Calculating my bet size if I know my bluff % to make villain indifferent

Question

I'm trying to work out the formula to figure out what percentage of the pot I need to bet if I want to make the villain indifferent to calling.

A similar question has a response by paparazzo where he solves for "f" which is the bluffing frequency. The right bluff frequency

I basically want that same thing but where you solve for "s" in his terms.

Using the classic simple example let's say I have 2 combos of value and 1 combo of bluffs. So my bluff percent is 33%. How do I calculate what percent of the pot I need to bet to make the villain indifferent to calling? I know in this example the value is 100% of pot, because that will make his pot odds the same as my bluff frequency; but I only know that because I know it from the other direction and it's so simple.

What about more complex ones like I know my bluffing frequency is 43%. How much should I bet? I just need a simple formula so I can build a calculator in javascript to help me out with some analysis.

Answer 1

I find practically, its better to memorize approximations and adjust from there. You alr know that 33% bluffs require a pot sized bet. As your bluffs tend to 50%, your bet tends to infinity, since with 50% your opponent wins half the time by calling, so hes essentially chopping the dead money, EV-wise.

For 43% bluffs, we can tell this is close to 50%, so the bet is going to be big.

The formula for bet size = (Bluff freq)*(Pot + Bet + Call)/100

Since call = bet, we put in 43%, we have betsize = 43/100 * (Pot + 2betsize)

If you solve for betsize, you shud get ~3Pot. So you should be betting 3x the pot if you have a bluff frequency of 43%. Unless you are very deep stacked, this is not always an option. Dont bluff so much.