From Daniel Negreanu's MasterClass

Game Theory and Math

Daniel discusses Game Theory Optimal poker and provides tips on how to calculate pot odds and fold frequency at game speed.

Topics include: Understanding Game Theory Optimal (GTO) Poker • Use a Hybrid of GTO and Exploitative Play • Set a Baseline and Adjust • Calculating Pot Odds • Calculating Fold Frequency • Quiz: Calculating Fold Frequency


Daniel discusses Game Theory Optimal poker and provides tips on how to calculate pot odds and fold frequency at game speed.

Topics include: Understanding Game Theory Optimal (GTO) Poker • Use a Hybrid of GTO and Exploitative Play • Set a Baseline and Adjust • Calculating Pot Odds • Calculating Fold Frequency • Quiz: Calculating Fold Frequency

Daniel Negreanu

Teaches Poker

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So the latest trend or fad in poker, and the latest evolution of it, is understanding game theory optimal play. So what exactly does game theory optimal play mean? Well, essentially, what it means is you create a strategy that is unexploitable. So let's use a real life example. You all know rock, paper, scissors, right? You throw a rock, you throw paper, you throw scissors. Well, now, what would be the game theory optimal percentage to throw each one? I'll let you think about that for a second. Well, obviously, throwing one third, one third, one third would be the game theory optimal approach. The problem with that is while you won't lose, you also won't win if you stick to that-- unless you get lucky, of course. But that's not an exploitative strategy. Now, what if you find-- you notice that your opponent throws rock a lot? You start to notice a pattern of he's throwing rock. Let's say he's throwing rock every time. Well, what should you do? So obviously, you throw paper. The question is, with poker, how often should you throw paper? Do you throw paper 100% of the time? That seems logical. The problem with that is if you start throwing paper 100% of time, he notices and says, I caught on to something you're doing, so I'm going to adjust as well. So what you want to do is instead of doing 33%, 33%, 33% across the board, if he's throwing rock 100% of the time, you up your paper to maybe 40% or 45% of the time. So you're going to exploit the weakness in his strategy, but you're going to do it while he doesn't even realize you're doing it. Because every time you deviate from a game theory structure, you become exploitable as well. Another way to look at it, really, is game theory is a defensive strategy. It ensures that I'm protected. There's no way that you're going to be able to exploit me. Now, exploitative play, which is something that I've been doing for 20 years before I fully had a understanding of game theory, is always looking for the mistakes in my opponent, and going on the aggressive, and trying to take advantage of them. Now, of course, a byproduct of that is, well, if they're being perceptive, they can start exploiting me because I'm willing to give up on the defensive side to play aggressively. So it's very important to have a mix of both, starting with a baseline of game theory and then exploiting from there. So there's a debate in poker, which is which is the better approach. Should we be focusing on playing strictly game theory optimal, or should we focus on playing strictly exploitative? And I think the right answer is somewhere in the middle. So you take what you can from game theory and then adjust to your opponents. Because if you're not doing that, you're not going to maximize profit. So for example, if you have Player A, who plays game theory in a game full of recreational players, Player A is going to win. But if you're a Player B, and you're using some of that game theory, but you're also exploiting...

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Hi, I had a couple questions: In which cases should you make a decision to call or fold based on "Pot Odds" vs making the decision based on "Fold Frequency"? Or, are they two different types of methods and people should choose what suits them? Also, a question regarding the math on pot odds. Let's say I'm on a flush draw from the flop and so calculate my odds to hit, by the river, at 35%, my odds with the pot are 2:1 so based on the math I would call. However, I know that my opponent almost certainly will raise on the turn 2-4x his last bet if I do not hit my flush on the turn. Does this change the decision to call in this case or is it always right to call, from the flop, based on odds to the river? Thanks!


The statistics given for to catch a flush when you have the suits in your hand given that you have two suits on the flop is misleading. It should not be 36%, it should be roughly 20% (9/47)

John H.

I am not very good at math. Is that going to be a problem trying to understand pot odds in the middle of a hand? I kind of get the basics of pot odds, hopefully it just becomes second-nature.


I am no math wiz and all this really makes my brain hurt but am I right in saying the fold frequency of a bet is actually the inverse percentage of the pot odds? Wouldnt just looking at the pot odds as a simple ratio give you a quick and easy ball park estimate of both without the brain numbing math when "in the field"?

Michael K.

So I was playing A2 offsuit from the small blind and had a straight draw on the board. I was looking for a 3 to complete the draw, and out came the 3 of clubs on the river to complete my opponents flush. My A-5 straight got gutted by my opponents J high flush on an all in, and that was the end of my stack for the night. This was a 1/2 NL 9-max table. Should I have folded or was it a good decision? It was a new player at the table so I didn’t get to consider plate tendencies.

David S.

This lesson has cashed me many tourneys. At the end of the day, I was telling my opponents what they had as I folded JJ.

Michael K.

So I was playing some table poker last night and on one hand, I had something like J6 Suited (Clubs) and there were 3 suited clubs at the river. The villain next to me bets big and I call. He too had 2 suited clubs with an Ace. Should I have folded or raised instead? He just arrived at the table, so I couldn't gauge his tendencies prior to.

www W.

So fold frequency minus 1 = percentage of ranked hands you SHOULD play? Ex 1 - 75% fold freq. = play top 25 hands?

Leo M.

Could someone please explain to me GTO, but with a poker example instead of rock, paper, scissors. Thank you.

A fellow student

Please correct me if I’m wrong with this, but I don’t think the term pot odds really doesn’t have much to do with odds at all, and that’s where I find it confusing. It’s a ratio of a bet to a potential profit, which produces a number that, when compared to the probability of drawing the card(s) you need, tells you if a call is warranted. So, if you need to call $20 in a pot that’s $80, that’s a ratio (expressed as a percentage) of 25%. If the odds of drawing a winner is greater than 25%, you should call. If the odds are less than 25%, you should fold. Do I have this correct? Appreciate the help.