QuantWolfPlaying Multiple Coin Toss Bets Simultaneously
A coin toss bet is one where you can win back a percentage of your bet with probability p, or lose a percentage with probability 1-p. Call the win percentage, the gain return (G), and the loss percentage, the loss return (L). In the most common type of bet, the gain percentage is 1, and the loss percentage is 1. This means that if you bet $1, and you win, you get back $2. If you lose, you get back nothing.
Now imagine that you can play any number of these bets simultaneously. Each bet has the same gain and loss returns, and the same probabilities. What fraction of your bankroll should you place on each bet? Below is a Kelly fraction calculator for this situation. Betting the Kelly fraction will make your bankroll grow as fast as possible with the minimum chance of losing everything.
Enter the number of simultaneous bets you are playing, the win probability of the individual bets, and their gain and loss returns. Note that the individual bets must have a positive return expectation, otherwise you should not play them. A positive return expectation means that G*p must be larger than L*(1-p).