Poker Optimal Bluffing Frequency

Bluffing in Poker - Proper Strategy. Bluffing and bluff strategy is one of the hardest but most fundamental parts of poker. Without a doubt, if you do not bluff in poker, there is no way you can be a successful poker player. That being said, bluffing is no small task, as it requires good poker sense, timing and guts to pull it off. There is no set optimum frequency for bluffing that covers every situation. It would be awesome if I could tell you that you should bluff once every 10 hands or something to that effect, but there are no hard or fast rules in poker.

Which poker stats are most important?

Our poker HUD software offers a large amount of statistics. Knowing which ones are relevant and important can be overwhelming. If you are new to poker software you can initially ignore all statistics except the essential three poker statistics. Once you have understood how to use the basic statistics, you can add more depending on your style of play, and your chosen table size.

The big three poker statistics (and one bonus stat):

  • Voluntarily Put $ in Pot (VPIP)
  • Preflop Raise (PFR)
  • Postflop Aggression Frequency (Agg)
  • A bonus stat: Big blinds won/100 hands.

These three statistics are a great starting point to get an idea of a person’s playing style. They only require 25 hands or so to reliably give a good idea of a player's tendencies.

Voluntarily Put $ in Pot (VPIP)

VPIP in poker measures how often you voluntarily pay money into a hand before seeing the flop. Paying the big blind, the small blind, or the ante is not considered voluntary. Therefore this percentage indicates how often you called, bet, or raised. The lower this value, the tighter your hand selection is. The higher, the looser. Only preflop betting is taken into account.

Good players know to only invest money in the pot when they have decent starting hands. A simple way to measure whether you are doing this is to keep your VPIP at a sensible value.

What is a good number for VPIP?

Simple answer: between 15% and 20%. This assumes you want to play tightly, you are playing micro-stakes, and you are playing on full ring cash tables.

Now the more complicated answer: it depends a lot. If you are still learning to play good poker, then you should be very selective in which hands you play, so your VPIP might acceptably be a tad lower than 15%. The less people on the table, the more hands you can play. If you are on a table full of ultralight players, you can also loosen up. An experienced player who understands the subtleties of the game can get away with a VPIP between 20% and 27%. In 6-max or heads-up, most players have a much higher VPIP. In Pot Limit Omaha, VPIP values will be even higher.

Preflop Raise (PFR)

The PFR statistic indicates how often you have raised before the flop is seen. A high value is an indicator of an aggressive player. A low value indicates a passive player. Good players are aggressive players.

Your PFR has a possible range between a minumum of 0% and a maximum equal to the value of your VPIP. That is, if your VPIP is 20%, then your PFR can’t be higher than 20%. Ideally it should be a little lower than your VPIP, but not much lower.

Poor players and beginners play timidly. They call too often preflop. Good players frequently fold or raise preflop, especially if no other players have yet raised. If you are not prepared to raise, then you should consider folding. Calling preflop just in case the flop is good for you is not a winning poker strategy.

What is a good PFR range?

Between 2% and 3% lower than VPIP. If your VPIP is 15%, PFR should be about 12%. These two numbers in combination indicate that you are only playing quality hole cards, and you are predominantly raising with them pre-flop. In other words, you are playing how most poker books and poker forums say you should play.

Postflop Aggression Frequency (Agg)

Agg indicates how aggressively you play postflop. The higher this number, the more aggressively you are playing. This must be interpreted in combination with VPIP. Players who see very few flops will naturally tend to have a higher aggression percentage because they are only playing top-quality hole cards.

Poor players play passively postflop. They’ll check or call too often. Good players know to play good hands aggressively postflop:

  • because players with speculative hands are forced to fold before they get free cards
  • because if they hit the flop or have a dominating hand, a bet or raise will increase their return

What is a good Agg range?

50% to 60% is ideal, assuming that you have a VPIP of 15% to 20%. Much higher, and you are probably overplaying speculative hands and bad hands, and bluffing too much. Much lower and you are not playing your good hands strongly postflop.

Leave the bluffing for the movies and for live play. At low stakes online play, bluffing is much less important than a good understanding of the probabilities of winning hands.

Big blinds won/100 hands

The three stats I've presented so far mean nothing if you can't keep your win rate positive. A nice way to 'normalize' your win rate across different stake levels, table sizes, and opponents is to measure how much you won in terms of the big blind. If you are playing at a table where the big blind is $0.50, and you won $20, then think of this as winning 40 big blinds.

If this number is not positive, then you are losing money. The best remedy is to drop to a lower stake level, where the opponents are weaker. If, according to this stat, you consistently win over time, then you should consider going up to a higher stake level.

