Myths and Misconceptions About Game Theory And Poker Solvers: Part Two

Poker Applications, usually called Solvers, are still in their early years, but have already provided some interesting ideas about a variety of poker situations. In my last column, I wrote about three common myths and misconceptions about game theory and solvers, which you can read on CardPlayer.com. Here are some more that I hope I can clear up.

Myth 4 – Game Theory leads to optimal strategies.

Many game theoretic solutions (not just those relating to poker) lead to a Nash Equilibrium. A Nash Equilibrium is not necessarily an optimal solution, it is only one where no single player can improve his results by changing his strategy in isolation.

For example, a group of players play $2-$5 no-limit at one casino every day from noon till 6 p.m. That casino rakes 5% of the pot up to $100 and charges for parking. A neighboring casino’s poker room offers a better deal. It will deal the same game, but only rake 4% and give free parking. Playing at the worse venue is a Nash Equilibrium.

There’s not one player who can’t benefit by changing his strategy and showing up at the other casino, since there won’t be a game. If the entire group makes the switch, they will achieve a new Nash Equilibrium, and a more optimal solution.

Myth 5 – Solvers can easily solve for all common structures.

Solvers use the assumption that a small blind is exactly half of the big blind. This is not always the case in live play. It is very common to see blinds in cash games of $1-$1, $1-$3, $2-$3, $2-$5 or $3-$5. Cash games can also frequently use a three blind structure. I often play $10-$20-$40 no-limit, and this often includes a big blind ante of $40. There are also games in which some players straddle. Even in tournaments, many remove the black 100 chips, and will then have a round with blinds such as 1,000-1,500. The solvers don’t account for this.

Myth 6 – Solver solutions are extremely accurate.

This is an illusion created by the precision with which results are reported or output. A typical solver may calculate the equity of one line as +4.21 big blinds and of another, quite different line as +4.22. It, therefore, adopts the second line. In reality, these tiny differences are vagaries of the particular program, and they should be ignored.

Some students make the mistake of trying to learn which play is best based on these miniscule differences. The same thing happens with split ranges. Solvers will split their ranges to be unexploitable over huge sample sizes. Don’t get caught up thinking that pocket sixes should raise to 3.3 BB 20%, 2.4 BB 43%, 2 BB 17% and fold 20%. Try to develop a feel for the fact that pocket sixes probably has close to a 0 expected value in this spot, and act accordingly.

As a side note, I frequently see players choose to split their ranges according to their current results. When they’re winning, they choose a conservative action to preserve the win, but when they’re losing, they pick an aggressive one.

Myth 7 – GTO is easy to learn and apply.

Solver output is incredibly detailed and complicated. Humans are not remotely capable of learning what the computer recommends for every situation. This is especially true when you consider that relatively small changes in one factor may lead to completely different strategies.

For example, in a tournament with 18 BB, a solver might recommend a button strategy which includes some folds, limps, min-raises and shoves. As the stack size decreases, the frequency of limps and min-raises will decline. Eventually, usually somewhere around 8 BB, the only options will be to fold or shove.

While you can’t learn everything, you should learn appropriate ranges to raise first in from every position. Decide if you want to learn a strategy that only uses one raise size or multiple sizes. Also, learn defenses against a raise from each position. Memorize these for the game you normally play. You may find that just this amount of memory work is quite arduous.

If you switch between cash and tournament that will at least double the amount you must learn. Instead, I’d recommend trying to develop a feel for what is right, instead of becoming too specific. This will also make it easier to adapt to special circumstances like a maniac in the game or being near a money bubble in a tournament.

Myth 8 – Mastering solver GTO solutions will make you a big winner.

These solutions will make you unexploitable. They will give you an advantage over players who make pure mistakes. A pure mistake is a play that should never be made.

For example, folding pocket aces before the flop is obviously a pure mistake. Unfortunately for those of us trying to grind out a living, players don’t make that many pure mistakes, and certainly few as egregiously bad as folding aces. Their most common pure mistake is playing a few hands that should be pure folds in a given situation.

If you want to become a big winner, you must learn to exploit your opponents. Solver solutions don’t teach you this, only how to avoid being exploitable, which avoids losses, but doesn’t produce wins. Exploits take advantage of frequency mistakes.

What is a frequency mistake? Just as the name implies, frequency mistakes are taking actions that should be taken much more or much less often than they should be. A player bets half the pot on the river. His opponent has a bluff catcher. GTO tells us that the bettor should make a half-pot value bet 75% of the time and bluff 25% of the time.

It also tells us that the bluff catcher should call (defend) 67% of the time. If both players do this, they will be unexploitable. But what if you know your opponent loves to bluff on the river. If his bets are bluffs half the time, instead of one-fourth the time, he is making a frequency mistake. If you follow the GTO strategy of defending 67% of the time you will miss out on a very profitable exploit. A big winner will call with their bluff catcher every time. (Although perhaps not quite every time, or else the opponent will eventually catch on and stop bluffing.)

Steve ‘Zee’ Zolotow aka The Bald Eagle or Zebra is a very successful gamesplayer. He has been a full-time gambler for over 40 years. With two WSOP bracelets, over 60 cashes, and a few million in tournament cashes, he is easing into retirement. He currently devotes most of his Vegas gaming time to poker, and can be found in cash games at Aria and Bellagio and at tournaments during the WSOP. When escaping from poker, he spends the spring and the fall in New York City where he hangs out at his bars: Doc Holliday’s, The Library, and DBA.