Calculating Middles

Calculating Middles For this 2h I have un 21 -110 and ov 20' +100. How often do I have to hit each for me to make these wagers +EV?

Let's assume 21 is the sharp line. So it goes OVer or UNder 21 with probability [I]p[/I], and lands on 21 with probability [I](1-2p)[/I]. If it goes UNder 21 then you break even, if it goes OVer then you lose $10, and if it hits the number then you win $100. [I]EV = -10p + 100(1-2p).[/I] You break even when [I]p = 10/21[/I], i.e., the push probability is [I](1-2p) = 1/21 = 4.5%.[/I]

You have to hit the 21 4.54% of the time to break even.

The proper way to play this is to bet 110/100 on under 21 and 105/105 on over 20.5. The breakeven is 4.54% on the 21, which is 1/22.

Thanks for the answers. So, the bets really weren't all that great I see.