Collusion absolutely provides unfair advantages (which is why it's against the rules).

Poker is a game of incomplete information. The more information you possess, the better your odds are of making the right decision.

So, in the instance of 2 poker bots colluding on a table (the 4 suits are (c)lubs (d)iamonds (s)pades (h)earts):

  Bot 1 has Ac5h and discards pre-flop (no money spent)
  Bot 2 has KcQc and calls. 
  Player 3 calls
  Player 4 calls
  All other players discard

  The flop comes up: 5c 10c 9c

At this point, Bot 2 has an excellent hand (a King-high flush), but it doesn't have the best possible hand; it's vulnerable to a higher flush due to the Ace. However, the because bot 1 & 2 have colluded, it knows with 100% certainty that it has an unbeatable hand and can play accordingly.

This is a pretty weak example, but it's the easiest I could think of without assuming any knowledge of poker. Having knowledge of cards that have been in play significantly increases a player's ability to make decisions in a way that give that player an unfair advantage.

> it knows with 100% certainty that it has an unbeatable hand

While your example is a good one, the bot actually doesn't have an unbeatable hand. Another player could have trips or 4/5 of a straight flush and hit a better hand (quads or a straight flush) on the turn/river. Or the board could pair twice and give someone a full house. Unlikely in any case, but not out of the realm of possibilities by any means.

Haha damnit, you're right. Thanks for pointing that out!

anyone with 130k hands would've caught that :)

but seriously, he means if the board is like: 2c 3c 7c Tc 4h, (not that he'd get much value from the guy with the lone Jc, though)

think of how easy squeezing is with two colluding bots.

The problem was that I changed the example after typing everything up. The first contrived example I came up with used a hand that Bot 1 wouldn't have realistically thrown away. My fault for not proof-reading :D

A more subtle example involves advertising. You want both to remain at the table. One is getting low. Then they both bet into a pot aggressively, everyone else drops out, then the richer one folds and the poor one shows the bluff. Now money has been transferred, and the table thinks one of the bots is a loose player.

Thanks, it didn't occur to me that you can discard pre-flop.

If you have N seats, you have better odds for the best hand than you do with N-1 seats, yes, but what's even more important than that is that you know what cards the other players don't have. You have considerably more information, and this is absolutely essential. Collusion is the big problem with bots, not just smart logic.

I haven't played Hold 'em since fixed limit died (RIP party poker) but knowing even just two additional cards would be a tremendous advantage. You have an easy fold in small pots if you know you only have 5 outs vs 7 (overcard and gutshot draw). Hell you probably couldn't even be beat in the short run if you knew of 4 additional cards in addition to your hole cards.