Hi,

please forgive and correct any blatant errors, miscalculations or oversights in logic or methodology. maths has never been my strongest asset but i'm determined to give it a go.

I have been reading Alex Fitzgerald's chapter on hand analysis in Jonathan little's "excelling at no limit" and this is where the method I am attempting to employ (for the first time) is coming from.

I have picked a spot in a low stakes MTT that I felt at the time I might have been able to attempt a 3bet bluff. I chickened out at the time but marked it in order to run some maths after to determine if it could be a potentially profitable spot to 3bet bluff with ATC

I think that perhaps one of the most daunting part of calculations such as these for me at the moment is trying to assign a hand range to a player that we have little information on. so criticism on this aspect will be much appreciated also.

method:

step 1: determine how often this bluff must work in order to show an immediate profit

In this hand I am in BB with roughly 50BB. Action folds to the btn with 100BB+
blinds 250/500/65. Btn raises 3x (1500). SB folds. I consider a 3bet bluff to 5000.
So, if my maths is correct. Then this bluff needs to work 61.3% of the time in order to show an immediate profit:

4500/(4500+2835)
=4500/7335
=0.613

step 2:Now to assign villains range.

Btn is unknown but is in good shape with 3.5x the average stack size, and 100BB+. I assume therefore that his range here should be wide, I would assume probably wider than that which I have assigned of 32% (22+,A2o+,A2s+,K7s+,K9o+,Q8s+,QTo+,J9s+,JTo,T9s,98 s,87s,76s,65s,54s)

step3:calculate what range villain must defend with in order to make us not 3bet with ATC:

villain opens 32%
villain must defend 61% of 32% = (0.61)(0.32) = 0.195 or 19.5%
therefore villain must defend 19.5% of hands, which includes 33+, all suited aces, A5o, KTs.

conclusion: This could potentially be a profitable spot to attempt a 3bet bluff as villain is unlikely to be defending smaller pairs and mediocre aces.


Further aspects that I should consider?

The hand I have is complete junk. Should I attempt this with, at least, a hand that has some potential equity if I am flatted, i.e a suited hand?

I have very little information on villain. would I be better waiting to get a better feel for how villain plays?

Thanks in advance for commentary and criticism.

PokerStars - 250/500 Ante 65 NL - Holdem - 9 players
Hand converted by PokerTracker 4

MP: 15.49 BB
MP+1: 17.5 BB
MP+2: 16.01 BB
CO: 10.81 BB
BTN: 101.4 BB
SB: 10.29 BB
Hero (BB): 48.55 BB
UTG: 44.07 BB
UTG+1: 10 BB

9 players post ante of 0.13 BB, SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 2.67 BB) Hero has J 3

fold, fold, fold, fold, fold, fold, BTN raises to 3 BB, fold, fold

BTN wins 3.67 BB

There are aspects to be considered. E.g. why do you 3b more than 3x 50 bb deep? Another aspect is how do you want to balance value/bluff when ready to 3b atc.
Another issue is ICM, the numbers you computed are valid only for chip equity, close to bubble you need more FE than it looks at first sight.

Giving the villain a range is a lot like that kids game 'Guess Who'. We start off by assigning everyone a 100% range, and then every time anyone makes a move we remove hands from their range.

To understand which moves they would, or wouldn't make, with the different hands in their range, you need to see the game as they see it. You need to look at the game through the villains eyes. If he see's that there are 8 people left to act after him, you can expect him to fold almost all his crappy hands. If he is facing a 3bet, again, you can expect him to fold a load of his crappy hands. Every single factor in the game helps us put the villain on a range so you basically have to learn everything if you want to do this perfectly.

You don't need to do it perfectly. Attempting to put the villain on a range is what we call Level Two. Level Two is pretty easy to think through but it is definitely impossible to perfect. All you have to do is put him on a range as best as you can and then you are a Level Two player. Instead of attempting to make an accurate assumption of his range at this Level it is far more important to understand the next Level, which will help you put him on a range. At Level Three we need to consider the way in which the opponent sees us. We need to consider our perceived range, which again, is impossible to perfect. You just need to try it and you will do better than most. Then Level Four is the last Level you need to learn. At this Level You consider what the opponent is pretending to have.

I hate maths too so I'm not even going to read that far into your post. But I can tell you that maths in a tournament is far more difficult than maths in a cash game because the prize structure is far more complicated.

I will comment more later but at a quick glance I think .61*.32 I'd wrong. Villain needs to fold 61% of the time so that means he only needs to defend 39% of the time.

Also I will add that equation is assuming your hands have no equity. If you choose terrible hands to do this with that don't block villain's calling range or flop a lot of equity you will need your hand to reach that fold equity without a lot going for it. On the other hand, if you choose better hands you get villain to fold more often just due to card removal or you get to make more money from your equity and don't need villain to fold as much.

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Sorry for the spamming. To add to this stack depth is going to play a big role here as well. If you can threaten villain's stack his open range may be smaller or villain may fold much higher in his range not wanting to play post flop.


