Betting math question (equilibrium profit)

What is the math needed to find the equilibrium profit point if you're able to get, say -105 at one book and +120 at another, and want to arb some (exact) small profit regardless of who wins? I can do this by trial and error and find it, but unable to figure out what the exact math formula is.

Thank you

Who cares as long as the House Edge is Negative.  In your example the House Edge is -3.44%.  Use a calculator.

https://wizardofodds.com/games/sports-betting/straight-bet-calculator/

If you want to figure stuff out like this, then American styles are not what you need to use.  Switch over to EU style.

Wouldn't that then yield (120-112.70) on the +120 and (120-100) on the -105? While risk free, that's not the equilibrium profit point on both sides?

I bet when I'm drunk, and my eekwa..............................equilabr..................

(I realize you are not addressing me)  Yes, but by using the calculator, you can determine the equilibrium profit point within a minute with only two or three tries and that was my only point.

Thorpe made that pretty simple.

The math is the simple part. Try to find a -105 favorite and a +120 dog. $8 is a fat payoff for these kind of situations.

You bet $105 @ -105 to win $100.

On the other side, 105 + 100/120+100
205/220 = $93.18 @ + 120

$6.82 profit on both sides

I clearly misread your explanation, Thorpe. Thanks! And thanks Esplanade