Prospect theory and poker

Remember last week when I posted a comment about prospect theory?  You might not have read the link to the journal article that I posted.  You might have even given up on the link to the Wikipedia entry explaining the basics.  However, I just read a post by Gary Carson on one of his blogs about enticing calls and was immediately reminded of my favorite scholars, Tversky and Kahneman, so I thought I'd give another go at explaining how this is related to poker.

Gary Carson writes:

I don't know why this works, but it does.

In a 1/2 game I limped UTG with KK. The limp left me with a stack of $125. Another early position player made it $15 and two players called. The raiser had another $75, the other two each had a couple hundred. I made a huge overbet, moving all in.

The initial raiser went into the tank and gave me his best imitation of a TV staredown.

Then I said the magic words. "Can you beat two jacks?"

Somewhat taken aback, he said, "Maybe".

I said, "Well, then you know what to do".

He called. One of the other two called, the other folded.

I turned my hand over, the board got dealt, they both mucked.

I don't know why causing them to focus their thoughts on a pair of jacks makes them call, but it does.

I have some thoughts about what the reason might be though.

When they mention a pair of jacks they'll tend to think about your hand as it relates to jacks, not as it relates all the other information they might have. They'll tend to think, "He might have jacks, he might have overcards to jacks, he might have a pair smaller than jacks and he might have a pair bigger than jacks. But he's thinking about jacks, so he probably doesn't have a bigger pair, he probably has TT and my KQ is a coin toss".

I don't really know though. But it works.

T+K's prospect theory (a nobel prize winning theory, btw) basically says that people's decisions in terms of risk are dependent on how their choices are presented.  They have proven this repeatedly with various experiments.  For example, someone might drive across town to save $5 on a $15 book, but would not drive across town to save $5 on a $1500 piece of jewelry.  Rationally, this does not really make any sense... $5 is still $5.  The expected value is the same.

Another way to see how this is explicitly related to gambling:

One of T+K's experiments told people to assume there was disease affecting 600 people and they had two choices:

Choice A: 200 of the 600 people will be saved.
Choice B: There is 33% chance that all 600 people will be saved, and 66% chance that nobody will be saved.

72% of people chose A, showing a preference for certainty.

They then offered another choice:

Choice C: 400 people will die.
Choice D: There is a 33% chance that nobody will die, and 66% chance that all 600 people will die.

78% of the same people then chose D, seeking to avoid the loss of 400 people.

You might notice however that the outcome of all four choices has the same expected value: 200 will be saved, 400 will perish. The only difference is the way in which the information is presented. 

Prospect theory shows us that if we want people to choose something, we should focus on potential gain.  If we want them to reject something, we should focus on the potential loss.  Whether this is something that can be successfully employed at the poker table remains to be seen, but Carson's story about the jacks is clearly a case of trying to get people to focus on the potential gain and having it pay off when they make a bad choice.