1

You get to the river and you have nothing but a bluff catcher. Bottom pair on a scary board. If they made their hand they have they have you beat. But you can beat on outright bluff.

But you are getting 3:1 to call
How often does your opponent need to be bluffing to call

2

This question seems difficult but when you start knowing what it means, things become easier.

When you say pot odds are 3:1 to call it means that in this situation you only need to win 1 time out of 4. Let's put on example, this pot odds occur when villain bets half pot:

Let's say on the river pot is 2€ and villain bets 1€. When you lose on showdown, you lose 1€ (your call), but when you win, you earn 3€ (his bet and the pot).

  • 1# lose 1€
  • 2# lose 1€
  • 3# lose 1€
  • 4# win 3€

So, what is happening? In this situation no matter what if you win 25% of the times, the EV will be 0.

Thus, the answer of your question is, if he is bluffing more than 25% of the times you can call him with all bluffcatchers

Always try to think what are meaning the pot odds and you will think for your own

0

b is bluff rate

EV = 0 = b*3 - (1-b)*1
0 = 4b - 1
b = 1/4

bluff rate is always 1 / (pot odds + 1)

what if they bet 5x pot
pot odds (1 + 5)/5 = 6/5
EV = 0 = b*6 - (1-b)*5
0 = 11b - 5
b = 5 / 11 1 / (6/5 + 1) = 1 / (11/5) = 5 / 11

what if they bet 100x pot
pot odds (1 + 100)/100 = 101/100
EV = 0 = b*101 - (1-b)*100
0 = 201b - 100
b = 100 / 101 ~ 1/2
The math does not change that much from 5x pot bet to a 100x
It is about intimidation

PO BR
1 = 1/2
2 = 1/3
3 = 1/4
4 = 1/5

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