Quote:
Originally Posted by cuserounder
If they're not playing straight up to maximize their own EV, then they're actually colluding, none of this back and forth matters at all, and the third player has WAY less than his ChipEV due to the chip dumping and whipsawing that can occur.
To clarify, whipsawing IS an effective collusion technique in a WTA SNG because it directly reduces the chip EV of the whipsawed player. Chip dumping is not an effective technique under WTA.
Quote:
I know how ICM works in WTA vs. paying multiple spots.
A) People say these are commonly chopped heads up.
B) Trooper and Harry are chopping 50-50 regardless of chip stacks.
Hence, there is ICM for Trooper and Harry. This means that their joint tournament equity does not always equal their joint chip equity. If they're not maliciously colluding with team play it could make their stacks worth less at times, but it also means that the short stack is playing tighter than he should in a winner-take-all... This means the third player will be blindly going up against a different set of ranges than he realizes. It also means that if Villain 1 is short stacked and Villain 2 is the chip leader, a shove against the other Villain on the team is very different than a shove against the victim... Even if the calling ranges are the same, etc.
Throw in a little soft play in blind vs. blind spots and it makes a MASSIVE difference.
I suppose you could say that Trooper and Harry are creating an ICM distortion between themselves, but this has no effect on the ICM value of an opponent's chips. For Trooper, his tournament equity if always = 50% (his chip EV + Harry's chip EV). For all opponents, their Chip EV = tournament EV. Soft play between Harry and Trooper makes no difference because they are just passing chips between themselves and this doesn't alter their collective EV.
And the fact that Harry and Trooper will always make a deal heads-up makes no difference. Let's say the game is 3-handed between Harry, Trooper, and Villain, and each has 1/3 of the chips. Harry and Trooper should collective have 2/3 of the tournament EV, regardless of whether they are making a deal.
At some point, the tournament will get heads up:
- 1/3 of the time, it will be heads-up between Trooper and Harry. In this scenario, the partnership has 100% of the tournament EV.
- 1/3 of the time, it will be heads-up between Trooper and Villain. In this scenario, the partnership has 50% of the tournament EV. (Of course, whoever has more chips will actually have more EV, but since they are starting the scenario with the same chips, it is random who will have more chips and how big a lead they will have, and all these random scenarios will reduce to 50/50.)
- 1/3 of the time, it will be heads-up between Harry ad Villain. In this scenario, the partnership has 50% of the tournament EV.
So, over all possible heads-up scenarios, the partnership has 1/3*100%+1/3*50%+1/3*50% = 2/3 of the tournament EV.
We could repeat this with unequal stacks, but it become a little bit difficult to sort out without a simulation. Let's do a simple one, where Trooper has 2 chips, Harry has 1 chip, and Villain has 1 chip. The partnership should have 75% tournament EV.
Let's say on a given hand, one random player transfers a chip to a random player:
- 1/3 of the time, Villain loses his chip, giving the partnership 100% of EV
- 1/6 of the time, Harry loses his chip to Trooper, leaving the tournament heads-up with Trooper having 75% of EV
- 1/6 of the time, Harry loses his chip to Villain, leaving the tournament heads-up with Trooper having 50% of EV.
- 1/6 of the time, Trooper loses a chip to Harry, leaving Harry in the lead, but the partnership has the same number of chips, so EV doesn't change
- 1/6 of the time, Trooper loses a chip to Villain, and now Villain has as many chips as Trooper/Harry combined, and presumably 50% of tournament equity.
Let's call the partnership's equity X. We thus get:
X = 1/3 + 1/6*3/4 + 1/6*1/2 + 1/6*X + 1/6*1/2
5/6*X = (8 + 3 + 2 + 2) / 24 = 15/24
5X = 15/4
X=3/4
So over all scenarios, the partnership indeed has 75% equity.