In chapter 2 of Playing The Player, Ed Miller explains the concept of optimal poker and contrasts it with both ABC strategy and real-world exploitative play.
Poker as a Mathematical Problem
Miller begins by framing poker as a mathematical system. While players do not need to perform calculations constantly at the table, the game itself can theoretically be solved using mathematical analysis.
Although no-limit hold’em is too complex to be fully solved with current technology, simplified models have been analyzed. Insights from these models have significantly influenced modern strategy and improved the overall skill level of top players.
If poker were fully solved, the resulting strategy would represent what Miller calls “optimal poker.”
What Optimal Poker Means
An optimal strategy would have two defining characteristics:
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It would break even against itself.
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It would be unbeatable over the long run by any inferior strategy.
In no-limit hold’em specifically, Miller suggests that optimal play would be highly aggressive. Since strong hands are relatively rare, aggression generates value through fold equity. As a result, optimal play would involve frequent betting and raising.
However, because such aggression must be balanced, optimal strategy would also require calling down more often than most players are comfortable with. Two optimal players competing against each other would frequently build large pots and exchange money back and forth at a pace that might seem excessive to typical players.
Why Optimal Play Isn’t Always Best in Practice
Miller then makes an important distinction: optimal strategy is mathematically sound, but it is not necessarily the most profitable approach in typical small-stakes games.
Against weak opponents who make predictable errors, strictly optimal play may include actions that appear unnecessary or inefficient. For example, balanced bluffing frequencies or marginal calls might be theoretically required to prevent exploitation—but these adjustments are unnecessary against players who are not capable of exploiting imbalances.
In fact, reducing certain theoretically required plays—such as bluffing too often against players who call excessively or calling too frequently against overly tight opponents—can increase profits.
Exploitation vs. Optimality
The key takeaway is that exploiting predictable mistakes can generate more profit than adhering strictly to optimal balance. While an optimal strategy cannot be beaten, it also does not maximize earnings against flawed opponents.
Miller emphasizes that most players do not know the exact optimal strategy anyway. What they can do, however, is identify recurring mistakes in others and adjust accordingly. The better a player becomes at recognizing and exploiting these errors, the greater their edge.
In this way, adaptive and exploitative play offers higher profit potential than both rigid ABC strategy and pure theoretical optimality.