NDJJ77 realized that I used to post under RainbowBright pre hack, so I decided to throw together a quick COTW. Hope you find it useful.

I've seen some misconceptions regarding bluffing which I thought I would highlight in a COTW. I prefer examining problems from a GTO standpoint, and then discussing the correct adjustments based on different opponent types.


MISCONCEPTION 1: Your supposed to lose money with your bluffs

MISCONCEPTION CLAIM
This misconception proposes that your bluffs should lose money, so your value hands will get paid off. I've seen this go so far as to suggest that you should play some weak hands preflop such as 45o, so the Villain will call you down lighter and you can make more money with your AA.

CORRECT LOGIC
The problem with this logic is that from a game theoretically optimal standpoint, you'll never be at a nash equilibrium if either player can change their strategy and improve their EV. So since you're losing money with your 54o, it would be correct for you to stop playing that hand pre flop. In fact, your pre flop range is the only range where you should never theoretically have a polarized range... you should only ever raise the top of your range.

EXPLOITATIVE COUNTER CLAIM
This is not to say that their could never be a reason to play a hand in a -EV manner to exploit your opponents. If you think for some reason that if you played a hand in a poor manner, and your opponents would adjust poorly to your mistake which you could capitalize, then it can be correct to play a hand in a -EV manner. For example, if you opened 54o, and you bluffed it off with a gut shot (which should have check-folded somewhere), and if you think your opponents will call you down much lighter FOR A LONG PERIOD, then it can be correct to play this hand this way. But the catch usually is that you don't know who's paying attention, even if they will actually adjust, if they'll adjust in the way you think they will, and that they won't re-adjust until you've had time to earn back your mistake plus more than you would have made playing a more GTO correct style.

BONUS POINT
Another misconception similar to that your bluffs should lose money is that from a GTO standpoint, your bluffs should always be 0 EV. But in reality, only the bottom of your bluffing range should be 0 EV, ALL the other bluffs in your range should be +EV.


MISCONCEPTION 2: You should bluff with the very bottom of your range

If you have a hand which has very little chance of improving on future streets, than you should use it to bluff because your not going to improve, you can fold out better hands, you don't care if you get raised, and it doesn't matter what hand you use to bluff when the Villain folds. Let's look at an example:

Hero Raises the Button with 3 2 because the blinds fold too much. However, the BB calls this time.

FLOP: K J 8
BB checks. Hero bets.

In this example, the Hero has the nut low hand. I'm going to critique the reasons for betting here one-by-one:

MISCONCEPTION CLAIM: Bluff because your not going to improve.
This is actually more of a reason NOT to bluff. As we already learned, in order for it to be correct to be bluffing than our bluffs should be +EV. This will often require us to choose hands which can improve on future streets to bluff. Here's another way to think about it that I think most of you are familiar with. There's a general rule that you should "use the TOP of your folding range, when you 3-bet bluff." Well the same logic applies here. You should use the TOP of your range which you're NOT checking-back as a bluff. Below is a diagram of a correctly constructed betting range:


Polarized Betting Range by RainbowBright2p2, on Flickr


MISCONCEPTION CLAIM: You don't care if you get raised
This ignores the fact that you VERY MUCH care that you got raised because you just lost your bet. In fact, after you get raised, your first instinct is that you wish you could go back and not bet. And while it's worse when you get raised and need to fold a hand with more equity, it's a lot better to have a hand with some equity when called which will happen a much higher % of the time. Which leads us to...

MISCONCEPTION CLAIM: t doesn't matter what hand you use to bluff when the Villain folds.
This is true, but it does very much matter when the Villain calls. The point of having strong bluffs in your betting range is that these hands will improve when your opponent does call. It's important to pick bluffing hands which will allow you to continue to bet when they DO approve. So in the example with A Q, we'll be able to bet for value when we hit the gut shot, and we will be able to profitably continue to bluff when a heart lands. However, when called with the 32o, even if we improve on the turn, we likely won't be able to continue bluffing profitably.


MISCONCEPTION 3: If you're going to bluff the turn, then it's mandatory that you bluff the river when the scare card comes in.
This logic is the flip side of the erroneous claim "If you bluffed catch the turn, then it's mandatory that you bluff catch the river when the river blanks." Let's look at an example.

Hero Raises the CO with A Q, the Button calls.

FLOP: K J 8
Hero bets. Villain calls.

TURN: 5
Hero bets. Villain calls.

