Interview Question for Software Development Engineer at Microsoft:

Now there is no condition between succesive flips; each filp has 50% chances to add one dolar, so in the end a good chance would be to have D/2 dollars on the table.
Start with 1 dollar and negociate up to D/2 (or a little bit more if D is small, but not too much if D is big!)

Is is a condition that you have to win the last flip? then there is a 50% chance to take the money!
This makes the game more interesting, but I don't think you have to change the limit to D/4 - is all about your taste...