Quote:
Originally Posted by Didace
And how does that hurt you?
Okay, I think I got it.
For the sake of the math, assume position and skill have no value and each player has exactly the same chance of winning each hand regardless of position.
Let's say the blinds are 1 and 2. You're playing 5-handed. Each player's EV of the blinds for each hand is (1+2)/5 = 0.6, but each player pays 3 for every 5 hands, so the -EV of posting blinds is -3/5 = -0.6 per hand, so it evens out.
This player comes in and makes the game 6-handed for 3 hands (can't come in on the button), plays his CO, HJ, and UTG hands and leaves. During that time, he never pays a blind. Now his EV of the blinds each hand is (1+2)/6 = 0.5. But the -EV of posting the blinds is 0 because he never does it. So his net blind EV is +0.5 per hand.
So it holds that for the other players their EV of the blinds is (1+2)/6 because there are 6 players each hand while he's there, but once he leaves, the EV of posting the blinds is -3/5 = -0.6 because he's gone again. So for those that post blinds while he's there then play after he's gone, they got one less hand of EV of the blinds of 0.5.
So let's look at the hands for the person in the BB when he sits. Hand 1, you post 2, and have 1/6 chance of winning it and the SB, so your EV is (-2+1/6*3) = -1.5. Your SB hand you post 1, so your EV is (-1+1/6*3) = -0.5. Then in your BTN hand your EV of the blinds is 1/6*3 = +0.5. Then the guy leaves. Your CO hand your EV of the blinds is 3/5 = 0.6 again and same for the HJ, but then you are in the BB again instead of getting an UTG hand. So for that round, that players total EV relative to the blinds is -1.5-0.5+.5+.6+.6 = -0.3 for that 5-hand round.
So in a 6-handed 1/2 game, we are talking about -30 cents over 5 hands for the 5 wronged players and +$1.50 for the guy that dodged the blinds.
I hope I got this right.