Adjusting your play based on the villain's poker stats

This is where our poker HUD software gets really useful: analyzing and exploiting opponent weaknesses. Let's consider some hypothetical players:

Tight Tim has VPIP of 5%, PFR of 5%, and Agg of 100%

With such a low VPIP, we can guess that this player folds anything except the very best hands. And with a PFR equal to VPIP, when he gets premium hands, he raises. So if this player raises, and you are next to act, you know that you should fold every hand except the best few hands, such as AA, KK, QQ. You can be almost certain that if you go to the flop, he'll raise postflop. So play tighter than usual with this player. But when you do get a premium hand, and he comes along, you can be sure that player B will put plenty of chips into the pot. Your pot, hopefully.

Passive Pete has VPIP of 20%, PFR of 16%, and Agg of 10%.

This player seems take have a good handle on preflop play. But when he gets to the flop, he gets timid. He is probably going to give you a chance postflop to see the turn and river for free. If you go to the flop with him and raise, there is a good chance he'll fold. So you can play a bit more aggressively both preflop and postflop.

Eddie the Eagle has VPIP of 22%, PFR of 19%, and Agg of 55%.

Eddie has a good all-round balance between preflop and postflop play. Preflop, he plays tight and aggressively. Postflop, he balances between pushing hard with his good hands, and being willing to fold or check with his weaker hands. Eddie would be well-served to move on to understanding more advanced poker statistics.

Tracking your poker stats

Poker players use poker software like Poker Copilot to automatically record their hands. Each hand is broken down into many statistics, which are then aggregated into simple percentages.

Poker Statistics Guide

What’s next after you’ve understood the basic poker stats? Read our Poker Statistics Guide for a comprehensive explanation of understanding and using all the main poker statistics.

By Andrew Brokos

Introduction

I had a nightmare last night that I was playing high-stakes heads up no-limit hold ’em with Phil Ivey himself. I knew he had picked up a tell on me that revealed the approximate strength of my hand as strong, marginal, or weak, but I didn’t know what it was or how to stop doing it.

The river had just completed a possible flush, and the final board read 5 [spade] 8 [diamond] T [spade] Q [heart] 2 [spade]. I was holding A [spade] T [heart] and checked. Phil gave me that look, like he’d just spotted my tell, and then announced, “All in.” The dealer counted the bet down: $14,000 even, into a pot of just $6000. Somehow, I managed to have the Great One covered. But could I call this bet?

Optimal Calling Frequency

OK, I don’t really dream about poker. At least not that vividly. But it’s a good example of a nightmare situation, facing a big bet on the river when your hand is clearly defined as good but not great. Unless you have some exploitable read on your opponent that he either bluffs too much or not enough, then your best defense in a situation like this is to use game theory to make your decision.

Let’s assume that this river overbet represents either a flush or a bluff. The real Ivey is probably good enough that his game can’t be pigeonholed so neatly, but this is my nightmare, and I make the rules. Is he going to bluff all of his air to make me fold one pair? Is he never going to bluff because he knows I know he knows I only have one pair and he expects me to expect him to bluff? He’s Ivey and I’m lowly old me, so I’m going to abandon any pretense of outthinking or outplaying him.

In a situation where I beat all of his bluffs and none of his value hands, I’m going to call with a frequency such that it doesn’t matter what he does. In fact, I could show him my hand, tell him what percentage of the time I’m going to call, and there would still be nothing he could do to take advantage of me. I need to find the calling frequency such that whether he bluffs 100%, 0%, or anywhere in between, it makes no difference to my bottom line.

To do this, I have to figure out what calling frequency will make Ivey indifferent to bluffing with this bet. He is risking $14,000 to win $6000, so his Expected Value (EV) for a bluff is equal to -14000 (x) + 6000 (1-x), where x is my calling frequency. We want to solve for x such that his EV will be 0, so

0 = -14000 (x) + 6000 (1-x)
0 = -14000x + 6000 – 6000x
0 = 6000 – 20000x
20000x = 6000
x = 6000/20000, or 30%.

One way to prevent Ivey from exploiting me with a bluff in this situation is to use a random number generator to call with an arbitrary 30% of my bluff-catching range. Dan Harrington recommends the second hand of a watch for this purpose. Any time I have a hand that can only beat a bluff, I check my watch. If the second hand is at 18 or lower, I call. Otherwise, I fold.

Again, even if Ivey knows that I am doing this, there is nothing he can do to exploit me. If he bluffs more, I catch him just often enough. If he bluffs less, then he misses out on just enough pots that he could have stolen from me.

Blockers

That’s one method, anyway. If I know that I need to call 30% of the time, then I can call with each of my bluff-catchers 30% of the time.

Optimal

But not all bluff-catchers are created equal. In this example, there is a big difference between my hand, which is A [spade] T [heart], and the nearly identical A [heart] T [heart]. Can you see what it is?

When I have the A [spade], Ivey has fewer flush combinations that he could be value betting. The equation we looked at above is just the EV of Ivey’s bluffs. Since I never have a hand stronger than a flush, his value bets are always going to be profitable. My EV on the river is going to be equal to the amount I win by catching his bluffs minus the amount I lose by calling his value bets.

