Do two or more players colluding against honest players gain on average more money, or not?

Question

Let's say there are two or more players that collude with each other while playing online poker against honest players. They have an obvious advantage of knowing of more cards that are in the play than the honest, non-colluding players and they can strategically bet against one another to increase the size of a pot (encouraging other players to play in hopes of winning). On the other hand, they also have an obvious disadvantage - they need to split their winnings and also stand to lose more money.

Do such players overall expect to win more money in the end, or are their cheating attempts ultimately useless? Has such a problem perhaps been analysed scientifically?

Answer 1

They have an obvious advantage and so will earn more in the long run, that's pretty clear! Also playing together and playing both separately would lead to the same amount money, so they are not risking more money just together (same argument for the profits.)

Now I don't really know to much about collusion and specifically what edge it can give you but I suppose situations such as this would be pretty profitable.

Assuming they share all the money at the end lets and imagine (for simplicity) we have only 3 players.

Colluding Player A (A) 500 Colluding Player B (B) 500 Smuck (S) 500

The hands are:

Colluding Player A (A) AA

Colluding Player B (B) --

Smuck (S) KJ

Blinds 25/50

A SB

B-BB

S- raises 150

A- Comes over the top all in.

Now lets pause and look at the two different situations. I player B was not colluding then he would fold and player S would have the following situation:

Pot odds: (700/350)=2:1 so they need a hand with 1/3=33.33% against player A to call. Now that means that they have to put player A on pockets 10 or worse or QJ or worse. This is a pretty easy fold and Player A does not get paid.

Now lets suppose that player B is colluding and now also moves all in. Now player S has this situation:

Pot odds= 3.3:1 so they need to have a hand that wins 23% of the times to make this call.

Player S is much more likely to make this call (based on pot odds) as long as they are not both holding QQ+ or AK, AJ the odds are pretty decent.

Now the colluding players should take the money and both make 250 as opposed to not colluding where player A only takes 200 a profit for both players!!

So a bit more accurately assuming a fold in the first case A make +200

In the second A make (500*0.85)/2=212.5 and so does player B (just accounting for when S wins the hand)

This is just a toy example of when it can be useful!

Thats just one example of how

Answer 2

First off, the statement in your question is not the norm:

They have an obvious advantage of knowing about more cards that are in the play than they should, and they can strategically bet against one another to increase the pot (encouraging other players to play in hopes of winning).

Almost always when players collude, they are typically protecting each other's hand, rather than trying to increase the pot size. Most of the time they are betting and raising with mediocre hands hoping everyone else will fold their superior hands. Why is this? Surely if colluders signaled to each other what their cards were, and then just played normally with that extra information, they would be better off. But most cheaters don't have the patience to wait around for their king high flush to be the stone cold nuts because they know that their partner folded the ace. Perhaps only 1 in 10-20 hands occur where it actually helps to know what their partners' cards were. So instead they try to win more pots than they normally should, by raising/reraising and scaring everyone away.

In general if players are colluding and their opponents do not know this, they have an advantage. How great that advantage is probably depends on too many factors to accurately calculate in terms of a percentage. On the flip side, if two players are colluding and another player knows this, and the colluding players do not know that the other player knows, then the other player can take advantage of this when he gets a monster hand, by just smooth calling to the colluders continuous raising.

Answer 3

Sadly, I dont know about any scientific proof, so I can give you just my thoughts.

Lets say we have 2 players, each one with a skill to win 1bb/100 hands. If they dont collude, each of them wins 1bb/100 hands = 2bb

When they start to collude, both of them get advantage as you mentioned, so lets say this increases their EV to win 2bb/hands. So they both wins 4bb/100 hands.

The disadvantages you mention are not disadvantages at all! Both of them now have bigger EV, so when they split, each of them get`s 2x times more money. Although they might expect bigger swings in their bankroll (only if they share one bankroll), the increased EV makes the probability of downswing much smaller.

The only situation, where colluding can be unprofitable is, when rake plays big role in calculation. For example 8 colluding players playing versus one ultra tight player can pay for rake much more, then they are able to get from tight player so overall they all loose.

Answer 4

In tournament play they definately have an advantage as they can tell the other person to fold when they have a monster hand therefore not risking their tournament life.

They can also very easily help to stack the other person up a bit if they are getting low on chips to keep them in the tourney that little bit longer etc.

As far as in cash games, I dont know how much more you can win this way. In cash people tend to play a lot looser anyway, so you might be able to build bigger pots say if person A raises and person B flat calls. You might get a few more callers because of pot odds. But you have no clue what hands your opponents are limping in with. They could be playing 2 7 for all you know. I know the same could be said for in tournaments, but people tend not to make strange plays with that sort of hand in a tournament, as much as they do in Case.

Answer 5

I know several people who've been asking about this for years.

Intuitively - you'd think the answer is surely yes. It's also pretty easy to construct scenarios in which you'd think you'd gain an advantage.

However - the reason I suspect you don't gain a significant advantage is that, as long as I've been playing Foxwoods and Vegas - the casinos make absolutely no effort whatsover to prevent collusion. I'm no high-stakes player, but I've played tens of thousands of hands all the way up to $5/$10 NL, and I've seen dozens of instances where two or three friends, married couples, etc. would attempt to discreetly (or even indiscreetly) collude. Anecdotally - they don't seem to win at a higher rate, but more importantly - the dealers, floor managers, other players just don't seem to care. At all.

Moreover - when playing online, it would be trivially easy to collude. And why stop at two players? Why not organize six or seven players at a nine-seat table?

I can only conclude that the "powers that be" know that the advantage is, at best, negligible.

It reminds me of counting cards... If you do it REALLY, REALLY well, you gain a very slight advantage. But most people do it sub-optimally, often putting themselves at a disadvantage relative to people who don't even bother.

Answer 6

Colluding players doesn't mean the sky is falling, usually. Most people who collude are awful players and they end up losing more than the edge they earn.