Return to Answer

It comes from game theory optimization (GTO)

The idea is the bluff rate is such that your opponent is stuck between call or fold. Call or fold has the same EV.

You know you are beat. Your opponent has a good hand but not the nuts. They will call every time with the nuts.

p is pot (before you bet)
b is your bet
f is you bluff rate
EV is expected value

EV = -b + f(p + 2b)

Set the EV to 0. Solve for f.

b = f(p + 2b)

f = b / (p + 2b)

So is p = b - you bet the pot you should bluff 1/3 of the time.
Note if you bet the pot you are giving your opponent 2:1.

Play three hands and you bluff once and have the nuts twice.
Your opponent is getting 2:1 to call and the pot has 100.
Your opponent folds all three:
0 + 0 + 0 = 0
Your opponent calls all three:
-100 - 100 + 200 = 0

To simplify set p = 1 and and fr just be the fraction of the pot you bet

bluff = fr / (1 + 2fr)

bluff   fraction 
rate    pot  
0.50    100.00
0.44      4.00
0.43      3.00
0.40      2.00
0.33      1.00
0.25       .50
0.20       .33
0.17       .25

Ironically you should bluff more with bigger bets.

You opponent also needs at least a bluff catcher to call.

Clearly you are going to get more bluffs through if a scare card hits on the river. Don't try and bluff a naked 2 on the river if you have shown not strength.

Very important is that does not mean bluff the river 1/3 time period. 1 bluff for every 2 value bets. If you get to the river against 1 then you are going to have the best hand about 1/2 the time and you are only going to be confident you have the best hand like 1/3. So in 6 hands you would value bet 2 and bluff 1.

If you watch the pros some even bluff more.

If you never bluff then players know to lay down. You have to bluff some to get paid off on your when you have it.

You can even do GTO on how often to call - assuming you have a bluff catcher.

Assume you put villain on GTO and bet the pot so you them on bluff 1/3
c = call rate

EV = c 2/3 (p + 2b) - c 1/3 0 - b
= c 2/3(3) - 1
= 2c - 1
c = 1/2

You should call back with a bluff catcher as often as you have hands that you would call back for value.

It comes from game theory optimization (GTO)

The idea is the bluff rate is such that your opponent is stuck between call or fold. Call or fold has the same EV.

You know you are beat. Your opponent has a good hand but not the nuts. They will call every time with the nuts.

p is pot (before you bet)
b is your bet
f is your bluff rate
EV is expected value

EV = -b + f(p + 2b)

Set the EV to 0. Solve for f.

b = f(p + 2b)

f = b / (p + 2b)

So if p = b - you bet the pot you should bluff 1/3 of the time.
Note if you bet the pot you are giving your opponent 2:1.

Play three hands and you bluff once and have the nuts twice.
Your opponent is getting 2:1 to call and the pot has 100.
Your opponent folds all three:
0 + 0 + 0 = 0
Your opponent calls all three:
-100 - 100 + 200 = 0

To simplify set p = 1 and and fr just be the fraction of the pot you bet

bluff = fr / (1 + 2fr)

bluff   fraction 
rate    pot  
0.50    100.00
0.44      4.00
0.43      3.00
0.40      2.00
0.33      1.00
0.25       .50
0.20       .33
0.17       .25

Ironically you should bluff more with bigger bets.

You opponent also needs at least a bluff catcher to call.

Clearly you are going to get more bluffs through if a scare card hits on the river. Don't try and bluff a naked 2 on the river if you have shown not strength.

Very important is that does not mean bluff the river 1/3 time period. 1 bluff for every 2 value bets. If you get to the river against 1 then you are going to have the best hand about 1/2 the time and you are only going to be confident you have the best hand like 1/3. So in 6 hands you would value bet 2 and bluff 1.

If you watch the pros some even bluff more.

If you never bluff then players know to lay down. You have to bluff some to get paid off when you have it.

You can even do GTO on how often to call - assuming you have a bluff catcher.

