Thursday, July 27, 2006

The Freakonomics of Tournaments, Chapter 2: Chaos Theory, the Butterfly Effect, and the Fundamental Theorem of Poker

(I posted this on 2+2 as well.)

Chaos theory in its most elemental version suggests that the forces of nature and reality are intertwined in such a way that what we do now will affect what happens in the future even in ways we may not see or comprehend. One of the ways chaos theory is most commonly expressed is by the "butterly effect". "If a butterfly flaps its wings in Peking the weather in New York changes the next day" or something like that. Among other things, it's a great reminder to a poker player not to be results oriented, and to only concern yourself with factors you can control.

How does this apply to the Fundamental Theorem of Poker, and more specifically, tournaments?

Well, the Fundamental Theorem of Poker states that every time your opponent plays his hand differently than he would if your cards were face up, you gain.

One big reason I play so loose is because I feel tournaments are absolutely about accumulating chips. The Fundamental Theorem of Poker speaks to the flipside: The other reason I play so loose is that it disguises my range so well and makes my hands hard to read. I induce more mistakes from my opponents than a predictable player can because their hands are much more readable with the information available. And that's the secret: My moves may be individually -EV on a particular hand, but they induce my opponents to make bigger mistakes than I make, because my hands are much harder to read than theirs.

Here's an example particular to me: Let's say we're in the mid stages of a tournament, antes are in and many people have Ms between 12-15 if not even shorter. A tight player opens in MP; his range may be, for example's sake, is 99+, AQ+. It folds to the villain in BB who has AQ. Now against a tight player it is usually right to fold because his range is such that AQ is being crushed. Now, my range in this spot might be 22+, 76s+, AJ+, ATs+, KQ, or some such. (My range is never set in stone; it depends on many factors, which is part of my style.) Now if the observant opponent knows me, he knows it's proper to push over me given the range I open with. As a result I usually have to fold the hands near the bottom of my range. I lose a small amount when I fold, but when I have a hand near the top of my range, I call and get the money in as a good favorite, and it's a much bigger pot than I would have been able to create otherwise. I generate more EV for myself this way, and I've found the huge mistakes I induce in my opponents when I have big hands make up for the small ones I make (frequently) preflop.

In addition, my aggressiveness at the table can occasionally induce others to play hands differently than they otherwise would against OTHER players. I've observed the following effect: After I raise several hands in a row, or, say, raise the same person's blind two or three times in a row, he may mentally decide "This is the hand I'll take a stand." So, say the next time I get garbage and throw it away. Someone else, a much tighter player than me, raises the blind, and the player who has already decided to take a stand does so again, and gets called by a much better hand and gets crippled or busts. In a tournament, where everyone's equity is affected by what happens on other hands, this can be huge. Instead of a simple blind steal or small pot, now someone is knocked out and we move up a pay spot.
The effects aren't always that pronounced, but they do exist.

This is a pretty rough draft and I'm sure needs work but I was thinking about this the last couple of days and so far this is the best expression of one of the benefits I've found of playing loose.

Questions, comments, and thoughts appreciated.

7 Comments:

Anonymous Ed said...

Hi Nath-
Here are some basic comments:

I'm not sure that what you're talking about is chaos theory so much as game theory. In game theory, one of the most important elements is information that is either public or private. For example, players who have greater information about the state of the world have an enormous advantage.

Additionally, players almost always have incentives to conceal their individual states. For example, if we were to model the lead-up to a fight (or war), we might want to have two types of people: wimps and tough guys. If you are a tough guy, you like to fight, so you want to be seen as a wimp so people fight with you. If you are a wimp, the opposite obtains since you don't like to fight. Either way, the goal is conceal some fact about how you play.

By giving up smaller gains, you might (falsely) signal that you are a poor player, when in reality you are much better. What you are doing by playing this way is introducing variance into other players' estimation of your talent level. Alternately, you might try to build (false) risk=aversion by sacrificing potentially good hands at some points and then capitalizing enormously at others.

It seems interesting, though.

Best,
Ed

6:50 PM  
Anonymous shiela.pizzolatto said...

Mom-now every one knows your strategy???But I am sure that you know what you are doing.Love, Mom

11:50 AM  
Anonymous Anonymous said...

"All warfare is based on deception. Hence, when able to attack, we must seem unable; when using our forces, we must seem inactive; when we are near, we must make the enemy believe we are far away; when far away, we must make him believe we are near. Hold out baits to entice the enemy. Feign disorder, and crush him."

Sun Tzu, the Art of War

-Alex

4:31 AM  
Anonymous Anonymous said...

Comments --

I agree with "Ed" above. I'm not sure how Chaos Theory relates to your aggression. I also agree that this seems more like Game Theory.

To the extent that your aggression leads to 'bad plays' by your opponents, whether agaist you or other players at the table, then this can be a benefit of your strategy. But, every player at the table takes actions which have an effect on every other player at the table, to one degree or another. Your strategy may just have a more pronounced effect.

You play LAG, others respond, the response spills over to the play between others at the table even when you are not in that hand. This happens every time I play in a live cash game with an ultra-LAG. In a cash game, this effect is isolated to a single table, while in a tournament this same result at one table will later have an effect on other players at other tables, and therefore the overall dynamics of the entire tournament, because (hopefully) you will move to another table later with a monster stack in relation to the big stacks (but smaller than yours) that have been created at other tables where play has not loosened up as much.

But, I don't think this enters the realm of Chaos Theory -- its just an explanation of the overall effect of the dynamics of your style at your table, and how it may affect your stack (or others at your table) as tables consolidate in the tournament.

I'm an occasional 2+2 poster, mostly lurker, and I've been following your progress and discussions. Good luck -- hope you're still in the Main Event.

SpeakEasy

12:12 PM  
Anonymous Anonymous said...

Comments --

I agree with "Ed" above. I'm not sure how Chaos Theory relates to your aggression. I also agree that this seems more like Game Theory.

To the extent that your aggression leads to 'bad plays' by your opponents, whether agaist you or other players at the table, then this can be a benefit of your strategy. But, every player at the table takes actions which have an effect on every other player at the table, to one degree or another. Your strategy may just have a more pronounced effect.

You play LAG, others respond, the response spills over to the play between others at the table even when you are not in that hand. This happens every time I play in a live cash game with an ultra-LAG. In a cash game, this effect is isolated to a single table, while in a tournament this same result at one table will later have an effect on other players at other tables, and therefore the overall dynamics of the entire tournament, because (hopefully) you will move to another table later with a monster stack in relation to the big stacks (but smaller than yours) that have been created at other tables where play has not loosened up as much.

But, I don't think this enters the realm of Chaos Theory -- its just an explanation of the overall effect of the dynamics of your style at your table, and how it may affect your stack (or others at your table) as tables consolidate in the tournament.

I'm an occasional 2+2 poster, mostly lurker, and I've been following your progress and discussions. Good luck -- hope you're still in the Main Event.

SpeakEasy

12:12 PM  
Blogger Nath Pizzolatto said...

Game Theory has much more to do with the randomizing effect, as little as I know about it.
When I mentioned Chaos Theory I was thinking specifically of the Butterfly Effect: namely that, as SpeakEasy said, "You play LAG, others respond, the response spills over to the play between others at the table even when you are not in that hand." Even when we don't notice or think about those effects.

2:38 AM  
Anonymous Anonymous said...

Now that you repeat what I said, I can kind of see the connection...Your play has an effect on the play of others even when you are not involved. That would not happen if you were not at the table.

SpeakEasy

8:32 PM  

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