Conjecture and Question

[Mason Malmuth]

Hi Everyone:

I have a conjecture that I believe is true and I have reasons for believing that this is true. But I'm hoping that others can explain the reasons a little better than I can, or perhaps explain why my conjecture is wrong. Here it is:

Suppose you are a great tournament player. Perhaps one of the best. You enter a $10,000 buy-in tournament and when the first hand is dealt, since you're such a great player your expectation is $40,000 even though you only have $10,000 in tournament chips. Now a very unusual first hand takes place and you double up. That is you now have $20,000 in tournament chips. My conjecture is that your expectation does not double even though your chip count has. So instead of having an expectation of $80,000 it may only be $78,000, or $75,000, or some other number less than $80,000, but it will definitely be less than $80,000.

So if my conjecture is correct, I would like to hear good reasons why this is the case. If it's not correct, I want to hear those reasons as well.

This should make for a good discussion and thanks in advance for the help.

Best wishes,
Mason