Game Theory

A lot of people are aware that poker can be extremely simple or deeply complex. When it is the latter, one of the most likely reasons is that the players are implementing aspects of game theory.

In its simplest terms, it is an attempt to study situations in which the success of an individual’s choices depends on the reading of the action sof others.

Let us give you an example, one that is quite similar to one posted last Friday and may leave the regular reader wondering if a) this column is turning into a series depicting dating disasters, or b) the team of writers ever get laid.

Three men are playing pinball in a hockey ‘n ribs bar.

Minutes later three women walk in, pay no attention to the carve-up on the rink and seem even less interested in the bbq’ed 4-piece combo.

The three men glance away from the table and the sight of the women causes tilt.

But there is a problem.

One of the women is more attractive than the others and is likely to garner all of the attention of the three men. If this happens, her two friends might become annoyed, the alpha female could become swell-headed and the only potential for multi-ball action is back at the flippers.

However, if one of the men realises this in advance, he can change his strategy and give all of his attention to one of the wing women. He lessens his competition, flatters the woman and stands a greater chance of losing his place on the high score table.

With a few embellishments, the above is a scene from A Beautiful Mind, the film about mathematician John Nash. He uses game theory and successfully gets a number. (Bear in mind it is a Hollywood movie. In-bar case studies are still being analysed.)

The same principle exists at the card table. If you can work out the thought process of your opponents, you can successfully alter your strategy.

The main difference is that when Nash changes his strategy, he not only increases his chances, he potentially benefits his friends because they (in theory) have a better chance now they are not in direct competition with him. His benefit does not occur at the expense of others.

Winning poker players implement strategies that work at the expense of others. Poker is a special example of game theory called a Zero-Sum game because a player’s win is the exact total of what the opponents lose (ignoring the rake).

There is an online zero-sum game maestro called Erik Sagstrom, Erik 123, who has an uncanny ability to remember past hands. He scouts for predictability and when he detects it, he changes his tactics and exploits the routine.

That is the way to play but you have to be careful as you can start thinking your way into trouble.

In low level limit games, hardly anyone will be trying to change their strategy and, if you select solid hands, you can let probability take its cause.

Fancy moves have little positive EV.

However, in reasonable NL games, you can use the principles of game theory to outthink your opponents – BUT – you have to know where to stop.

Start by working out the player’s style and assign levels.

Level One is someone who plays his hand and pays no regard to what you might hold

Level Two is someone who thinks you are a Level One.

Level Three is someone who thinks that you know he has classified you as Level One.

We hope you are still with us....

The levels than progress indefinitely, each one a further variation on Level Three and based on working out how far your opponent will go. All you have to do is play according to what level of thought you think they are using.

Play Level Ones just based on the board. Have you flopped a better hand, or has he missed? If so, bet. If not, fold. Do not pursue a big pot unless you have a very strong holding

Play Level Twos as if you are always betting your hand – if you raise on 99 and the board has either an ace, king or queen – bet.

Things are a little more complex with Level Threes – he has given you scope for advanced play and so his actions will be less predictable and he is aware you might bluff. You have to deduce how far he will take it.

The good news is that a lot of online players, even at medium stakes, are playing Level One. Multi-tablers can afford to be patient and won’t take many risks and so there can be steady gains if you take a few shots and remember when to stop.