I have a question I have been trying to challenge myself with, but unfortunately I don't have a method for obtaining the exact solution. The question is this:
You have 1,000 dollars. If you wager any amount, you have a 90% chance of receiving double the amount of the wager and a 10% chance of losing the amount. You want at least a 50% probability of reaching X dollars through multiple wagers. How do you wager so as to maximize the value of X?
I have determined that I can, with at least 50% probability of success, attain the value of 3,402,823,669 dollars by wagering 60% of whatever I have each time. However, I am sure that this is not the optimal solution; it is merely "close" and I'm not sure how to arrive at the exact answer.