Another Interesting Hypothetical Question

[David Sklansky]

Similar but easier than one I asked a while back.

You are playing the following proposition:

A head up no limit hold em match.

You and your opponent both ante one dollar each hand.

Your opponent is dealt AK suited face up, every time.

Your opponent moves you in (if you call) everytime.

The game is over as soon as you see a flop.

You can buy in any integer amount that you choose.

What's interesting about this question is that if you are decidng between small buy ins, you should choose the smaller but if you are deciding between two big buy ins you should pick the bigger. Hopefully that is obvious.

I have two questions. And I think it would be fun for you guys to guess at the answers before someone actually calculates them.

1. How big a buy in do you need to have the best of this game?

2. Where is the point of inflection such that buying one extra dollar, helps rather than hurts? (If you don't immediately realize that this number is smaller than the answer to #1, you are not understanding the question.)