Why Study With A Solver?

Poker is difficult to study because the result of a hand does not always tell you whether it was played well.

You can make a bad bluff and get a fold. You can make a good call and lose. You can value bet correctly and still run into the nuts. If you judge your decisions only by whether you won the pot, it is very difficult to improve.

A solver gives you a way to study the decision itself. Instead of asking “Did I win this hand?” you can ask “What does a strong strategy look like in this spot across all my hands, and how close was my decision?”

The solver provides truth in a game of imperfect information.

What Is a Solver?

Game Theory Optimal (GTO) refers to a strategy that is mathematically unexploitable. A solver is a powerful piece of software that computes these strategies using proven algorithms.

A solver does not guess what an opponent happens to have. It works from the full situation:

• Hero/villain ranges
• Stack depth
• Pot
• Board
• Available bet sizes
• Rake structure

From there, it shows how each player’s range wants to play. The solver’s strategy is unexploitable – no matter how villain plays, a GTO strategy cannot be exploited, even if villain knows our exact strategy.

Toy Game: KK vs. AA, QQ

To understand what a solver is trying to do, let’s start with a simple river game:

You reach the river on 5♠6♠7♥8♦T♣ and your opponent checks.

• The pot has 100 chips
• You each have 100 chips in your stack
• Your opponent has K♠K♥
• You are randomly dealt either A♠A♥ or Q♠Q♥

What should your strategy be to win the most chips?

Let’s try always checking: You win half the time at showdown. With AA you win 100 chips. With QQ you win 0 chips. The EV of always checking is (100 × 0.5) + (0 × 0.5) = 50 chips.

Let’s try always betting 100 chips: Your opponent’s best strategy is to always call (can you figure out why?) With AA you win 200 chips. With QQ you lose 100 chips. The EV of always betting is (200 × 0.5) + (-100 × 0.5) = 50 chips.

Let’s try always betting AA and bluff 10% of your QQ for 100 chips: Your opponent’s best strategy is to always fold since your value to bluff ratio is 10:1 and their break-even percentage is 33% which is how often their hand needs to win to profitably call. With AA you win 100 chips. With QQ you win 100 chips 10% of the time and win 0 chips otherwise. The EV of this strategy is (100 × 0.5) + (100 × 0.1 + 0 × 0.9) × 0.5 = 55 chips.

How Can We Find The Best Strategy?

The Game Theory Optimal strategy for you to play is found by making the opponent indifferent between calling and folding. Notice how if we increase our QQ bluffs to 20% our opponent’s best response is still to fold every time, and our EV increases to 60 chips. So we must dial up our bluffs until the opponent is indifferent.

A bet of 100 into a pot of 100 gives our opponent 2:1 pot odds, or a break-even percentage of 33.3%. To have 33.3% of our range composed of bluffs, we must bluff 50% of our QQ.

If our opponent always calls, our AA wins 200 chips and our QQ loses 100 chips half the time and wins 0 chips the other half (when we don’t bluff). Our EV is (200 × 0.5) + (-100 × 0.5 + 0 × 0.5) × 0.5 = 75 chips.

If our opponent always folds, our AA wins 100 chips and our QQ wins 100 chips half the time and wins 0 chips the other half. Our EV is (100 × 0.5) + (100 × 0.5 + 0 × 0.5) × 0.5 = 75 chips.

Any mixing of our opponent calling and folding also gives us the same EV of 75 chips. Some other considerations:

• In a perfectly polarized nuts or air situation like this, the all-in bet size is the highest EV bet size to use.
• Our opponent’s GTO response is to call exactly 50% of the time because our alpha is 50% and them calling at that frequency makes us indifferent to bluffing or checking back QQ. If they call more or less often, we can adjust our bluffing frequency to win more than 75 chips.
• We should always bet AA because betting is strictly better than checking: If we bet we might win more chips. If we check we definitely do not win more chips.

Why Solver Study Helps

This was a long explanation, and don’t worry if some of the details felt a bit complicated. What matters is that you understand the concept of an equilibrium strategy: a strategy that maximizes your winnings even if your opponent knows your exact strategy and plays optimally against you.

It is often not the case that your opponent plays anywhere near equilibrium. In that case, an equilibrium/GTO strategy will gain EV even before you start adding player-specific exploits.

Practical GTO

Equilibrium solutions can be computed using powerful software, but no human could ever dream of mimicking it perfectly. Instead, we study GTO to understand the principles so we can play a rock-solid strategy and identify the holes in the strategies of our opponents.

GTO Genesis is designed to make this process easier. With high-quality No-Limit Hold’em solutions, clear strategy views, reports, and other tools, you can build practical heuristics from real spots you will face at the tables.

Now that you have an understanding of what GTO is actually doing behind the scenes, the next step of the Microstakes Plan is to get you a bit of experience actually playing Microstakes. (to be continued)