Let A be a condition like: "the game will end with a draw" or "this player will score" or "There will be a red card in the game" etc.
A refund is getting offered if A will happen.
The refund is offered on a particular combination bet: "1x2 + Under/Over 2.5 Goals", which has 6 outcomes for a normal football match. The condition varies instead.
How do I maximize the expected value of this promotion?
A = "There will be a red card".
My bet = "Team B will win and there will be more than 2.5 goals in the match".
If there is a red card AND I lose my bet, I will be refunded.
If there isn't a red card OR I win my bet, I won't be refunded.
My thoughts are:
- Obviously betting all the 6 outcomes of that combination bet would result in losing money (because of bookie fees which are around 7%). So if I bet 100 on all this 6 outcomes I will get 93 back no matter what: EV = -0.07%
- If the probability of condition A to happen is higher than 7%, then there should be a way to maximize this bonus and get a +EV bet.
- I was thinking about betting against condition A, so if it happens I have the refund, if it doesn't I still win another bet; but this isn't totally convincing.