Game theory exercise: Bet size with two rounds to bet

[pzhon]

Suppose you are playing NL, and there are two rounds of betting. There is already $1 in the pot. You each have $x. There is no drawing. You can assume that you are playing high card with at least 5 cards, and your opponent has the second highest card face up.

[img]/images/graemlins/diamond.gif[/img] How much should you bet on the first round, as a function of the stack size x?
[img]/images/graemlins/diamond.gif[/img] What is the optimal strategy?
[img]/images/graemlins/diamond.gif[/img] Do you gain from having multiple rounds to bet?