Quote:
Originally Posted by heehaww
In a heads-up match with no cheating, if Villain is playing GTO then it doesn't matter if his range is face-up, you still can't exploit it. In 3-way poker I think people on here have said that it's not known whether GTO exists (that's in a normal game, let alone against colluders). But in this discussion I've been wondering, what would happen if the victim were minimizing the colluders' advantage as much as possible, ie playing GTO-like?
You misunderstood me, that's not the sense in which I was using the word "theoretical". By "theoretical advantage" I mean, "if Villain plays perfectly, we still have an advantage". You can lack a theoretical advantage and still have a real-world one if real-world opponents aren't playing perfectly. That's why I agree colluders manipulating their lines have the EV advantage you're talking about (real-world villains aren't playing GTO), even though I'm not sure they'd have it against a perfect opponent.
If you're asking about colluders' advantage against a GTO-like victim, then there is one answer. But if you're asking about the colluders' advantage against exploitable villains, there are different answers for different victim strategies. I see, though, in another paragraph you mentioned averaging out the encountered villain strategies to arrive at one answer. So now I think I finally know what you're asking.
Statmanhal had a good idea posted earlier in this thread.
Quote:
Originally Posted by Abstinence
I like it! Thanks.
You could program these bots two different ways and run two seperate simulations over millions of hands. Compare results at the end and see how much the 3rd bot loses under either scenario.
During the 1st simulation, program the bots strictly, giving them an "informational advantage" only. In other words, don't let either bot know that any other bot at the table has such knowledge. Just give both "cheating" bots the other's hole cards so they have a combinatorial advantage. That eliminates the "collusion" aspect as each bot is "playing for blood" to maximize it's own EV, and yet two of them will have a combinatorial advantage.
In the 2nd simulation we could program the two bots to work together, so that they not only know one another's hole cards, but they play as a unit with the sole objective of maximizing their earn as a "team" through exploitation. The "victim bot" should not be given the knowledge that the other two are colluding ahead of time.
Of course, If that "loner bot" is smart enough to figure it out and "adjust" then good for "it".
This would clearly define both the singular informational advantage as well as the combined informational/collusion advantage under GTO circumstances.
In scenario (1) the two bots with only the informational advantage will show up with increased EV relative to the bot without such an advantage. The informationally advantaged bots EV relative to one another will be equal. In scenario (2) it is reasonable to conclude that the EV, as measured by "team big bet / 100," of the informationally advantaged+colluding bots will increase further over the non-colluding bot.
Proof is in the pudding. Anyone feel like programming?
Last edited by Abstinence; 01-31-2015 at 02:15 AM.
