Heuristics wrote:
I doubt you can find the perfect equilibrium, as the game is just too dynamic.
Do you think that the perfect equilibrium is unique? In the case of Kuhn poker for example, it exists an infinite number of equilibrium. Furthermore, what do you mean by dynamic ? If you mean your opponent can change strategy, it doesn't affect the way you compute an equilibrium. So it cannot be a reason to not find one.
Heuristics wrote:
I offload the burden of finding the optimal strategy - which can be either exploitive or balanced, depending on the opponent - to the range computation. In most situations, I have a pretty good idea of what ranges should look like based on what we know. I think the strategy is quite close to being non-exploitable (and thus the nash equilibrium) in the situations it wants/needs to be.
What range are you speaking about ? The range of cards your opponent may hold ? Or the range of cards you play ? Anyway, if you are modeling your opponent and making decision based on this modeling, your strategy is fully exploitive but far away from equilibrium and so exploitable (unless your opponent play an equilibrium strategy).
Heuristics wrote:
A good example would be pre-flop 3-betting behavior. You can either approach it mathematically, or empirically through statistics & experience. Of course, the latter approach results in faster computations and it's also easier to adjust the behavior to get maximum expected value.
The problem is your statistics and experience are opponent dependent. So you cannot compute equilibrium but surely exploitive agent.
Heuristics wrote:
The whole idea behind this is of course the polarization of your range. The more hands you raise from the bottom of your range, the more you will have to raise from the top of your range. If you want to apply a non-polarized strategy, you will have to significantly decrease your aggression and narrow down your range if you're playing against a good player or a balanced strategy.
Raising really weak hands to bluff doesn't mean you should raise almost all your hands.
Heuristics wrote:
In the end, I just believe that an unexploitable style can never be a winning one, so what is the point of finding this so much sought-after equilibrium?
An unexploitable style can never be a loosing one, so that is the point of finding it Statistics: Posted by Romesnil — Sun Mar 17, 2013 5:46 pm
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