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A Thought: Game Theory Optimal (GTO) (or Playing Nash)

THE WEEKLY SHUFFLE, 2014-04-27, by Erik Lemarquand

On many of the major poker forums, you may come across various poker savants speaking about how close the games are to being "solved." The solved referring to how close any one person is to knowing how to play Game Theory Optimal or Nash. This incurs two things; a) poker is a game that can be solved, and b) there are specific mathematical formulas that can be used in a various game types and settings that cannot be exploited over the long run, at best multiple players can be playing game theory optimal and come to a Nash Equilibrium. In this case it would not make any sense for a player to deviate from playing GTO or Nash because they will be exploited by the other player who is playing GTO.

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How Close To Nash Have We Come In Regard To Poker

Right now, a majority of very good poker players understand Nash shoving ranges in regard to tournaments, and shallow stack sizes. We have push fold charts, and Nash ICM calculators that can be found online. Basically, these calculators take into account the Independent Chip Model (ICM) in relation to stack sizes, payout structures, and blind levels - and comes up with Nash pushing and calling ranges. The most simple way to understand this is by using a HU (Heads-Up or one-on-one) example:

Blinds are at 100/200, and player A is on the SB (Small Blind) with a stack size of 3400 or 17BBs [3400/200= 17 Big Blinds]. Player B is on the BB (Big Blind) with a stack size of 2600 or 13BBs. If we input these statistics into the Nash Calculator we come out with: the SB shoving range being 49% with this range consisting of, 22+ Ax+ K2s+ K4o+ Q3s+ Q8o+ J5s+ J9o+ T6s+ T8o+ 96s+ 98o 85s+ 75s+ 64s+ 54s. And the BB range at 31.8%, with their calling range consisting of 22+Ax+K5s+K8o+Q8s+QTo+J9s+JTo.

In the above example, if both players are playing a perfect push/fold strategy, they would follow these percentages and ranges. However, not everyone plays according to Nash. A simple example in relation to the above example, would be if I am playing against a recreational player that I know will only shove Ax and better, then I obviously should not be calling with a lot of the range that has been dictated by the Nash Calculator. However, the recreational player having so few big blinds should figure out fairly quickly that he will lose the game in no time at all, if he employs this strategy - and will most likely try to adjust his shoving range.

Why We Are Not Close To Solving Poker

After demonstrating that there is a Nash calculator online that has figured out a mathematical formula for a perfect push/fold strategy in poker, we can assume that games like HU hyper turbos (where the stack sizes are shallow, and blind levels rise quickly), may in fact, be close to being solved. But, no one has come up with a perfect formula that takes into account deep stack sizes where players are not just shoving and folding. When we throw various raise size factors into the mix, limping, and various post flop play - we can start to imagine just how deep the rabbit hole goes. And after taking all of this into account, we might imagine that push/fold charts can be likened to kindergarten math in comparison to Game Theory being used in more complex areas of poker with more variables than just shoving and folding.

However, this is not to say that no one has figured out other areas of poker and are coming close to playing GTO in other areas like certain board textures in post flop play - just that the players that have this knowledge are probably harboring it and using it to gain an advantage at higher stakes. The first person that comes to mind when I think of a player that is constantly striving to come closer to playing GTO is Ben "Sauce1234" Sulsky, and he is currently crushing the highest HU limits online.

Conclusion

I hope this short explanation has helped some of you understand the meaning behind players using the term "GTO" or "Nash" in the poker forums. For the beginners and amateurs that are reading this - I hope this article has opened your eyes to the amount of studying that it takes to become a great poker player, and that you continue your quest to be the best. And for the advanced players, that there is still a lot more to figure out and learn in the game of poker - never start thinking that you know enough - you are probably not even close.

The Weekly Shuffle is our Sunday column with our observations and commentary on the poker world. Have an idea for an article? Leave a suggestion on the feedback page.

 


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