Poker Optimal Bluffing Frequency Analyzer

The A [spade] in my hand removes twelve combinations of flushes from my opponent’s range. When I call with A [spade] T [heart], I will run into a flush a lot less often than when I call with A [heart] T [heart]. Thus, even though both hands beat all bluffs and lose to all flushes, one of them will be shown a flush far less often and is thus a far superior candidate for bluff-catching.

I will have the A [spade] 25% of the time that I have AT. Since it is a better bluff-catcher than my other AT combinations, I want to call with it over the others whenever possible. Thus, I should call 100% of the time that I have A [spade] T and use a random number generator to call 5% of the time that I have any other AT combination, so that I am still catching bluffs 30% of the time but paying off value bets as infrequently as possible.

Hand Strength

This, then, is one of the characteristics of a good bluff-catcher: it has blockers to my opponent’s value betting range.

Another important characteristic is that a bluff-catching hand should be able to beat all of your opponent’s bluffs. That may seem obvious, but I’ve had a river bluff called by a hand that I beat on more than one occasion.

In this example, since we don’t expect Ivey to be value betting one-pair, it may seem like AT and 33 are functionally the same hand. The catch is that Ivey could be bluffing one-pair. What a disaster it would be to “correctly” snap off a bluff only to find that he was turning 66 into a bluff and just took you to Valuetown, completely by accident!

Stronger hands are also better if there’s any chance of beating a hand that your opponent is betting for value. As I said before, Ivey is an extremely good player, so he might try to confound all of this reasoning by betting a hand like KT for value. Even if I don’t think that’s likely, all other things being equal, I might as well call with AT rather than 33 just in case.

Practice Avoidance

The best tactic of all for dealing with a situation like this is to avoid it altogether. You never want to be in a spot where your hand is as clearly defined as mine is in this example. Hopefully you do not regularly compete against opponents with reads as rock-solid as those of Nightmare Phil Ivey, but you should still be careful about avoiding situations where your range contains nothing stronger than bluff-catchers.

We don’t know the action leading up to the river in this hand, but let’s say that I bet the turn with my top pair, top kicker, and then checked the scare card on the river. That’s a fine way to play it as long as I’m also capable of checking a strong hand like the nut flush in the same spot. Doing so won’t prevent Ivey from value betting or bluffing, but it will make both of these plays less profitable.

By the way, if I were capable of showing up with a value hand when Ivey shoves the river, I would need to adjust my bluff-catching frequency accordingly. For example, if 10% of my range were flushes and the rest were AT, then I would only need to call with AT 20% of the time, since my overall calling frequency still needs to be at 30% to prevent exploitation from bluffing. That means I’d never want to call with any non-spade AT, and even with the A [spade], I’d only need to call 89% of the time.

Where did that number come from? When flushes are 10% of my range, AT is the other 90%. One-fourth of those AT combinations include the A [spade], so overall A [spade] T is 22.5% of my range. But I only need another 20% worth of calls, so I don’t want to call every time I have the A [spade], and 20/22.5 is approximately 89%. To translate that into seconds on a wristwatch, multiply by 60 to get approximately 53.

Real-Time Decision Making

Poker Optimal Bluffing Frequency Examples

Poker Optimal Bluffing Frequency

You’re probably wondering what good all of these calculations are going to do you at the table. Well, we practice this kind of mathematical precision away from the table so that our understanding and our instincts are better when tough spots arise in live games. Even if we aren’t able to be quite so precise in the real world, we can use our understanding to make good approximations.

If I really found myself in this situation, the first question I’d ask myself is how the hand I’m holding compares to all of the other hands I would have played in the same way. If I rarely or never check a hand stronger than AT on the river, then I know that I have to call sometimes with AT or a comparable bluff-catcher to avoid being exploited by bluffs.

The math behind my optimal bluff-catching frequency isn’t hard: it’s just the size of the pot divided by the sum of the pot plus the river bet, or Pot/ (Bet + Pot). Once I know that I need to call 30% of the time, I think about my range and try to decide what are the best 30% of hands that I could have in this situation for catching a bluff?

Remember our criteria for a good bluff-catcher: (1) able to beat all of the hands he could be bluffing with; (2) blocks some portion of the opponent’s value betting range; (3) possibly even ahead of a thin value bet. If all I can ever have in this spot is AT, then even without doing any math I can recognize that a hand with a spade is a much better bluff-catcher than the alternatives. Calling when I have a spade and folding when I don’t would be a very close approximation to the optimal solution, costing me only about $300 in EV for the 5% of the time that he gets away with stealing a $6000 pot.

Poker Optimal Bluffing Frequency Definition

Poker Optimal Bluffing Frequency

Poker Optimal Bluffing Frequency Calculator

Playing high-stakes heads up no-limit hold ’em with Phil Ivey and losing no more than $300… now that’s a dream come true!