02 Nov 2024 Advanced This material is for experienced players combinatorics GTO ranges Today, we’ll discuss mixed strategies based on the concept of Nash Equilibrium in game theory. Mixed strategies are essential in modern poker, and understanding how to use them effectively can take your game to the next level. What is a Mixed Strategy? In GTO, mixed strategies occur when multiple actions have the same expected value (EV). In poker, when both players are using optimal strategies, a mixed strategy — combining checks and bets — is often necessary. If you always choose the same line (action), you become predictable and exploitable. Let’s explore why mixed strategies are crucial and how predictability can lead to exploitation. Rock-Paper-Scissors Example A common example for understanding mixed strategies is the 'rock-paper-scissors' game. Here, a mixed strategy means using rock, paper, and scissors equally, at 33% each. Any deviation from this balance makes you exploitable, leading to losses in the long run. For instance, if your opponent uses rock 40%, scissors 30%, and paper 30%, you can counter by using only paper, thus winning more often. This illustrates the importance of a balanced mixed strategy. Now, let’s see how this applies to poker. Example in Poker In many poker spots, the highest EV is achieved using a mixed strategy. Here’s an example: Scenario: Stacks: 100bb each Preflop: BTN raises to 3bb, SB 3-bets to 10bb with A♥5♥, MP calls Flop: A♠8♦7♠, pot 21bb SB ? What is the best play for SB here? Should you bet every time with top pair? The correct play for SB is a mixed strategy of checking and betting. Betting every top pair means top pairs are excluded from your checking range, allowing your opponent to exploit you by aggressively betting against your checks. Like in rock-paper-scissors, balance is essential in poker. The actual GTO SB results are as follows: You can see that A5s is a mixed strategy with green (check) and purple (bet). Pure Strategies Apart from mixed strategies, there are also pure strategies. Pure strategies involve taking a single action that has the highest EV, rather than mixing actions. Scenario: Stacks: 100bb each Preflop: BTN raises to 3bb, BB calls with 3♦3♠ Flop: 9♦5♣3♥, pot 6.5bb BTN bets 2.15bb (33%) BB ? Here, BB should always raise. Unlike mixed strategies, pure strategies call for a single, mathematically correct action. In the actual GTO solution, 33 is solid blue, so raise is a correct option: Even if you raise all of your 33 sets here, you won't be exploited by the BB. The raising range includes straight draws and backdoor flush draws, and if the BTN folds all of his hands that are weaker than the set when he is raised, he will be exploited by the BB instead. Therefore, a pure strategy makes it correct to take a particular action. However, pure strategies are rare in optimal poker, and mixed strategies are the norm. Benefits of Mixed Strategies The main advantage of mixed strategies is that they make your range harder to predict. Even with the same hand, different actions make it harder for your opponent to narrow down your range, giving them fewer chances to exploit you. Is Mixed Strategy Always Correct? If you’re wondering whether memorizing GTO solver solutions makes poker easy, the answer is no! Memorizing all solver solutions is impossible, and they are only valid for specific settings (e.g., 33% and 75% bet sizes, 5% rake). Real GTO allows for infinite bet sizes and minimal errors, making it extremely accurate and complex. Since humans can't come close to playing perfect GTO, both large and small mistakes happen, and exploiting these often yields the highest EV How to Learn Mixed Strategies? Using GTO Wizard is the best way to learn mixed strategies. While analyzing with GTO+ or PioSolver can be helpful, GTO Wizard allows you to practice by adjusting frequencies and seeing how close you are to the correct strategy. Conclusion Mixed strategy is a vital skill in poker. Large deviations from the correct frequencies can make you exploitable by skilled players. Keep your strategy balanced in a competitive environment, and throw balance out the window if you're playing with recreational players.