Assume you put villain on GTO and bet the pot so you them on bluff 1/3
c = call rate

EV = c 2/3 (p + 2b) - c 1/3 0 - b
= c 2/3(3) - 1
= 2c - 1
c = 1/2

You should call back with a bluff catcher as often as you have hands that you would call back for value.

It comes from game theory optimization (GTO)

The idea is the bluff rate is such that your opponent is stuck between call or fold. Call or fold has the same EV.

You know you are beat. Your opponent has a good hand but not the nuts. They will call every time with the nuts.

p is pot (before you bet)
b is your bet f is you bluff rate

EV = -b + f(p + 2b)

Set the EV to 0. Solve for f.

b = f(p + 2b)

f = b / (p + 2b)

So is p = b - you bet the pot you should bluff 1/3 of the time
Note if you bet the pot you are giving your opponent 2:1

Play three hands and you bluff twice and have the nuts once
You opponent is getting 2:1 to call and the pot has 100
You opponent folds all three
0 + 0 + 0 = 0 -100 - 100 + 200 = 0

To simplify set p = 1 and and fr just be the fraction of the pot you bet

bluff = fr / (1 + 2fr)

bluff   fraction 
rate    pot  
0.50    100.00
0.44      4.00
0.43      3.00
0.40      2.00
0.33      1.00
0.25       .50
0.20       .33
0.17       .25

Ironically you should bluff more with bigger bets.

You opponent also needs at least a bluff catcher to call.

Clearly you are going to get more bluffs through if a scare card hits on the river. Don't try and bluff a naked 2 on the river if you have shown not strength.

Very important is that does not mean bluff the river 1/3 time period. 1 bluff for every 2 value bets. If you get to the river against 1 then you are going to have the best hand about 1/2 the time and you are only going to be confident you have the best hand like 1/3. So in 6 hands you would value bet 2 and bluff 1.

If you watch the pros some even bluff more.

If you never bluff then players know to lay down. You have to bluff some to get paid off on your when you have it.

You can even do GTO on how often to call - assuming you have a bluff catcher.

Assume you put villain on GTO and bet the pot so you them on bluff 1/3
C = call rate

EV = c 2/3 (p + 2b) - c 1/3 0 - b
= c 2/3(3) - 1 = 2c - 1 c = 1/2

You should call back with a bluff catcher as often as you have hands that you would call back for value.

It comes from game theory optimization (GTO)

The idea is the bluff rate is such that your opponent is stuck between call or fold. Call or fold has the same EV.

You know you are beat. Your opponent has a good hand but not the nuts. They will call every time with the nuts.

p is pot (before you bet)
b is your bet 
f is you bluff rate
EV is expected value

EV = -b + f(p + 2b)

Set the EV to 0. Solve for f.

b = f(p + 2b)

f = b / (p + 2b)

So is p = b - you bet the pot you should bluff 1/3 of the time.
Note if you bet the pot you are giving your opponent 2:1.

Play three hands and you bluff once and have the nuts twice.
Your opponent is getting 2:1 to call and the pot has 100.
Your opponent folds all three:
0 + 0 + 0 = 0
Your opponent calls all three:
-100 - 100 + 200 = 0

To simplify set p = 1 and and fr just be the fraction of the pot you bet

bluff = fr / (1 + 2fr)

bluff   fraction 
rate    pot  
0.50    100.00
0.44      4.00
0.43      3.00
0.40      2.00
0.33      1.00
0.25       .50
0.20       .33
0.17       .25

Ironically you should bluff more with bigger bets.

You opponent also needs at least a bluff catcher to call.

Clearly you are going to get more bluffs through if a scare card hits on the river. Don't try and bluff a naked 2 on the river if you have shown not strength.

Very important is that does not mean bluff the river 1/3 time period. 1 bluff for every 2 value bets. If you get to the river against 1 then you are going to have the best hand about 1/2 the time and you are only going to be confident you have the best hand like 1/3. So in 6 hands you would value bet 2 and bluff 1.

If you watch the pros some even bluff more.

If you never bluff then players know to lay down. You have to bluff some to get paid off on your when you have it.

You can even do GTO on how often to call - assuming you have a bluff catcher.

