The idea is to bluff at a frequency that gives your opponent 0 EV to call or fold.
f is bluff frequency
s is the fraction of the pot you bet
What f gives your opponent an EV of 0?
0 = f(1 + s) - (1-f)s
0 = f + sf - s + sf
0 = f + 2sf - s
s = f(1 + 2s)
s / (1 + 2s) = f
The mathematical number of s / (2s + 1) is a good number.
That is a bigger bluff frequency than most people would guess.
A pot size raise should mathematically bluff 1/3 of the time.
Take an example. They bet the pot and are bluffing 1/3.
If you call three: -1 -1 + 2 = 0
If you fold three: 0 + 0 + 0 = 0
This assumes your opponent has a bluff catcher and capable of calling a bluff.
So you should actually bluff more than this equation.
The most important part of a bluff is selling it. Your betting history on the hand needs to support the hand you are trying to represent. And the hand you are representing needs to beat the hand they have. If you did not bet out on the flop or turn and blank turns up on the river it is pretty hard to sell that bluff. The best time to bluff is when a scare card comes up and opponents have not shown strength.
Let say you played 89 suited and totally miss the flop. Decide the range of hands you want to represent. Bet enough to try and take down the pot right then. Or put in a value bet to make your later bluff believable. You may need to fire three times at the bluff.
Early position is in some ways better. Open early with 1/2 or full pot bet is a strong statement. In late a position a 1/2 or full pot bet is also a strong statement but if you are behind bet(s) it is also more expensive as pot is bigger.
Also make sure you have a player capable of laying down a hand. You get some poor players that just don't lay down hands. And you get some poor players that lay down too easily.
Note EV is not symmetric. Bluffer would rather you call.
EV = 1 + 1 - 1
You need to call back enough to give them 0 EV to bluff.
Related question is how often should player 2 call?
Answer: Often enough to make player 1 indifferent to checking or bluffing.
Check has 0 EV - player 1 is on a stone cold bluff
In this case fc is frequency of call
0 = (1-fc) - fcs
fc + fcs = 1
fc = 1 / (1 + s)
So mathematically you should call a pot size bet you know could be a bluff 1/2 the time
Mathematically a big raise should not get called as often. The problem there is you are putting more money at risk. The player can be on a monster. You have to convince them you are at least representing a better hand.