collusion odds calculation

ive been playing more online poker than i usually do and have had a few times recently where i am almost certain collusion was happening. after the last time i started thinking about the odds and advantage of it and came up with a scenario i would like to calculate the odds for but cant figure out how to do it.

when playing texas hold 'em heads up, before looking at the hole cards, each player has a 50/50 chance to win right? not accounting for the probability of a chopped pot, im not sure what that is. but looking at it from the point of view of two people colluding in a three handed game (2vs1) what would the odds of winning be for the colluders assuming that they looked at their cards and played only the hand with a higher preflop percentage.

for the purposes of this analysis i am making several assumptions
1. Every the hand is played to the end.
2. one of the hands will be played each time no matter what. for example if the two hands were 7-2 & 7-3, both off-suit, the 7-3 would be played and the 7-2 folded.
3. ONLY the hand with the higher preflop % will be played. ex AK suited & pocket 8's, the 8's would play and the AK folded.
4. in the event of duplicate hands (ex. both have KQ suited) one of the hands is still folded.
5. there is no knowledge of the cards held by the opposing player.

does anyone know how to calculate the odds for something like this? i know its not the same odds as if both hands were played (2vs1) all the way out, but i would also think it has to be better than the odds of 1vs1.

thanks

Quote: sdgambler

ive been playing more online poker than i usually do and have had a few times recently where i am almost certain collusion was happening. after the last time i started thinking about the odds and advantage of it and came up with a scenario i would like to calculate the odds for but cant figure out how to do it.

when playing texas hold 'em heads up, before looking at the hole cards, each player has a 50/50 chance to win right? not accounting for the probability of a chopped pot, im not sure what that is. but looking at it from the point of view of two people colluding in a three handed game (2vs1) what would the odds of winning be for the colluders assuming that they looked at their cards and played only the hand with a higher preflop percentage.

for the purposes of this analysis i am making several assumptions
1. Every the hand is played to the end.
2. one of the hands will be played each time no matter what. for example if the two hands were 7-2 & 7-3, both off-suit, the 7-3 would be played and the 7-2 folded.
3. ONLY the hand with the higher preflop % will be played. ex AK suited & pocket 8's, the 8's would play and the AK folded.
4. in the event of duplicate hands (ex. both have KQ suited) one of the hands is still folded.
5. there is no knowledge of the cards held by the opposing player.

does anyone know how to calculate the odds for something like this? i know its not the same odds as if both hands were played (2vs1) all the way out, but i would also think it has to be better than the odds of 1vs1.

thanks

in poker, collusion is more than your impression of choosing the better hand amongst the 2 persons to play.
i think it's more about betting and squeezing money out your opponent or forcing them out.

Quote: andysif

in poker, collusion is more than your impression of choosing the better hand amongst the 2 persons to play.
i think it's more about betting and squeezing money out your opponent or forcing them out.

I would have to agree. Even at the highest skill levels of poker, how often do you see the highest EV hand, or even the best hand after the flop, fold because of position, bet sizing, pot odds, relative stack size, etc? Happens a LOT. What also happens a lot is that the best EV hand isn't the best playing hand come the community cards.

So maybe there's an edge to be captured by best EV out of 2 vs. your 1 hand, but it seems to me to be slight at best, especially if you're not the only 3 at the table, but even then (per your stated conditions). I think that, in the normal course of evaluating your stay or fold pre-flop, if the 2 always stay with the better EV hand, a lot of times they're staying on a hand that normally (and more wisely) would be folded, even if you're virtually playing heads-up with its slightly wider range of playable hands.

Quote: andysif

in poker, collusion is more than your impression of choosing the better hand amongst the 2 persons to play.
i think it's more about betting and squeezing money out your opponent or forcing them out.

Of course that is true, but it also does not answer the OP's question. There will be someone here who can answer it... I am not one of them, but I'll guess you win 63% of the time in the scenario the OP lays out..

Which is a better hand, 89s under the gun, or 78s on the button? I am pretty sure I would rather have the second than the first. Collusion isn't that easy.

Evidently you think collusion is limited to playing the best hand or raising when you partner has a good hand. Those are chump plays from poor players. Successful collusion is much more simple. I want to know what cards my partner has. In online that is easily done. Now I know my King high flush is the nuts, if he had A of that suit. I will fold small pairs if he has a matching card.
If he folds 2 suited cards and 2 of that suit are on the flop, I know odds are less than apparent for anyone on a flush draw. All i want is to win 2 or 3 extra pots per hour.
After Black Friday, I expected too see new players in poker room. All I saw was low lives and cheaters. Had no doubt what they had been doing online.

Guys i understand that there is a lot more that goes into collusion. if two people are doing it correctly, betting and reraising at the right times, the cards are largely irrelevant. However, that is not what i asked. So if you could stop overanalyzing and actually try to answer the question i would appreciate it. I did forget to mention in the parameters that for this analysis position is irrelevant, but i think you could figure that out if you actually read it.

Quote: SOOPOO

Of course that is true, but it also does not answer the OP's question. There will be someone here who can answer it... I am not one of them, but I'll guess you win 63% of the time in the scenario the OP lays out..

thank you soopoo, i had the exact same thoughts after reading the other responses. I like your guess, i think it is also somewhere in that area.

I am also very interested in how this type of analysis would be performed, and believe it could have other implications.

Quote: sdgambler

Guys i understand that there is a lot more that goes into collusion. if two people are doing it correctly, betting and reraising at the right times, the cards are largely irrelevant. However, that is not what i asked. So if you could stop overanalyzing and actually try to answer the question i would appreciate it. I did forget to mention in the parameters that for this analysis position is irrelevant, but i think you could figure that out if you actually read it.

I did read what you wrote, but I'm not sure you read what I said. I think your conditions of playing crap hands when both should be folded, and folding an near-equal strong hand (not identical), and forcing the play of one of 2 identical hands when you KNOW improving that hand is significantly harder because you folded a hand that fit with it (which means the hand is significantly less likely to improve via community cards), negates most of the advantage you have pre-flop by knowing 2 hands (you as in one of the colluders).

I said a slight advantage, because no matter how good your two cards are, they're still only 2/7th of what you (and your opponent) will be working with, and roughly 1/3 of the time your opponent will have the best EV hand of the 3 anyway, and you're playing a nothing hand all the way to the river, while your opponent is folding his crap hands and flop misses, and not exposing as much money. I would put your colluding gain at less than 5%, maybe around 3%.

All of this is true based on your conditions, regardless of position, stack size, and the rest. I think it's possible to get closer to SOOPOO's estimate if you change your conditions, and play the better EV hand using best poker strategy otherwise (fold all crap, fold missed flops when necessary, play 2 good hands and whipsaw the fish, bet stronger when your folded cards were likely necessary to the opponent's hand, fold copy hands when they diminish each other, etc. etc.)