Alex ‘Kanu7′ Millar on the basics of game theory

PokerStars Team Pro Online are here to help you crush. This month Alex Millar explains game theory and how it can help you win big

PokerPlayer: What is game theory?
Alex Millar: Game theory is a field of mathematics and, as the name suggests, is about how to play games well. The definition of ‘game’ is not the same as the everyday usage though and it includes anything to do with strategic decision making, like poker.

There was a guy called John Nash (there’s a film about him called A Beautiful Mind with Russell Crowe) and he won a Nobel prize for proving that in any fair two player game, there is a solution to that game which you can play, tell your opponent that you are playing and still not lose over the long run! That’s game theory.

Can you give a simple example of how game theory can be applied?
Let’s say you are playing Rock, Paper, Scissors. For that, the solution is easy – you play each of the three options one third of the time at random. Nobody can have an edge versus that strategy.

That makes sense. So how does game theory relate to poker?
In poker the solution to playing heads-up NLHE is extremely complex and would involve taking different actions with the same hand certain percentages of the time.

So let’s say you face a min-raise preflop. There will be a perfect way to play against that min-raise that you could tell your opponent you were going to play and he still wouldn’t be able to exploit you. The way you play would include a load of stuff like calling 65% of the time with K-9 suited and three-betting the rest of the time etc.

Can you simplify that?
A good way to think of it is by imagining a heads-up opponent. If you think he folds too much to a min-raise you will raise more hands to take advantage. If you think he folds too little then you will raise less hands. If you think he plays as tight/loose as he should do, there is no way you can take advantage of him – you have to just play your own strategy as well as you can.

Now imagine your opponent plays that way in every single situation on every street. That would mean he is playing game theory optimal poker and there would be no way you could beat him in the long run. If you’re playing optimal poker you want to learn how to take advantage of mistakes others are making.

Is game theory only applicable in heads-up poker or can it be useful when playing six-max or full ring?
It’s much more difficult to implement in multiplayer games whereas heads-up you are guaranteed not to lose in the long run if you use game theory optimal (GTO) poker.

But if GTO poker can’t be beat then why isn’t everybody playing this way?
Everyone isn’t playing GTO strategy because nobody knows exactly how to! Any attempt to play exactly GTO will fail because you will always have leaks [faults in your game] that other players can exploit.  

Is GTO strategy more effective the deeper-stacked you are?
I don’t think so – in fact the best players are probably much closer to perfect GTO strategy when playing quite shallow stacks heads-up. So, for example, if you were to play 5BBs deep versus the best short-stacked heads-up player in the world, he would probably be playing very close to perfectly against you and you would have pretty much no chance of ever winning [over a large sample]. But if you played 200BBs deep versus the best player in the world, he would be playing further away from GTO strategy so you would have some chance of overtaking him in skill in the long run.

Is it worth even thinking about GTO when playing low stakes heads-up?
It’s definitely worth studying and considering, but the only thing you need to be careful of is that you don’t take it too far and fail to exploit the much more obvious mistakes your opponents will be making.

Once you have built up a lot of history with a certain opponent do you have to rely more on reads and notes than playing a ‘robotic’ GTO style?
Yeah, the more you know about an opponent, the more you rely on knowledge about them. If you are playing someone for the first time that you assume is a very good player, all you can really do is play your best attempt at a GTO strategy and hope that it’s better than his attempt. But as you both find out more about each other, the two players will then adjust their strategies to take advantage of any perceived weaknesses.

How quickly would you say it’s possible to gain enough reads on a player that you can attempt to exploit them rather than ‘GTO them’?
It depends how good or bad they are. If they open shove the first three hands 100BBs deep you can probably make some judgements about them pretty quickly!

If they are world class then you may not get anything particularly useful for quite a while. It’s also a gradual process, you don’t suddenly switch from trying to play GTO to playing exploitatively, you gradually build up areas where you want to adjust your strategy while keeping the main part of your strategy as close to GTO as possible.

What advice would you have for someone who thinks this sounds interesting and wants to start approaching $100NL HU from a GTO perspective?
There’s a book I read a few years ago called The Mathematics of Poker that helped me start to get a better understanding of how GTO play works. That’ll give you some ideas and get you thinking in the right way and then I’d probably suggest talking about it with other players, and watching videos from any very good players that you know have a good understanding of it.


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