Suppose you have the opportunity to place multiple bets, all related to a single event.
As in roulette, for example, some bets represent mutually exclusive outcomes like red/black, specific numbers etc., while others have a degree of overlap (red/odd, even/3rd-dozen, etc.). The bets have a variety of payoffs and crucially, unlike roulette, some of them offer a postive EV.
How do you go about determining the optimal total amount to bet, and how to distribute this among the available bets? (Assuming that, if faced with just a single bet, you would be employing a utility function to assign a fraction of your bankroll to the bet, proportional to the EV.)
The more I've tried to ponder this, the more I've managed to confuse myself. Presumably the key is to identify the variance of various individual and combined bets, in search of the highest overall Certainty Equivalent, but this is very much where I start to venture outside of my mathematical comfort zone.
As in roulette, for example, some bets represent mutually exclusive outcomes like red/black, specific numbers etc., while others have a degree of overlap (red/odd, even/3rd-dozen, etc.). The bets have a variety of payoffs and crucially, unlike roulette, some of them offer a postive EV.
How do you go about determining the optimal total amount to bet, and how to distribute this among the available bets? (Assuming that, if faced with just a single bet, you would be employing a utility function to assign a fraction of your bankroll to the bet, proportional to the EV.)
The more I've tried to ponder this, the more I've managed to confuse myself. Presumably the key is to identify the variance of various individual and combined bets, in search of the highest overall Certainty Equivalent, but this is very much where I start to venture outside of my mathematical comfort zone.