Optimal value-to-bluff ratios are easiest to calculate on the river because our bluffs should have 0% equity when called.
This is in contrast to preflop, the flop, and the turn, where our bluffs will almost always have some equity when called. So, let’s work backward and start by evaluating a river example.

Suppose the pot is $100 on the river and we want to bet 75% of the pot with a perfectly balanced and polarized range.
This means that our opponent will risk $75 to win a $250 pot ($100 pot + our $75 bet + his $75 call), which means that he needs to win 30% of the time ($75 / $250 = 0.30) with his bluff-catchers in order to break even on his call.