Concepts: Pure Bluffs

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Pure Bluffs

Before I start with the work on the topic some admonishing words:

In general, pure bluffs are only appropriate in very few exceptions ( i.e. HU – situations in unraised pots). Never ever try to frantically find spots where you might bluff. This is strongly –EV.
Spots for pure bluffs are very rare. It may happen twice in ten minutes or never in 1000 hands.

Okay enough, let’s go back to topic: Pure bluffs are situations in which you bet and raise without holding a hand that has any realistic chance to win the showdown. The only intention for this move is forcing your opponent to fold to win the pot with a worthless hand. In general you actually always have small chances to win but they still very small. A pure bluff is a move with a hand that simply is not the best and does not have more than 3 outs.

The mathematical Aspect

You want to know how to evaluate how profitable a bluff might be? The calculation is pretty simple, you only need 3 variables:

- Pot size (Pot) (Note: it is essential that you take the pot size after your move)
- Probability of your opponent to fold = Fold equity = P (fold)
- The amount of bets the bluff costs (Bets)

A pure bluff is profitable, if:

Example: You are on the button playing against the small blind on the turn, your hand is worthless. The pot size is 7 BB, the SB bets. You can either fold or you can try to bluff him out of the hand. But how often does the SB have to fold to make this bluff profitable?

The size is 10 BB.

P(fold) * 10BB – 2BB > 0

If we fold equity would be 20% we would get following result:

0,2 * 10BB – 2BB = 0

The border of profitability lies at a fold equity of 20%. If the opponent folds more than 20% the bluff is profitable, if he does not the bluff is –EV.

The bluff is profitable if,

P(fold) > Bets/Pot

You can neglect that it might be possible that you hit a miracle card on the river. Ok, that’s all very well, but we deal with a dynamical variable called fold equity. How can you calculate the probability of an opponent to fold? Of course you can not be exact. You have to learn to evaluate the value under estimation of PT-Stats of your opponent, previous action, board texture, pot size and personal reads.
In the following capitals I will explain some ground rules and give some examples where a bluff MIGHT BE profitable.

Some basic Rules

Without dealing with certain spots some ground rules, that describe general conditions that have to be granted if you want to bluff.

a) The opponents: A bluff has the goal to win a pot forcing all opponents to fold. Only try to bluff opponents who know the “fold” button. As a result a bluff works best against rocks and TAGs. Never bluff callingstations and maniacs.

b) The board should offer no draws at the best. We want our opponent to have a tough decision causing him to fold. The decision whether to fold or to call is in dependency of the pot odds, if he thinks that he is behind. If he holds a draw (quite usual for boards with lots of draws opportunities) he might have an easy decision – good for him but not for us. A board like K , 7 , 2 or 8 , 8 , 4 is more suitable for a bluff than a board like J , 9 , 8 . for instance.

c) The number of opponents should be as small as possible. This sounds plausible because the chances of 3 opponents folding is a lot smaller compared to one opponent. A bluff versus 3 and more opponents is very rare. But I will give a example later on.

Heads-up in unraised Pots on the Flop

This bluff is also described in the HU-Standardmoves article, but it also fits here. This is one of the situations where a bluff is profitable in almost every situation.
Because a PokerStrategy player pretty much never makes use of open limping, this situation is very common if you are sitting in the blinds. For example: You are BB, MP2 limps and all others fold. You hold a trash hand like 72o and check.
It is always the same procedure: You bet – no matter the flop, the opponent and your own hand.
Our opponents only has to fold in one out of three cases to make this bet profitable, even though it is possible that you can improve your hand to the winning hand on the next street(s).

To sum it up it can be said: In unraised HU pots you always bet the flop in position (if your opponent checked to you) and out of position as well.

The Pot nobody wants to have

A reason why you might bet with an worthless hand is obvious weaknesses of your opponents who just want to get rid of the hand. Example:

A lose $2/4 full ring table

1) PreFlop: Hero is UTG with J , T
Hero calls, 7 folds, Sb (ROCK) completes, BB (TAG) checks

Flop: (3 SB) K , 3 , 3 (4 players)
SB checks, BB checks, Hero???

