The question is this: if your objective is simply to maximize your winnings after some very large number of tosses, what is the optimal fraction to bet on each flip? Secondly, if your objective is to maximize something else (eg: sharpe, etc) what is the optimal fraction to bet? ![]() Nevertheless, the 'best' fraction of your bankroll is not just "as much as possible." If you bet everything, one tails and you lose everything. This is obviously a very good game to play assuming a fair coin the "odds" are clearly in your favour. so if your stake grows to $200, you are now committed to betting $10 on each flip. Note that if you choose 5%, for example, then you bet 5% on each flip. ![]() If it comes up tails, I take what you bet (eg: you bet $5 and get tails -> you lose your $5). If it comes up heads, I pay you double what you bet (eg: you bet $5 and get heads -> you get your $5 back plus another $10). You decide in advance what percent of your stake you are going to bet on each flip of a coin. ![]() It really depends.Īs an exercise, take the following game. ![]() There are other cases where it is best to risk more. There are cases where you can make more money (not just higher risk-adjusted return) by risking less on each trade. The optimal amount to risk on any given trade depends (rather dramatically) on the distribution of profits and losses that underlie that strategy.
0 Comments
Leave a Reply. |