I've posted a similar question some days ago: Maximize a welcome bonus. , but I didn't specify some details that turn this in a different question (maybe). (If this has the same answer of the previous one I'll edit that question).
A betting website offers to refund your first bet in case of losing. In case of winning you can keep all the money and have the possibility to withdraw, in case of losing the site gives you the same amount of money to bet in another event. In case you win this second bet you can withdraw.
I don't want to risk any money so my intention is to bet on the other possible outcomes of the match with another bookmaker to have a little margin of profit.
In this scenario how can I maximize my profit?
Consider the probability of winning a bet is $p$ and the payoff is $r$ (both as ratios of your bet) and $pr = k$.
Should I choose a bet with low $p$ or high $p$ in the new website? Will this influence the profit?
Thanks in advance!