If you allowed probabilistic strategies, then the first player would have the option of occasionally passing when he has a strong hand so that he can also pass when he has a weak hand without giving away that he has a weak hand. Basically, probabilistic strategies allow bluffing.

Another interesting variation might be to add risk aversion. That is instead of the goal being to maximize expected wealth, the goal could be to maximize expected wealth minus standard deviation of wealth.

In any case, it’s an interesting post.

]]>Another simple problem (not game theory) I found intriguing is

this one on Tom Cover’s website.