Interview Question for Software Development Engineer at Microsoft:

Use binomial distribution to express the expected cash on the table after N rounds.... In series form, one can see that the summation does not converge...the expected cash is INFINITY.

there are 50% chances to win a dollar, 25% for 2 dollars, 12.5% for 3 and so on...
there are also 50% chances to loose your investment!

So the chance to win N dolars is .5^N
this is aslo the chance to match your investment of N dollars.

N %
0 100
1 50
2 25
3 12.5
4 6.25
5 3.125
...

Now is about what kind of risks you may want to take:
1 dollar - you are a moderate risker;
2 dollars - better;
3, 4 - high risk invester;
5, 6 - caution!
7 or more - stupid?

Pesonaly I would preffer to go with 0 - you may not win but you cannot loose;
but it wouldn-t work... (will it?)
So I'll start with 1 and I'll negociate up to 2 or 3.

(binomial distribution?!?)

As stated it seems my winnings = # of heads flipped before the first tails. This has a geometric distribution. So I would pay $1 or less to play (mean of the distribution), assuming a linear utility function.