I am more interested in the methodology then the actual answer here because I can get the answer or there about by messing around in excel but was more wondering a formula/ algebra way of solving it.

odds in decimals eg 1.9 means a bet of $1 would give us our stake back plus 90 cent or $1.90

a Bookie offers odds on a game with team A vs Team B of
Team A to win 1.9
Draw 3.4
Team B to win 5

however the bookie offers a bet in play refund with the terms that if we place a bet before the game we can have a matched in play bet but up to a max of $50.

we can have as many bets before the game as we like and as many bets during the game as we like but its only the $50 that get matched and that is matched according to the highest bet. eg if I bet $50 on Team A to win and $30 on Team B then any in play bet up to $50 would be refunded if it does not win.

only the in play bet gets refunded and we are assuming that the odds don't change in play.

(they do obviously but i want to keep methodology simple here)

my questions are
1. How do we work out how much money to bet on each scenario if we have unlimited budget to get the max EV
2. how do we work out how much money to bet to get us best gaurentead profit? eg not nec the max ev but the smallest risk etc.

note I know I am studying maths now so should know this but I have not covered this area yet and there is a reason I decided to study maths.

also if anyone is doing or has done A level maths in the uk what module would this relate to?

I am guessing we need quadratics and linear inequalities somehow but also some other stuff?

Why dont you explain with an example how this works for those not familiar with this kind of refund.

Like what happens here that is refunded vs the regular bet.

Does it mean that your bet is refunded if at some point it was winning or what? By not giving a clean example you restrict the answers to only those familiar with such structures/refunds etc.


Also it may be needed to know more to answer this like how often the player is correct historically (if we can model this on a per range of odds level with enough data) (and even more like the volatility of eg a lead as the game develops etc).