A flop that does not give many opportunities of improvement. There is no flush and straight draw on the board and our opponents don’t seem to be interested at all. A TAG usually bets because he does not want to give any freecards even with a hand like 44. The rock will probably not call a weak hand and he will not be tricky in most likeliness. You can assume that your opponents fold in more than 25% of all cases, for that reason you can bet this hand and try to buy the pot.

A second example, written in How good is your Limit Hold’em:

15$/30$, 9 handed: The table ist loose and passive, the opponents are not tricky at all

2) PreFlop: Hero is BB with 7 , 4
2 folds, UTG+2 calls, MP2 calls, 3 folds, Sb completes, Hero checks

Flop: (4 SB) Q , 8 , 2 (4 players)
SB checks, Hero checks, UTG+2 checks, MP2 checks

Turn: (2 BB) 2 (4 players)
SB checks, Hero???

Here you should take advantage of a pure bluff. Hero bets! The reasons are:

- nobody seemed to be interested on the flop
- The opponents are neither tricky nor aggressive
- The turn card did not help anybody and it did not increase the chances of a flush draw

You can assume that your opponents fold in more than 33% of all cases, for that reason you can bet this hand and try to buy the pot.

An example of a hand I played:

3) Party Poker 10.00/20.00 Hold'em (6 handed)

PreFlop: Hotte is BB with 3 , 9 .
1 folds, MP calls, CO calls, 1 folds, SB completes, Hotte checks.

Flop: (4.00 SB) 6 , 2 , T (4 players)
SB checks, Hotte checks, MP checks, CO checks.

Turn: (2.00 BB) 8 (4 players)
SB checks, Hotte checks, MP checks, CO checks.

River: (2.00 BB) 2 (4 players)
SB checks, Hotte bets, MP folds, CO folds, SB folds.

Final Pot: 3.00 BB.

The situation is very much alike with the last example. I hold nothing. The opponents are tight and lose, semi aggressive and aggressive. According to my reads they are no fools and no players who would not bet their hand on the turn to protect it. The 2 on the river was the final aspect for me to bluff, because I was quite sure that it did not help anybody. Of course you might run into slow played trips or so, but I didn’t think that these players would do something like this. They didn’t look like ace high downcallers neither. So I assume that I win this hand in more than 33%.

Bluff Raises

Up to this point we only talked about situations in which the hero tries to buy the pot with a single bet with a worthless hand. Of course it is also possible to force all opponents to fold if you use a bluff raise. These spots are even more delicate to find. On the one hand a bluff raise costs twice as much compared to a single bet and on the other hand people tend to call a raise in more likeliness than a single bet if they already invested money. For that reason you should start these kind of moves if you have seen that they are able to laydown their hand after a raise. Usually this makes sense versus players who try to play the optimal way. There are no standard situations in which a bluff raise might be perfect. I will give some examples of situations which are more suitable for bluff raises than others.

The Bluff check/raise on ragged Flops OOP without Initiative

This situation usually arises when we want to defend our blinds.
Let's use the following example:
Everybody folds to MP2 who raises; everybody folds to Hero in the BB, holding T , 9.
Hero calls. We already watched MP2 playing for some time. According to the PT stats, he plays somewhat tighter than the PS.com Open Raising Standards. When he has a hand, he's relatively aggressive; plays his draws rather passively; almost never bluffs and doesn't make any strange call downs with high card ace, as well as no stupid calls without pot odds. Overall, a rather solid TAG who plays quite predictably though.

4) The flop shows 7 , 5 , 2
Hero checks, MP2 bets, Hero ???