RIVER: 2
The claim is that it's mandatory that the Hero bets here because the scare card came in. So the point of bluffing the turn is so you can bluff the river, when the scare card comes in.

CORRECT LOGIC
So in theory, you want to balance your value range with bluffs on every street in order to hand a balanced range on the river. This means that you will stop bluffing with some hands on every future street. In other words, you have lots of bluffs on the flop, and not so many bluffs on the river. Let's try and see how this plays out with this hand. However, I'm pretty confident that we should not be bluffing with our entire range on the river, since I think this card should help the Villain's range as much as it helped ours.

Let's say that we make 2/3 size pot bet on the river. The Villain will be getting 2.5 to 1, so we should have the same ratio of value to bluffs. Let's assume that we can value bet middle set or better. We might have at most 15 value hands which means you should have 6 hands.

So on the river, we should be bluffing with hands which have blockers to the Villain's calling range. So we should be bluffing with the following hands first:
- A Q
- A Q
- A T
- A T
- A T
- Q T
- Q T
- Q T
- 8 7
- 8 7
- 8 7
- 8 9
- 8 9
- 8 9

So although the scare card came in, this is not necessary a theoretical reason to bluff with our entire range. We need to have a check-folding range, so the Villain has a reason to call the turn

EXPLOITATIVE REASON TO BET YOUR ENTIRE RANGE ON THE RIVER
There can be an exploitative to bluff the turn with the intention of betting all rivers with your entire range if the Villain calls the turn, but he folds the river a ton. In other words, you're betting the turn to set up a bluff on the river. This usually happens when the turn is a card which strengthens the Villain's range to mediocre hands with a draw. So the Villain calls the turn, but he folds the river.

FLOP: K J 8
Hero bets. Villain calls.

TURN: T
Hero bets. Villain calls.

RIVER: 2
Hero bets the river.

In this scenario, KQ makes up a large % of the Villain's range which will call the turn and fold the river. In addition, most regs at this level are incapable of slow playing a big hand on the turn. In other words, most Villain's will raise two pair or a set earlier (which is probably correct as long as the Hero is incapable of over-betting rivers). In this situation, the Hero should probably bet lots of river, since the Villain will fold a large % of the time.


MISCONCEPTION 4: If the Hero can bet the bottom of his range as a bluff profitably, then he should.

If the Hero can make a +EV bluff with the bottom of his range, then he should because it's higher EV than check-folding.

CORRECT LOGIC:
Just because it's +EV to make a bluff with the bottom of your range, doesn't mean that it's not HIGHER EV to check. Even though check-folding is 0 EV, just because you check doesn't mean the Villain is going to bet 100% of the time. Not to mention, if you don't have a check-folding range, then there's no reason for your opponent to have a bluffing range, since you'll never fold.

THEORETICAL REASON TO BET BOTTOM OF YOUR RANGE
You need to always make the highest EV choices with all your hands. And it can be theoretically correct to bet your entire range if the Villain folds at a high enough frequency that it's higher EV to bet then to check. However, just because betting is +EV, doesn't mean that it's enough of a reason to bet the bottom of your range.


Hope you found this helpful. If you have any misconceptions regarding bluffing that you would like to share, then feel free to add it to the thread. Or feel free to ask any questions regarding bluffing.

good post, but just out of interest, where are you pulling these "theorems" from? i have never heard anyone mention these concepts before, let alone propagate them as being true.

Well most of them are just provable by math. But I'll do a quick breakdown in case people want to look at my assumptions. Fwiw, I'm unable to do back algebra, so most of this stuff is provable if you have the time.

Misconception 1:
It is provable by a nash equilibrium which states that a game theoretically equilibrium is when both players cannot gain anything by making any adjustment. So there is no theoretical reason for a player to make -EV play, since he could always make an adjustment which is higher EV. And John Nash won a nobel prize for his game theory writings and they made a movie of his life, A Beautiful Mind.

Misconception 2:
This can be proven in a similar manner to Misconception number 1. We know that you should only bluff if it's +EV from misconception number 1. If you can profitably bluff the very bottom of your range, then one of two things needs to be true. Either you should be able to bluff your entire range OR the Villain is doing something wrong. So let's for now assume that the Villain is doing something wrong, since it's a fine assumption to assume that you shouldn't be able to profitably bluff your entire range. In other words, the bottom of your BETTING RANGE should be 0 EV to bet, therefore any weaker hand then this one, by definition, will be negative.