Assume you put villain on GTO and bet the pot so you them on bluff 1/3
c = call rate

EV = c 2/3 (p + 2b) - c 1/3 0 - b
= c 2/3(3) - 1 
= 2c - 1 
c = 1/2

You should call back with a bluff catcher as often as you have hands that you would call back for value.

It comes from game theory optimization (GTO)

The idea is the bluff rate is such that your opponent is stuck between call or fold. Call or fold has the same EV.

You know you are beat. Your opponent has a good hand but not the nuts. They will call every time with the nuts.

p is pot (before you bet)
b is your bet f is you bluff rate

EV = -b + f(p + 2b)

Set the EV to 0. Solve for f.

b = f(p + 2b)

f = b / (p + 2b)

So is p = b - you bet the pot you should bluff 1/3 of the time
Note if you bet the pot you are giving your opponent 2:1

Play three hands and you bluff twice and have the nuts once
You opponent is getting 2:1 to call and the pot has 100
You opponent folds all three
0 + 0 + 0 = 0 -100 - 100 + 200 = 0

To simplify set p = 1 and and fr just be the fraction of the pot you bet

bluff = fr / (1 + 2fr)

bluff   fraction 
rate    pot  
0.50    100.00
0.44      4.00
0.43      3.00
0.40      2.00
0.33      1.00
0.25       .50
0.20       .33
0.17       .25

Ironically you should bluff more with bigger bets.

You opponent also needs at least a bluff catcher to call.

Clearly you are going to get more bluffs through if a scare card hits on the river. Don't try and bluff a naked 2 on the river if you have shown not strength.

Very important is that does not mean bluff the river 1/3 time period. 1 bluff for every 2 value bets. If you get to the river against 1 then you are going to have the best hand about 1/2 the time and you are only going to be confident you have the best hand like 1/3. So in 6 hands you would value bet 2 and bluff 1.

If you watch the pros some even bluff more.

If you never bluff then players know to lay down. You have to bluff some to get paid off on your when you have it.

You can even do GTO on how often to call - assuming you have a bluff catcher.

It comes from game theory optimization (GTO)

The idea is the bluff rate is such that your opponent is stuck between call or fold. Call or fold has the same EV.

You know you are beat. Your opponent has a good hand but not the nuts. They will call every time with the nuts.

p is pot (before you bet)
b is your bet f is you bluff rate

EV = -b + f(p + 2b)

Set the EV to 0. Solve for f.

b = f(p + 2b)

f = b / (p + 2b)

So is p = b - you bet the pot you should bluff 1/3 of the time
Note if you bet the pot you are giving your opponent 2:1

Play three hands and you bluff twice and have the nuts once
You opponent is getting 2:1 to call and the pot has 100
You opponent folds all three
0 + 0 + 0 = 0 -100 - 100 + 200 = 0

To simplify set p = 1 and and fr just be the fraction of the pot you bet

bluff = fr / (1 + 2fr)

bluff   fraction 
rate    pot  
0.50    100.00
0.44      4.00
0.43      3.00
0.40      2.00
0.33      1.00
0.25       .50
0.20       .33
0.17       .25

Ironically you should bluff more with bigger bets.

You opponent also needs at least a bluff catcher to call.

Clearly you are going to get more bluffs through if a scare card hits on the river. Don't try and bluff a naked 2 on the river if you have shown not strength.

Very important is that does not mean bluff the river 1/3 time period. 1 bluff for every 2 value bets. If you get to the river against 1 then you are going to have the best hand about 1/2 the time and you are only going to be confident you have the best hand like 1/3. So in 6 hands you would value bet 2 and bluff 1.

If you watch the pros some even bluff more.

If you never bluff then players know to lay down. You have to bluff some to get paid off on your when you have it.

You can even do GTO on how often to call - assuming you have a bluff catcher.

Assume you put villain on GTO and bet the pot so you them on bluff 1/3
C = call rate

EV = c 2/3 (p + 2b) - c 1/3 0 - b
= c 2/3(3) - 1 = 2c - 1 c = 1/2

You should call back with a bluff catcher as often as you have hands that you would call back for value.