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Poker Strategy: Myths And Misconceptions About Game Theory And Solvers

Card Player Columnist Steve Zolotow Explains How Poker Solvers Actually Help Players


Game Theory was invented by the brilliant mathematician John von Neumann, who also co-authored the first book on the topic with Oscar Morgenstern, an economist. (I actually took a course in Game Theory with Morgenstern at NYU while getting my MBA.) That book was Theory of Games and Economic Behavior, published in 1947, and it does make some brief mention of poker and bluffing.

Since then, game theory has been used to analyze a variety of interesting situations including politics and elections, economics (especially cooperation and collusion between firms, price fixing), sports (finding the hot hand in basketball to which way a goalie should jump in soccer), auctions, and many other topics. Applications of game theory to a variety of subjects has multiplied, especially with the ease of using computers for complex calculations and the concept of a Nash equilibrium.

Poker Applications, usually called Solvers, are still in their early years, but have already provided some interesting ideas about a variety of situations, both common like starting hand selection and uncommon like strategies for four-bet pots on the river.

Here are some common myths and misconceptions that I hope I can clear up.

Myth 1 – Poker Has Been Solved

A game is considered solved when the best response to any move and the final outcome have been calculated. So far, only some relatively simplistic games like tic-tac-toe, rock/paper/scissors, and checkers have been solved. Neither chess nor Go has been solved, although computers are now much better than the best humans.

Heads-up limit hold’em was either solved or close to being solved. No-limit hold’em has made some progress toward a solution but has a long way to go. Other poker variants such as PLO, Omaha eight-or-better, and other mixed games are still far from solved. But the fact that no-limit hold’em has not been solved does not mean that GTO can’t provide valuable insights, strategies, and tactics that you should try to integrate into your game.

Myth 2 – All Solvers Provide The Same Solutions For Each Situation

To create a solver, the designer must make a series of assumptions and simplifications. Many of these are made to make it possible to arrive at a reasonably accurate answer without taking too much time or using too much computing power. In no-limit hold’em there are a huge number of possible bet sizes at every point, and solvers tend to choose or let you choose a few for each situation, but they don’t all make the same choices.

One example is the size of the Raise First In (RFI). Usually, a choice must be made between using a fixed size (number of big blinds) like 2 or 2.2. Some allow limps and some don’t. There may also be a variety of sizes, based on position, stack size, or both.

Myth 3 – Solvers Give Answers To All Common Situations

Many live players consistently use larger sizes than solvers suggest are best. So for example, you must learn how to deal with cash game players in a $2-$5 blind game who raise to $20 or $25 (4 or 5 times the big blind) when most solvers use a maximum of 3×. Live cash games are frequently played with very deep stacks. It is not uncommon to see stacks of 300 to 500 big blinds, which are much larger than the sizes normally seen in solver solutions. Cash games may also be played with straddles, either optional or mandatory, which isn’t accounted for.

In general, larger RFI sizes produce tighter ranges than smaller ones. Likewise, decisions must be made about three-bet sizes. It may seem counter-intuitive, but larger bet sizes on the river should include a higher percentage of bluffs.

For example, old-fashioned hand calculations proved that a 50% pot river bet should include one-quarter bluffs, a full-pot bet should have one-third bluffs, and a bet of twice the size of the pot needs 40% bluffs. In theory, no matter how large your bet size, you never have more than 50% bluffs, or your opponent can show a profit by always calling. But in practice, you can exploit an opponent who folds too much by bluffing very frequently.

Additionally, not every solution includes an option for whether there is an ante or rake. Tournament solutions should include some sort of payout structure and ICM. Cash games have to include some huge stack-to-pot ratios. For these and other reasons, each solver produces its own set of ranges and strategies.

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 ZolotowSteve ‘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.