How to find expected value?

It's a little late for a full ysis. I know there would be an infinite series or 2 to evaluate, and that takes time. A simulation on Excel was easy to set up (believing you'd be out of money quickly). After 50 plays (repeated many times) you rarely have a balance less than $10,000. It's that winning double that makes the difference. Doubling on losses against the House in Vegas is futile and a very quick way to lose. If I have time in the morning and can find this question again (and don't simply forget) I'll work it out exactly, if I can.