Sklansky-esque Collusion Theory question (thanks NW for the idea)

[DcifrThs]

ok, so the recent collusion thread and neverwin's (rediculous) challange prompts me to write this post.

Assume 3 players A B and C are playing 3 handed high limit poker (lets say 200-400 for calculation's sake).

player A is better than player B and C.

Player A is so confident his 3 handed skillz are da best, he allows B and C to collude in any possible way over the internet (IM collusion etc.)

Player A is normally a 0.5bb/100 winner vs. players B and C at this limit.

what is player A's expectation in the collusion game in bb/100 or $/hr or whatever.

Barron

[pokerhooker]

I'm not sure you could come anywhere near estimating an expectation until you formulate the collusion strategy. I'm not sure how much discussion we want to get into regarding that, lest people get ideas, but I think it would eventually boil down to "best-handing" him.

[DcifrThs]

[ QUOTE ]
I'm not sure you could come anywhere near estimating an expectation until you formulate the collusion strategy. I'm not sure how much discussion we want to get into regarding that, lest people get ideas, but I think it would eventually boil down to "best-handing" him.

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good points. lets say B and C will collude in the following fashion:

-they split all profits/losses from the game.

-if one or the other has a big hand, B or C bet/raise/call in order to inflate the pot and otherwise trap A.

-if B and C are in a hand HU together they just check it down and split the remaining chips in the pot.

-Dealing with As bets/raises/calls after the flop though is a bit more difficult...but to bluff, A has to bet both B and C of their hands. B and C can team up to make A pay through the roof with draws or inflate the pot b/c w/ two hands (1 made 1 draw or something) the chance of making a winning hand increases. this is compensated by putting 2x the $ inthe pot but i think it works out to the colluders favor either before or after you factor in folding equity (ONE of them has to have something right? ). if A does not let up, a default may be to simply call down (one of B or C would call down) some big % of the time so that A has little bluffing ability and BandC get 2x the hands and the ability to manipulate A when they want. so to take away A's bluffing ability, BandC may need to do some serious passive defense play at times and call down a huge % of the time (which would earn A some money overall but save BandC every pot he would have won if he was bluffing and manipulates him further from being able to bluff effectively)

in terms of the NW challange:

if he thinks he has an edge in this game, i'd be willing to put a large amount of money up, as im sure others would be as well to play as high as he'd like.

Barron

[phish]

My opinion: If B and C are any decent and have any understanding of poker theory at all, then player A can never win.

Even if their collusion is as simple as playing the better of the two hands against A (unless of course they both have good hands), that will be too much of an edge for A to overcome, even if (or especially if) he knows what they're doing.

If I were in such a situation, I would actually raise very little pre-flop. I would want both hands to see the flop as cheaply as possible. I would of course still throw away garbage. But, for example, if my hands were JT in the BB and AK on the button, I would not raise the AK. Post-flop, fold the worst hand and just play regular poker with the better hand. And if A knows you're folding the worst, then you don't even need to have a hand, since oftentimes he won't have anything and you are MUCH more likely to have something since you're starting with 4 cards. You can bluff him left and right with nothing oftentimes. And even those times where you both have something, you're much more likely to have a better hand.

A cannot win. In fact he'll lose at a much faster rate than you'd suspect.

Now of course, it is possible for B and C to be morons and actually do stupid things like raising and reraising with nothing to try to drive out A when A is sitting there calling passively with the nuts.

[tongni]

The biggest advantage of collusion, if the other player knows its going on, is that it costs you 3 bets to bluff on the turn while potentially costing him 8 to call down. If you mixed up your play to sometimes only bluff bet/raise on the turn and give up if he comes along, and sometimes 4bet on turn as a bluff (or even with hands that have reasonable equity) you commit him to paying 8 bets with every hand he wants to showdown.

Imagine this:

Player A
Neverwin
Player B

On the river, Player A bets. If Neverwin calls, then we can assume he will go to showdown and then if they can beat him it will get raised behind and then he will face 4bets on the river. If they can't win, then they've only lost 1 BB to bluff at the pot. Of course, some percentage of the time he should call one bet and fold to 2 more back to him, but it would be impossible for him to get this right.

[pokerhooker]

Hi Barron,

Right, it was understood they would split the profits. What I was getting at was that since Player A knows that B and C are colluding, he should rarely choose to draw and allow him to get trapped.

B and C could choose to stay in the pot with each other, and spring to life once either of them has something worth protecting (inflating the pot), but with Player A still managing to win some of these hands, I still think the "best hand" strategy is the best option (and the easiest to employ).

[DpR]

I think player A would get so creamed even if collusion was only allowed starting on the river. B&C get 4BBs every river they know they are ahead, it is painful just thinking about this from player A's perspective. Can you imagine the tourture of constantly getting raised over and over again and having to call 4 bets on the river with your 1 pair?

[daisyglaze]

Neverwin would be getting 2/1 on many of those bets. I'm not sure how often multi bet squeeze type plays would be a good idea if the mark knows I am colluding. One of the colluding hands would need to be very strong.
The more common situation would be on the flop or turn. Most of the time only one colluding hand would want to continue, but the bet could come from either one, and the other one will usually fold after wasting one or zero bets on the squeeze.

[disjunction]

What a great question! You should read all of the responses to mine in the other thread before proceeding, though.

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Theoretical question for anyone who wants to guess -- how much is collusion worth in BB/100 in this situation if the victim knows you're doing it? If you consider this to be only a 2-player game, where one player holds two hands, that player has these advantages (1) The double bet (2) Knowledge of 2 additional cards (3) Ability to trap . Are there more? Is this really worth more than .5 BB/100? As the above hand shows, you can give your opponent on some tough decisions, but I didn't see a theoretical advantage. Now factor in that you can't be too overt. I don't get it, I just don't see the incentive to collude at limit hold'em for the risk.


[/ QUOTE ]

[pokerhooker]

[ QUOTE ]
I think player A would get so creamed even if collusion was only allowed starting on the river. B&C get 4BBs every river they know they are ahead, it is painful just thinking about this from player A's perspective. Can you imagine the tourture of constantly getting raised over and over again and having to call 4 bets on the river with your 1 pair?

[/ QUOTE ]

If, as you say, by rule the colluders can only start raising for one another on the river, their advantage is somewhat balanced by the fact that they both would have had to put in flop and turn bets the times that player A is ahead/outdraws and manages to win the pot.

The utility essentially becomes extreme value betting, moreso than trapping, as both sides are going to want to showdown a hand when it gets 4 bet on the river. Thus, the colluders need to make sure their hand is at least 7/4 favorite to win at showdown, or if it's a bluff, similar odds that he will fold his hand.