Alright, the bet doesn't amaze us, as Villain knows what a continuation bet is and would bet any flop which we check to him. Considering our reads we now make the following assumptions:

1) Villain's range is 99+, ATs+, AJo+, KJs+, KQo.
2) Villain calls the flop raise with overcards and folds the turn if he doesn't hit.
3) Villain plays call flop, raise turn with an overpair.

Is a bluff check/raise on the flop +EV under these quite realistic assumptions? Actually you should acknowledge that it isn't a real bluff if the opponent has overcards, as in this case we'd have 6 outs, but let's see if a move also makes sense here without considering the outs.

The expected value is calculated as follows:

EV(Hero bluffed) = P(Bluff works) x profit – P(Bluff doesn't work) x costs

These variables now have to be filled in.
For the bluff to work, the opponent has to have overcards AND must not hit an out on the turn. That implies:

P(Bluff works) = P(Villain has overcards on the flop) x P(Villain does not hit an out on the turn)

What is the probability now that Villain has overcards on the flop? For this we simply have to compare every possibilities of his raise range. Offsuited cards have 12 possibilities, suited cards 4 and pocket pairs 6. Villain has no overcards but an overpair (= bad for our bluff) if he has AA-99, and combined there are 6 x 6 = 36 possibilities (theoretically less, as we have a 9 and a T, but let's ignore this for now); for AJ, AQ, AK, KQ, KJs and ATs there are a combined 72 possibilities. This means that Villain has overcards on the flop with a probability of 66%.

Furthermore, Villain must not hit an out on the flop if he has overcards. As overcards represent 6 outs, the probability to not hit one of them totals up to 41/47. That implies:

P(Bluff works) = 0,66 x 41/47 = 0,58

In every other case the bluff does not work, which implies:

P(Bluff does not work) = 1 - P(Bluff works) = 0,42

The costs sum up to 4 SB. 2 SB for the C/R on the flop and 2 SB for the bet on the turn. The profit amounts to 6,5 SB when the bluff works. It is made up of the 4,5 SB which were already in the pot on the flop, and the 2 SB from Villain which he has paid for the bet/call. Thus every variable has been defined and the total EV is:

EV(Hero bluffs) = 0,58 x 6,5 SB – 0,42 x 4 SB = +2,1 SB

Under these quite realistic conditions a bluff would be profitable with any hand.

Extreme scary Board – River Bluff

This bluff move should be used very carefully, because it may cost 2 BB. But in the right situation versus the right opponent it may be quite profitable. I want to introduce this move on two different examples.

A , J , T , 6 , Q

Let’s say hero holds something like 7 , 6 in the CO. There were some people on the flop, hero betted his flush draw for value on the flop and had a couple of callers. On the turn he was confronted with a donkbets that he just called and he finds himself being heads-up versus the MP2 who bets. Hero can be quite sure that he does not have any possibilities to win this SD. But could he buy the pot with a raise (2 BB)?

Another example:

Q , T , 7 , 5 , 2

Hero holds K , J with the same betting sequence as described above. Could he bluff? Hard to say, but under following conditions he could try:

- Villain is able to fold his hand on the river.
- Villain is able to place small value and desperation bets.

A small value bet is a bet with top pair with weak kicker versus an passive opponent. If you have observed behaviour like this you can try this move.

The Psychology

You don’t need nerves of steel at limit Hold’em to place a bluff, because in contrary to NL Hold’em this bluff does not cost more than 2 BB (or 4 BB if you are a maniac bluffer). Nevertheless you feel bad if a bluff did not work out giving the feeling of wasting money. As I said you should not bluff too frequently and you should keep 2 things in mind, if it does not work.
First of all remember your mathematical analyses. Your bluffs usually have to be successful in less than 50% of the times. You are +EV even if it does not work in most cases. The second point is the impact on the table image. There are 2 types of images people like to have. The image of always holding a strong hand when you give action – good image for bluffs. The other image that is quite useful is the image of being a bluffer – you will get lots of action for your strong hands.
Well, after all, we lost some money in bluffs, but this will pay off in future. Of course you need opponents who notice that will react on your obvious behaviour.