I've got a model that gives me totals for basketball, and with it I use it to calculate the probabilities of winning overs and unders. Let's ignore odds and say I've got a profitable middle where I'm betting:

Over 210.5 (% chance of being over 210.5 = 57.6%)

Under 215.5 (% chance of being under 215.5 = 47.8%)

(As I said, let's ignore odds, but if the over was paying 1.99, and the under 1.99, this would obviously be a +EV middle with some risk (i.e. no pure arbitrage)).

My question is: given the probabilities I have above, how do I calculate the % chance I win both bets? I feel like intuitively the answer is: (1-(1-P(over)-(1-P(under)) = 5.4% [equivalently (1-P(lose over)-P(lose under))], but I'm not at all sure.

Anyone have better ideas?

Over 210.5 (% chance of being over 210.5 = 57.6%)

Under 215.5 (% chance of being under 215.5 = 47.8%)

(As I said, let's ignore odds, but if the over was paying 1.99, and the under 1.99, this would obviously be a +EV middle with some risk (i.e. no pure arbitrage)).

My question is: given the probabilities I have above, how do I calculate the % chance I win both bets? I feel like intuitively the answer is: (1-(1-P(over)-(1-P(under)) = 5.4% [equivalently (1-P(lose over)-P(lose under))], but I'm not at all sure.

Anyone have better ideas?

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