Our opponent bets $70 into a $100 pot on the river. How often to we need to win to make the call break even?
The answer given was $170(X) - $70(1-X) = 0, so X = 0.292 or 29.2%
How was this answer reached?
Are you sure you have copied the problem correctly? It should be "us" who bet $70, not "our opponent". What they are saying is that if you win "X" of the time, you will lose 1- X of the time. When you win you win $170 dollars. When you lose, you lose $70 so in the long run you will win 170X dollars and lose 70(1- X) dollars. "To break even" means you neither lose nor win any money: 170X- 70(1- X)= 0. That is the same as 170X- 70+ 70X= 240X- 70= 0 so 240X= 70 and X= 70/240= 7/24= .2916666 or about 29.2%.