RPS vs. Poker
Posted by AF3
Posted by
AF3
posted in
Mid Stakes
RPS vs. Poker
poker is a worthy pursuit because "poker is not like rock, paper,
scissors" in the sense that:
The GTO strategy in rock, paper, scissors guarantees that your opponent
will not be able to improve their expectation. It also fixes your own
expectation (to zero) against every possible strategy. In other words,
if one player plays the GTO strategy of strategy of Rock, Paper,
Scissors, both players have zero expectation. End of story.
Vs.
In poker, it is often claimed that the GTO strategy guarantees that the
best which your opponent can do is tie you, and they will lose money by
deviating from the GTO strategy (so long as you are playing GTO).
Certainly, this isn't true of all toy games which are designed to mimic
poker. The Half-Street Clairvoyance Game with 50% Nuts/50% air for the
attacker, for example, gives the same results as Rock, Paper, Scissors.
When either player plays their end of the equilibrium, it fixes the
expectation of the other player's strategy.
What is it about the structure of full-street poker which makes it
different than Rock, Paper, Scissors? Is the statement that "deviations
from GTO against a player playing GTO will lose expectation" in poker
even accurate?
Is there a term for games which have the property of Rock, Paper, Scissors, and games which have the property of poker (if in fact the above description of poker is true)?
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For any game which has strategy choices that should be played 0% at equilibrium, the GTO strategy wins against a non GTO one that uses one of the 0% options. Strategies that should never get played are called dominated strategies. For example, folding AA preflop is a dominated strategy in nlhe. Another less obvious example is that open raising to 25bb with AA is a dominated strategy too, etc. RPS does not have dominated strategies because at equilibrium [R 1/3, P 1/3, S 1/3] all the strategies R, S, P, are played with a probability above 0.
That was a great explanation and it made sense immediately.
In any constant sum (competitive) game, a strategy which uses a strictly dominated option will lose money, by definition.
The Clairvoyance game has no dominated option for OOP at the equilibrium since the GTO strategy makes OOP's whole range is indifferent, and hence we get the same results as RPS.
The Half-Street AKQ game has the quality of "real" poker in the sense that OOP has the (dominated) option of check-calling with a Queen, and so we get a different results, and could theoretically make money playing the GTO strategy, while in the The Clairvoyance game we could not. Right?
That's right.
There are definitely many dominated strategies in full scale poker, so GTO will win substantially from all human opponents.
What was interesting about that explanation is that it shows the relationship between indifference (between various strategic options) at equilibrium and domination.
If a strategy makes one player indifferent to various strategic options, then none of those strategic options are dominated by any other one (by definition). Therefore, the frequency at which we play any strategic option to which we are indifferent does not matter (if Villain plays GTO).
We wouldn't want to do that (because then Villain could exploit us), but we're not losing money (against the GTO strategy) by playing any strategic option to which we are indifferent to playing at some totally out of whack frequency.
For the simple toy games in the first chapter of MOP on game theory, picking a dominated strategy would amount to doing something real stupid, but I guess as the game tree expands it gets more and more difficult to figure which strategies are dominated.
Thanks again, I think that was one of the few times that I've asked somebody for help with game theory and actually got the sense that they knew what they were talking about.:) I'm glad to help
IE are you saying that the vastness of the decision trees in most poker games inevitably results in many far flung dominated strategies that are extremely difficult to identify (let alone understand how to exploit)? Thus one benefit of GTO play is that (if achieved) it would relieve us of the burden of identifying and exploiting dominated strategies vs non-GTO playing villains. And that such villains would exploit themselves every time they chose to play a dominated strategy.
or is there a next step of this discussion going in a different direction? thanks in advance for taking the time to start the thread and if you can respond to my questions.
Thus one benefit of GTO play is that (if achieved) it would relieve us
of the burden of identifying and exploiting dominated strategies vs
non-GTO playing villains. And that such villains would exploit
themselves every time they chose to play a dominated strategy.
That's the whole point, yeah. I just didn't understand the definitions well enough to understand how we actually make money by playing the Maximin strategy, but as Ben pointed out, it turns out they're trivial consequences of the definition(s) at play.
OK so if GTO wins vs dominated strategies does it also win vs non dominated strategies that are played at a wrong frequency? Lets say that the GTO solution in one particular spot is to 5bet shove A5s 30% of the time and fold the rest. Would I lose vs GTO if I shoved 100% of the time?
Ok - this is my take on this situation....if 5b shoving A5s 30% is part of the GTO solution then the EV of 5b shoving is = the EV of 3b/folding. So against a player playing a GTO strategy your EV would remain the same if you chose to 5b shove A5s 100%.....however what would happen is now the GTO player could deviate to increase his EV and then that would decrease the EV of shoving A5s 100%. At least that is my understanding and if I am wrong I am sure someone will let me know.
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