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Generally speaking, the most profitable 3-betting hands will be those that block villain's calling range (or 4-betting range, if you're not going all in) and/or that have good equity against the hands that do call.
e.g. A5s would be a better 3-betting hand than J3o, since not only does A5s reduce the number of Ax hands villain calls with (so he's folding more often), but it even has 33% equity if villain wakes up with kings.
You should only be 3-betting with trash hands if villain has a stupidly high folding frequency. (Sometimes he has to fold very often due to strong ICM pressures, for example, but then he should realise that and not open very wide when he realises you can jam with trash and print money).

Blocking the villains range is a very minor factor, and you didn't mention playing cards that the opponent wont expect. That is huge! Its pretty much all you do using the third exploitative Level.

Hmm, an experienced Reg like Arty missing such an important factor. It's almost seems like his mind has blocked his access to the third Level of thought...

Alex Fitgerald in his chapter on hand analysis suggests that betting bigger from OOP can sometimes have the effect of neutralizing positional advantage by forcing opponent to either continue with a range so good that we will not be touching a chip in further streets, or fold.

I quote " If you make it 6500 (i.e 3.25x), most people will think you are nuts. They will think you are one of those guys who is afraid to get his jacks cracked. What they are certainly not going to think is, "I bet I can 4-bet this guy off his hand"...your bet doesn't need to work too often. You'll be risking 5,500 to win 10,000. Your bet will need to succeed 55% of the time in order to be profitable."

There is a reason that an opponent wouldn't expect hero to be 3betting with certain cards.

I don't necessarily agree with his logic but inflating the pot can reduce positional advantage because there is less poker to play before no more betting can occur.

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Let's say villain opens with the following hypothetical range:

AA,KK,QQ,AK,AQ,AJs

Total number of combos without card removal: 54

Now let's say you have Ah5h

Total number of combos for villain's range:
42

Total range reduction: 54-42 = 12

12/54 = 22.222% so you have reduced another players extremely tight range by over 1/5th just by holding an A.

The effect I would imagine holds pretty well as ranges get wider as most people prefer to add Ax to their range before other combos (probably for similar reasons).

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I think I understand my error here. Please could you confirm If this stream of logic is correct:

We calculate though direct odds what percentage of the time our bluff raise must succeed in order for it to be +ChipEV (no ICM considerations).

- in this case 61% of the time

Now we need to determine, as closely as possible, whether or not this is likely to be the case: We attempt to do this by assigning villain a range, and then decide wether or not villain is likely to fold that percentage (in this case 61%)
of their holdings, or more. If the answer is yes they will likely fold that much and more then our bluff raise becomes +ChipEV.

The maths we use however determines what percentage of villain's range they must defend (not fold). If we then feel that the range which that percentage represents is wider than we assume villain will defend then it is likely that our bluff will be +EV.

So in this case bluff must work 61% of the time to show an immediate profit.
Therefore villlain must defend 39% of his hands to prevent us from realising this immediate profit.
We have assigned villain a range of 32%

So .32*.39 = .125 or 12.5%

Therefore If we believe that villain will not continue with a number of hands in this range then he is folding too much and the bluff becomes +ChipEV.

In this case 12.5% represents a range that includes lower pocket pairs such as 44, 55 and hands like A7s and KJs.

Yes that seems better to me. I think everything else was fine just pointing out I think you wanted to use the calling frequency not the folding frequency.

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Having addressed the theory, in practice, would anyone here consider a 3bet bluff in this spot with trash against an unknown? If not, then what would you consider a reasonable bluffing range?

I think most people that 3-bet trash hands went busto in 2011. The ones that didn't seem to have made this year's Main Event final table though, so maybe you're right!

To support/extend JG’s premise, here are some required folding frequencies if you raise with a semi-bluff which has some equity.

Equity Rqd FE
0% ….. 61.3%
5% ….. 58.3%
10% ….. 54.7%
15% ….. 50.3%
20% ….. 45.1%
25% ….. 38.7%

Thank you for this information. Would you be so kind as to explain how you made these calculations?

Oh boy! OK-here goes.

I have the EV equation for a hero raise programmed in Excel-VBA, which employs its Goal Seek function to find the value of a particular variable to set EV to 0, break-even. The EV equation for hero is as follows:

EVhero_raise = fe(Hpb+Pot)+(1-fe)EVvill_call

EVvill_call = eq(Pot+Vbet+Hraiseof) –(1-eq)(Vbet+Hraiseof -Hpb)

where
fe = fold equity (TBD)
eq =card equity (variable)
Hpb= hero’s previous bet (500, the big blind)
Pot = pot before villain bet (1335)
Vbet= villain bet (1500)
Hraiseof = hero raise-of (5000 -500-1000=3500)

The calculation assumes we realise our equity, which is not true with our stacksizes.
Somebody wrote sooner that a hand Axs has about 30% equity against monster like KK. Such a hand has 0% eq as it always folds to push pre.
Actually blockers are more important and quality of hand less than it looks.