[kerze]

Lets say he has a 7 high on river (which has to better than your 7) or better x% of the time, he has an 8, y% and a 9 or worse 100-x-y %. Based on your conditions, x% of the time you will be out 1BB by betting rather than checking, y% of the time you will gain 1BB by betting rather than checking , and 1-x-y you will even by betting rather than checking.

x* -1 + y*1 +(1-x-y)*0 = 0 is your breakeven point.

This works out y-x = 0 or x=y so essentially you must think it is just as likely for him to have an 8 as you do a 7 or better.