Myths And Misconceptions About Game Theory And Poker Solvers: Part One

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.

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.

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.

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.

Be sure to check out next issue when I continue with even more common misconceptions about game theory and solvers in poker. ♠

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.