Imagine that you are in the finance profession. You know that x% of the time when you pick a stock it ends up positive. Conversely, 1-x% end up negatively. With this in mind is there an ideal portion you should be betting to achieve maximum return? How would you do this type of problem mathematically?
For example, if you know you get 100% of the time correct. You would want to invest all your all the firm's money. If its 99% of time correct, you would probably still do most of money. If your 50/50, you can set aside half of your money just in case you will lose or any number between 0-100%. If its zero, then you probably don't want to bet at all. This problem has been knawing at me for some time now. Please help.