?

[LetYouDown]

[ QUOTE ]
Someone else argued that since P1 was only a 4:1 underdog, his share of the $40 pot was $10

[/ QUOTE ]
This is wrong...and would be correct if the odds are 3:1.

P2's reasoning seems correct. He's taking $32 out of the pot and the other player is taking $8 out of the pot, which is a 4:1 split.

[bobman0330]

Did the other players fail to realize that this is costing them money, and that it is against the rules??

[Macedon]

Great question. Nobody seemed annoyed [at this friendly home game] about the idea of these players making a deal.

Before anyone had a chance to speak up against it, the player with Queens rejected the deal and went for his long-shot.

Result: He lost and busted out.