Quote:
Originally Posted by CarliC
what is GTO? looks like an interesting thread
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http://en.wikipedia.org/wiki/Game_theory
http://en.wikipedia.org/wiki/Strategy_%28game_theory%29
http://en.wikipedia.org/wiki/Nash_equilibrium
Basically its a solution (ie a well defined strategy of how to play given what is happening from opponent and your own data) that no player can deviate from without ending up in a worse result on average.
Think tic tac toe and how you need to play so that nobody wins. Knowing how to play regardless how opponent chooses to play prevents them from winning and if he/she knows what to do also you cant win either. So at this point both players are in equilibrium and they cant win unless one deviates from that solution.
In the poker case every well defined game situation will have some strategy how to play it that yields a result that cannot be reduced by the opponent doing anything. The opponent can only make things worse (for them) by not knowing hot to respond to such strategy.
Such strategy becomes valuable if one assumes perfectly rational knowledgeable opponents so it doesnt necessarily become the best choice in real life where people play making many errors as if they are not rational or knowledgeable, either because the problem itself is ultra complex or because they are bad at choosing ways that are not easily identifiable as naive after brief study. To exploit those errors you can either try to create a strategy that is fit to manipulate opponents exploiting their bad choices assuming those choices persist or select to play GTO if known (usually in the most general kinds of poker situations its not known but may be approximated). However in doing so you open the door to becoming yourself exploitable (by the very definition of GTO) because that strategy is generally different than Game theory Optimal (GTO). So you choose yourself an exploitable strategy to exploit your opponents better than what you would do if you chose a GTO strategy that would still lead to decent result but not as great in general. It is exploitable but if nobody realizes how to exploit it, its a better alternative!
So you exploit opponents 2 ways when they play non GTO themselves. You either play GTO if you know it or you create an exploitable strategy that capitalizes on their mistakes which itself is an exploitable strategy if these opponents changed and decided to exploit yourself too by adjusting properly. Eg if you steal too often against a tight player you become yourself exploitable if that player changes gears and counterattacks with a better frequency than their tight nature had them do before. If you had tried to steal optimally they wouldn't be able to exploit you but you would be losing profit (opportunity loss) because in most cases people make errors they fail to notice easily or they notice too late.
In any case knowing for a situation the Nash equilibrium solution (GTO here) allows you to play in a way that is not exploitable, basically you secure the minimum value that your situation guarantees if your opponent knew how to play ideally.
Here is an example for a 2 player game with 1 prize when their stacks are 10bb each in the push or fold mode (usually good enough for small stacks). The suggested behavior in pushing or calling ranges constitutes the Nash Equilibrium of that problem. Deviating from it will lead to worse results by the one doing it if the other remain in it.
http://www.holdemresources.net/hr/sn...6=&s7=&s8=&s9=
What this means is that if the SB pushes wider like say 80% of hands or tighter like 10% of hands the BB by maintaining the calling ranges or the pushing ranges when they themselves become SB they will do better on average.
Clearly such strategy changes as the stacks change so it needs to be updated from one move to another.
Notice also the concepts suggested above. If you know the SB is very tight you can modify the calling range and make it tighter , much tighter actually (why call a tight range with semi good hands?) . In doing so you can be exploited if the SB turned to Nash solution and pushed wider. If they cant adjust though and continue to be tight your best plan is to call tighter than Nash suggests when they push and to push as Nash suggests when its your turn to be SB. This is a different strategy than the equilibrium one that will be exploited if the opponent stopped being so tight. But until that happens its a strategy that is superior to the Nash solution. Against an unknown opponent until you establish more information you can always play according to Nash solution and this secures that you cannot be denied what your situation deserves if both played perfect.
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