Bluffing in No Limit Holdem
The ability to bluff is a big part of poker. We can use it to exploit opponents and also to help us get value from our strong hands when playing against good, observant opponents. Some have said "Bluff just enough to get the job done." How do you decide whether a bluff is a profitable play or not?
You can remember the equation x / (x + y) where x is the size of the bet we must call, and y is the size of the pot before our call. Well, the equation to determine how often our opponent must fold when we bluff is the same, except now x is the amount of our bet instead of the amount of our call. So let’s say the pot is $10, and we bluff the pot with a $10 bet.
x = $10
y = $10
10 / (10 + 10)
10 / 20 = 0.50
So, our opponent must fold more than 50% of the time to have a +EV bluff. Now, let’s take this scenario to the next step. Our
opponent is deciding whether or not to call our pot-size bet. He again uses the x / (x + y) method and comes up with the need to be good 33% of the time.
Take a second and think about that. The reason x / (x + y) works in both these situations is because it’s always a reward to risk ratio. We're risking a certain amount to win a certain amount. The caller always has to be good less often because by the time it gets to him, the pot is larger. Let’s examine table.
Reward:Risk ratio at work.
|Ratio||Considering Bluffing||Considering Calling||Must be Good >|
|Risking x to win .5x||Pot-Size Raise||67%|
|Risking x to win .8x||1/2 Pot-Size Raise||55%|
|Risking x to win x||Pot Bet||Never Happens||50%|
|Risking x to win 1.5x||2/3 Pot Bet||Call 2x Pot||40%|
|Risking x to win 2x||1/2 Pot Bet||Call Pot||33%|
|Risking x to win 3x||1/3 Pot Bet||Call 1/2 Pot||25%|
In this table, "x" will always represent the same amount. In our example, we were risking x to win exactly x. We must win more than 50% of the time. By the time the action got to the caller, he was risking x to win 2x. So, he must be good greater than 33% of the time. Notice, in hold'em, you will never have to risk x to win x when calling. This is because the pot is always larger than what you’ll have to call. This is even true preflop because of the blinds posted. If the pot is $1, and your opponent bets $9,000, you’ll be risking $9,000 to win $9,001.
9,000 / (9,000 + 9,001)
9,000 / 18,001 = 0.499
Notice the two rows on the top of table: a half-pot raise and a pot-size raise. Making a pot-size raise is much different than making a pot-size bet because you have to put a lot more money in the pot to offer your opponent 2:1. A pot-size raise is similar to making a bet that’s 2x pot since, in both cases, you’ll need your opponent to fold 67% of the time. Determining how much to bluff is tricky business. Some have said you want to bet just enough to get the job done. While that makes sense, what that job is needs to be defined. Let's look at an example.
Villain: TT, JT, QJ, KJ, AJ, KQ, AK
The pot is $100. You have $180 left, and your opponent has you covered. You're thinking about bluffing with your A high since you don’t feel it's ever good here. You're thinking about making a pot-size bet. When you make a pot-size bet, you need your opponent to fold 50% of the time to break even. You have the following assumptions. To a pot-size bet, you'll feel he'll fold
TT, JT, QJ and AJ, but he'll call with his KJ, KQ and AK. What percent of his range is he folding?
TT, JT, QJ and AJ total 39 combinations. KJ, KQ and AK total 30 combinations. His folding range consists of 39 out of 69
39 / 69 = 0.565
That's about 56% of his total range. Your bluff is +EV given these assumptions. Looking at our chart and not changing his
folding range, you could even bluff $125 on the river. But, you do not need to bluff that much. We realize that, in general, as we lower our bet size, his calling range increases. As we raise our bet size, his calling range decreases. When we're trying to fold out those Js, we need to make assumptions about what bet size he starts to call with them and keep our bet just over that hump. Obviously if he'd fold his Js to a $33 bet (1/3 pot), we'd rather make that bet. Looking at the EV of each of these bet sizes, we see these results.
Betting $125: 0.56($100) + 0.44(-$125) = $56 - $55 = $1
Betting $100: 0.56($100) + 0.44(-$100) = $56 - $44 = $12
Betting $33: 0.56($100) + 0.44(-$33) = $56 - $14.52= $41.48
But, if he started to call with his Js to a $33 bet, we'd need to reconsider. A 1/3 pot bluff must work 25% of the time. If he now calls with his Js, only the TT combinations are folding. The TT combinations represent 6 out of 69 combinations, for about 8% of his range. Obviously that's lower than the needed 25%. Looking at our EV of that bluff, we have the following.
.08($100) + 0.92(-$33) = EV
$8 - $30.36 = (-$22.36)
So, we need to think about our opponent’s range and what he’ll fold to different sized bluffs. Saying "bet enough to get the job done" is a bit narrow for the purposes of poker. Our job isn't to bet just enough to fold a certain range. It's to choose the line that makes the most money. We can even look at another option here. Let's say we shove. Let's say our assumptions are if we shove, he'll only call with KJ. KJ is 9 combinations out of 69. This is 13% of his range, which means he's folding 87% of his range. When we shove $180 into a $100 pot, to break even we need to have it work 64% of the time (180 / 280).
Let's look at the EV for shoving given our assumptions.
0.87($100) + 0.13(-$180) = EV
$87 - $23.40 = $63.60
Notice this is more profitable than any other option we've listed so far. So, our job is to make the decision that makes us the most money. There are a lot of possibilities as the bet sizes and folding ranges change. You may be looking at the all this thinking "How on earth am I going to figure this out, especially while I'm playing?" There's no magic wand answer. The
best recommendation is to spend plenty of time away from the table working on different scenarios. This will help you develop
a strong intuition when you're playing. You'll begin to get used to different ranges and what sizes work well against those
ranges. It's hard work and takes a lot of effort and dedication. The great players have done so.