Chapter 5 of 38 from Daniel Negreanu

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

Daniel Negreanu Teaches Poker

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Put yourself across the felt from Daniel Negreanu—the biggest live tournament poker winner of all time. The six-time World Series of Poker champion teaches advanced theory and practice through hand-reviews of his winning games. Learn how to sharpen your mental game through demos on reading opponents and spotting tells. Join Daniel at the table to learn how to increase your win rate, grow your ROI, and get your game “In the Money.”

See the table through Daniel’s eyes with case studies of body language and hand reviews of winning games across 38 on-demand video lessons.

A downloadable workbook accompanies the class with lesson recaps, assignments, and advanced play terminology guide.

Upload videos to get feedback from the class. Daniel will also answer select student questions.


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I was always good at poker, I've just always had a knack for reading people. This class opened up a whole new world of poker to me. I never knew how much the numbers really ment until I took this class! Thank you so much Daniel!

Awesome class I have had immediate hand reading improvement at my local game!! Cheers Dan N

If you are a seasoned recreational player looking to up your game, there is information here to help you. I bet even some pros will learn a thing or 2


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.

A fellow student

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.


When discussing fold frequency, with regard to a bet that is 3x the size of the pot, Daniel says: "you should be folding (to a bet size that big) 75% of the time. That means that you should only call the top 25% of the range of the hands that you have". My question is: when he says "you should only call 25% of the range of your hands that you have" does that top 25% range change according to your position at the table? I assume so but just want to check. Thanks in advance for your reply :)

A fellow student

i do not understand the pot odds in the example of a pot of 100 and the opponet bets 500 there is 600 now in the pot ,the pots odds are 6:5 how is that 45% ?

Victor D.

I absolutely love the math (odds) side of Holdem. Here's one that I never see anyone bring up. In a nine (9) hand game, the odds of winning at the start of each hand is just over 11%. Therefore, the odds of loosing at the start of ever hand are just under 89%. Since this combined with the rake and tips gives horrible odds, should I play Holdem? I heard that 20% of the players win 80% of the time. Is this true? If so, if you are in the 20%, thanks to the 80%. What are Holdem players in the 80% to do? Some of this is in just but I think the odds in the first paragraph are darn close. Comments?? Vic

Rick E.

I'm not completely understanding the application of fold frequency. Is it mostly for pre-flop decisions following a raise? If the FF is 25% pre-flop then should I NOT call a raise with the bottom 25% of my range? Thanks

Maxime G.

Most of the cash games take charges of between 3 to 6% of the pot, do you guys include those fees in your calculations ?

Alex U.

On the "odds to hit your draw" part of the PDF, some of the ratios have commas in them (i.e. 2,4:1). What does that mean? I've never seen a ratio written out like that


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...