I was asked this question in a trading interview: how much would you bet in a game where you win 300 on tail and loses your 100 on heads? how much will you bet if you can play game once or multiple times with a $1m bankroll?
Here is my thoughts and was wondering if this is correct or there was a better way to answer it:
On a 1 bet, our expected gain is 1 and standard deviation is 2, thus sharpe is 0.5. Since we need to risk 1 to win 3, we have 3 to 1 odds and thus need to win only 25% of time to break-even. This is a really a high EV game for us and we should bet "a high amount".
Using Kelly Criterion, f= (bp - q) / b yields f= (3*0.5 - 0.5) / 3 = 1/3. This is the theoretical bet size to maximize the expected growth rate of your wealth.
So we should bet 1/3rd here of our bankroll if we can play the game once. I would bet less if we can play it multiple times since we'd lose a lot of EV in the future should we go bankrupt. I said 1/10th if we can't change bet sizing, does this make sense and how can we quantify the bet sizing here for the multiple game scenario. Theoretically, Kelly says we should bet the same here 1/3rd?
There was a similar question here but it doesn't address the multiple game scenario. Thanks!