1) this is not binomialy distributed by your later assumption.


2) It is also impossible to determine expected profit - for several reasons: For starter one could bet $100 on each of the 9 jumps (after the first). This method has an expectation of $300.

By increasing the bet amount one can increase this expectation.


3) Suppose you have just $1000 - now what strategy has the best possible expectation?? back at you..