Betting related terms:
Multiple: a bet you make on two or more events where you win only if you guessed right all the outcomes of the events.
Odds: will be expressed in decimal, eg. in a bet at odds 2.5 if you bet 10 and win you get 25 (net won +15).
Suppose we have to make a multiple bet on n events. And we are given the possibility to bet on single events at the same time. How could we minimize loss disregarding the possible outcomes of the events?
In other terms, if I have to make a bet on a multiple, how can I find how much to bet on each single to lose the minimum?
Event 1: Federer vs Nadal; odds (Federer: 1.8; Nadal: 2.1) P(Federer)=0.54 P(Nadal)=0.46
Event 2: Djokovic vs Murray; odds (Djokovic: 1.5; Murray: 2.8) P(Djokovic)=0.65 P(Murray)=0.35
If we bet a 15 euros multiple on Federer and Djokovic winning, our EV will be: 0.54* 0.65 * (15 * 2.7 - 15) - (1- 0.54*0.65) * 15 = -0.78 euro
But obviously there will be 2 different scenarios:
We win both events: net +25,5
We lose: net -15
I want to make these 2 numbers converge on the minimum loss (-0.78). In order to do that I could make single bets on single outcomes of that event in addition to the single bet. The problem is, how can I find how much to bet on every single event in order to lose the same amount for each of the possible outcomes?