Once we have gained some facility in thinking about maximally exploita- tive ranges, we can put it to use to gain strategic insights. There is an exer- cise to help in doing this which we have dubbed the equilibration exercise for reasons which will become clear shortly. It is a particularly effective way to practice developing exploitative strategies and to think about how this material might be used to improve your own play. The exercise goes as follows.
1) Consider a situation
It is helpful to visualize your situation explicitly as a tree. Draw it out. It can be either a full decision tree, or you can focus on one subtree. That is, it may start in a particular preflop or postflop spot and consider only the play for the rest of the hand. If this is unclear, our examples should help. 2) Specify a strategy for one of the players, Player 1
Specify ranges for all decisions in the tree for one of the players. These ranges might represent your default play in the spot, or how you expect a specific opponent to play, or what you think most players might consider “standard”. Your choice will depend on what you want to learn.
3) Find Player 2’s best response
The next thing to do is to find the most profitable way for the other player to respond, and to find the expectation of his new strategy.
the situation. Then, here you will find what opponents should be doing to best exploit you. Consider the following questions.
♠
Is Villain’s best response making a lot of money versus you? (That is, is your default strategy very exploitable?)♠
What might you notice in terms of Villain’s statistics, frequencies, hands shown down, etc., if Villain was exploiting you in this way? These are things you should look out for at the table.♠
It is important to realize how your default play is exploitable and be wary of being exploited. Do you often see players in your games making these adjustments?Thinking about the incorrect adjustments which Player 2 could make is very helpful too, but not our primary focus presently.
Suppose now that you started out (in 2.2.2) by considering an opponent’s play in the spot. You can ask yourself questions similar to those above to similar advantage. You may also simply start out with the plays of stan- dard player stereotypes. Additionally, it is often helpful to work out strate- gies for combating standard plays that are popular with players in your regular games. Is check-raise bluffing paired flops a common trick in your player pool? How should you adjust and counter-adjust?
4) Find Player 1’s best counter-adjustment to Player 2’s adjustment, etc. Now, go back and find the original player’s best response to his opponent’s adjustment. Then repeat. It is often enlightening to go back and forth a few times, looking at the players’ strategies and answering the same ques- tions.
It is important to keep in mind, however, that the worse your opponents are, the less relevance these later iterations will have to a particular game- play situation. Suppose you start out by identifying Villain’s play in some spot and make an exploitative adjustment. How should Villain respond? The adjustment found by the equilibration exercise is his best choice only
if he believes that you made your first adjustment correctly. Afterwards, how should you re-adjust? You can only rationally trust the second ad- justment found by the equilibration exercise to be your best response if you know that Villain knows that you correctly made your first adjustment and you believe that your opponent correctly found the best response to that. And so on. In fact, the terms perceived ranges and perceived strategy refer to what Villain thinks your strategy is. In practice, if you are trying to stay one level ahead in this adjustment process, it is Villain’s response to your perceived strategy that is most important.
When choosing spots to analyze in this way, do not focus merely on special or uncommon situations. Every single situation which arises or decision you have to make can be approached in this manner, and the more common the spot, the more money you will make in the long run by playing it correctly. Finally, the way games play in certain card rooms is always changing. It is good to go through this exercise whenever you notice that some move or tendency is becoming more or less popular in your player pool.
The strategies themselves are the most valuable part of this exercise, but we saw earlier that the process of finding them is nontrivial. However, in many cases, the simple process of setting up the problem can lead to im- portant insights. Hero’s best response to his opponent’s strategy will often be clear after simply specifying the decision tree and the opponent’s strat- egy. This is because almost all players’ strategies have large leaks which become apparent when they are written down and looked at closely. In practice, these players are saved primarily by the hidden information as- pect of poker.
For example, suppose that Hero is raising his SB with a wide range of hands, and Villain is 3-betting from the BB fairly frequently. In one particular pot, Hero calls a 3-bet, and the flop comes A♠-9♥-3♣. Suppose that Villain’s strat- egy at this point is to bet the flop 100% of the time, and then, if called, to check and fold to a turn bet whenever he does not have an ace or better. This probably describes, with good accuracy, the strategies of many mediocre tight-aggressive players and is likely to work well for them against many opponents, at least until their tendency is found out. Once you have it, how- ever, Hero’s maximally exploitative postflop play becomes obvious for a
wide range of stack and bet sizes. He should call the flop bet 100% of the time and then bet his bluffs on the turn when checked to.
Finally, calculating exact best response strategies manually can be tedious, especially when considering decision trees which include many strategic options, cards to come off, etc. A computer program is thus very useful for solving these situations. All of the game theoretic calculations in this book were performed using custom software. However, there exists publicly- available software which is capable of doing exactly what we are discuss- ing in this section: defining an approximate decision tree, defining one player’s strategy, and finding his opponent’s best response. Using a soft- ware package to find the exact answers is also helpful for testing one’s in- tuition. We can first try to “solve” a situation using our best guess, and then calculate the exact strategies to see how close we were.