[pzhon]

[ QUOTE ]
Here's a typical representation of reference dependent prefereces with loss aversion.

[/ QUOTE ]
You wrote the economics version of technobabble. Did you really think that would pass inspection by a mathematician? This was not a plausible set of preferences for an advantage gambler.

First, reference dependent preferences are a descriptive tool for explaining the actions of apparently irrational agents, not a normative tool for saying how rational advantage gamblers should behave. Why not say that hedging is right if it leaves you with $8888, because eights are lucky?

Such a nondifferentiable point in your utility function is a sign your preferences are time-inconsistent, and that you are making choices you will regret later, choices inconsistent with your other choices. As advantage gamblers, we are not done. We will continue to find more advantage wagers in the future. So, whether we are above or below this reference point will not be determined only by this wager. Even if for some strange reason we really care extra about ending up below +$475, the fact that we may play another session of poker soon can easily push us above or below the reference point, which smooths out the kink you forced at the reference point unless the preferences are inconsistent over time.

Second, it is absurd to set the reference point to be $475 above the advantage gambler's starting point. Even in the descriptive theories, there is usually only one point where the utility function is not differentiable, and you are trying to say that by some unbelievable coincidence, that point is not at the starting point, but at the value of the 100% hedged position. That is not a plausible description of why advantage gamblers hedged 100%. It would say that people would make at least small wagers, betting 10 to win 11, at almost every point except after gaining the magic $475. You are saying that if people won $10 elsewhere or lost $100 elsewhere, they would hedge less than 100% since they no longer have the magic +$475. This is absurd.

Is it so hard for you to believe that people made a mistake? I often err, and I see other people make mistakes more frequently. It's part of being a winning poker and backgammon player. The key is to learn from your mistakes, not to attempt to rationalize them and ridicule anyone who dares to tell you that you made a mistake.