I could show why having a polarized range is better than having a depolarized range with some long math, but it more or less comes down to the fact that a polarized range realizes its equity better. This is because the value hands are for value and the bluff hands are clearly bluffs. However, it's important to remember that you want to use the top of your non-check-calling range as your bluffs... (This last part might seem confusing, but I don't have any other better way of putting it... not to mention that a made hand should sometimes be in your bluffing range, and some unmade hands should be in your check-calling range... maybe I'll try and explain this later if someone is interested).

MISCONCEPTION #4:
This is also provable based on a nash equilibrium. A nash equilibrium tells us that we should always take the highest EV line with all hands at all points. So while it might be +EV to bluff the bottom of your range now, it's also very likely that it can be HIGHER EV to bluff later. This makes logical sense because when you check and the Villain checks back, his range on the turn will be weaker than his range on the flop. Therefore, the EV of your bluff against his turn range will be higher than the EV of your bluff against his flop range. Hope this makes sense. This is actually pretty advanced concept that is not often played correctly at the micros or small stakes. Almost all players who are able to make a +EV bluff will take it as soon as possible. This is why it's often a problem when someone checks behind as the pre flop raiser on a Kxx board because his range is almost always a weak made hand because he bluffs all his air.

MISCONCEPTION 3
This was proven in the mathematics of poker. Now if all our made hands had 100% equity and all our bluffs had 0% equity, it would be easy to find out game theoretically optimal frequencies for bluffing for a particular bet size. However, since our value hands will get drawn our sometimes and our bluffs will sometimes out draw the opponents bluff catchers, the math is a little more complicated and can't be completely solved. However, it is possible to come up with a close number if you can make some assumptions on the equity of our value and bluff hands (which Matthew Janda has shown in a video... and I could show here if people care). But the point to remember is that you're not supposed to be betting 100% of your range on the river to make the Villain indifferent to call on the flop. Therefore, there is no reason for you to be betting 100% of your range when the scare card comes in UNLESS it hits your range so much harder than your opponents that the highest EV line for all your hands is to bet.

bump for afternoon crowd

Very nice break-down sir.

Great post. Also....

Only ever heard of the Nash Equilibrium after looking in to heads up Nash poker charts....but had no idea it was linked John Nash...love that movie.

The "one brilliant idea" he's after in the film is the concept of a game-theoretical equilibrium.

Many of these misconceptions stem from the fact that some theoretical analysis doesn't properly account for multi-street games with dynamic equities, i.e., draws. Other problems arise from mixing optimal play and exploitative play.

Edit: Concept #2 is correct for river play. On earlier streets even Doyle Brunson advocated "bluffing with an out", i.e., semi-bluffing.

Didn't know that. It's been a while since I've seen the film (probably before i even started playing poker). I just remember loving Paul Bettany's character....



I don't really understand this. So are you saying that we shouldn't have a bluffing range pre at all? Not even in an exploitative sense. Or am i just reading it incorrectly?

The way I understand it, if you decide not to open-limp, it doesn't make sense to fold the middle of your range and raise (bluff) the bottom of your range; it would always be better to fold the bottom part and raise the middle part. Hence, polarisation comes into play if you have a passive option (checking or calling) for your middling hands. Of course if limping or cold-calling is an option then our raising/3-betting range will be polarised. Again this is muddled by the fact that the equity isn't static, so we're talking semi-bluffs here.

I always understood this as: When I get raised I'm not put in a tough spot since I have an easy fold. So I'd rather raise a c-bet with a gutshot or middle pair than with a non-nut flush draw as I can easily fold to a 3-bet.

Ahhh, that makes a lot of sense. When he said 'pre flop range' i was thinking more of a 3betting range and getting confused.

I for one am definitely interested. Nice thread. I've revisited the Rainbow Bright "Roshambo" thread over and over the past few months and have been patiently waiting for the sequel. Love to read (and attempt to absorb) your stuff.

I have been looking for an excuse to open pre with every pair. Is this it?

Bluff if you think they're gonna with X% frequency of the range of hands on that street.
X%= 42% if you bet 2/3. 33% if you bet 1/2. 50% if you pot it.

I think having a balanced bluffing range is going to cause greater harm than good at micros. It's almost impossible to determine villain's range well enough.

Whole idea of having a balanced is to disguise actual hand strength. In theory balanced poker= break-even poker= unexploited poker= losing to rake poker.

The pros of disguising hand strength by polarizing hand strength by position, is heavily outweighed by the cons of having to play a weak range OOP.