Calling 3 bets

When is it ok to call a 3 bet? Pretty broad I know and I know "it depends", so bare with me here. Say effective stacks are 100bbs deep. From a mathematical standpoint, what would constitute a call? You need the implied odds and I have heard that 20-1 is what you need. This seems high to me and should be lower.

I know that this all is situational like depends on the player, stacks, position, etc. But, I am looking from a general standpoint. Lastly, what type of hands can you call the 3 bet with if you are getting the correct implied odds? In other words, what hands would be profitable to call with? pps? scs?

*Cliff notes*

We need 135bb effective stacks before calling to set hunt becomes a breakeven play against an opponent with a reasonably wide 3 betting range. Thats almost 20:1. Against ultra tight 3 bettors (AA/KK) a call becomes only marginally correct with an EV of +0.47bbs getting 12.5:1.

*Math Post*

You need implied odds of 8:1 or more. That is an average so it has to take into account all the times villain has AK and misses, all the times he has QQ and an A comes etc. There will also be times when villain flops a higher set and you get stacked, or he flops a draw with strong equity (i.e. a straight or flush draw) so bump it up to 10:1 for that.

Now whether or not we can stack them depends mostly on how tight their three betting range is. If his 3bets mean AA/KK then we are stacking him on any non A flop and 10:1 will probably be close to profitable for us. Assuming he stacks off with overpairs+

AA- Always stacks (6 combos)
KK - stacks off 77% of the time

So on average hes stacking off 89% of the time. (100+77)/2

We raise to 4bb preflop with :6d: :6h: UTG+1. TAG villain reraises from the CO to 12 bb with AA/KK. If we call the 8bb...

1) 87.5% of the time we miss our set and c/f. :EV -7bb

12.5% of the time we flop a set. We check to the raiser and he cbets 18bb. We raise and eventually get it allin.

Of the times we flop a set, 11% of the time, we c/r him and he folds and we pick up +34bbs. EV +0.47bbs

And 89% of the time we get allin with 80% equity. 80% equity means we expect to end up with 160bbs of the total 200 that will be in the pot. We have 96bbs in our stack at the moment so that is + 64bbs. EV +7bbs.

So the total EV of calling an ultra tight 3 bettor with 100bb effective stacks is +0.47bbs.




In a real game a TAG will be 3 betting ALOT more than that. A more normal 3betting range is something like, TT-AA/ AQ+. If we assume all of the hands will stack off when they are overpairs, but not as underpairs, and AQ+ will stack off when it hits a pair then we get

AA- Always stacks (6 combos)
KK - stacks off 77% of the time
QQ - stacks off 59% of the time
JJ - stacks off 43% of the time
TT - stacks off 30% of the time

AK and AQ will stack off 1/3 of the time (roughly) and there are 16 combinations of each so the number of times we expect them to stack off is given by

[6*(1+0.77+0.59+0.43+0.30) + 16*0.33 ] / 46 = 18.54+5.28 = 52%

So hes only actually stacking off half the time. When he does chose to stack off we have around 80% equity so the total EV looks like this.

We raise to 4bb preflop with :6d: :6h: UTG+1. TAG villain reraises from the CO to 12 bb with AA-TT / AQ+. If we call the 8bb...

1) 87.5% of the time we miss our set and c/f. :EV -7bb

12.5% of the time we flop a set. We check to the raiser and he cbets 18bb. We raise and eventually get it allin.

2) Of that 12.5%, 48% of the time he will fold to our raise, and we will win his cbet + preflop for +34bbs . :EV +2bb

3) The other 52% of the time when we flop a set we will stack off with 80% equity. The pot will be 200bbs, we will get back 80% of that so we will expect to end up with 160bbs. We have 96bbs in our stack at the moment so that is + 64bbs. : EV +4bb.

The total EV is then -7 +2 +4 = -1bb. So a call is unprofitable.

In order for the call preflop to be profitable we need the third term to be bigger at least +5bb. Assuming he will stack off with the same range when stacks are deeper we need

0.125*0.52*[(0.8*2S) - (S-4)] > 5

0.065*[0.6S-4] > 5

0.039S - 0.26 > 5

S > 135bbs

So we need 135bb effective stacks before calling to set hunt becomes a breakeven play against an opponent with a reasonably wide 3 betting range. As his 3 betting range becomes wider, the likelihood of him stacking off when we hit becomes smaller, and the less profitable calling 3bets becomes.

That's very insightful Pelion. Just what I was looking for. When would it be correct to call with something other than pps? I understand that calling for value with big hands and such and maybe 4 betting if our image sucks and they are just making a play. But, when is it correct to call with let's say scs? I'm assuming that we would need deeper stacks since it would be more difficult to stack someone. Forgive me if this seems noobish.

Great maths post Pelion interesting stuff.

To sprayed, my contribution to the topic
To start imagine you guys only had 12bb effective stacks.

So when he 3bets you, you can only call or fold.

If this were the case you'd have to call 8bb to win 17bb (your 4bb raise, his 12bb 3bet and 1bb for blind.)

This means due to pot odds you should call if your hand has 32% equity vs his 3bet range.
If he has a really tight 3bet range like QQ+, Ako+, you can only call with
any hand in his 3bet range or a pocket pair profitably.
If has a really loose 3bet range say 99+, KQo+
you can still call with any hand in his 3bet range and any pp, and non-dominated sc's.

With full stacks we should still play the same all things being equal,
but unfortunately there are alot of factors to take into account...

1.The first and most important is "iniative/aggressor" ev - the pfr usually gains alot of ev in the hand esp. if the opponent just tries to play hit to win poker and set hunt as in the example above. (ie. he takes down the pot too often pre-flop or on the flop than should be mathematically correct, ie. you may fold your Ak to his Aq cbet on a flop you both missed, or your 55 to his AQ on K96 flop.)

2.The second is positional ev, if the 3bettor will have position on you post flop you will lose alot of ev trying to play a hand with 33% equity vs his range for 3 streets. (but less than iniative ev)

So because of having to deal with this ev draining post flop scenario, it is actually in practice rarely very profitable to just call a 3bet.

You should instead maximise your ev by at least 4 betting any hand in the top 1/2 of his 3bet range (you are over 50% to win those hands)
You should also 4bet weaker hands about 1 in 4 /5 times (depending on the pot odds you're giving him with your 4bet.)

a) Because he can't do anything to counteract it if the frequency you "bluff" 4bet is in line with the pot odds you give him. (You'll have to read up on Sklanskys optimal bluffing frequency if you are not familiar with it.)
b) Because you regain the iniative in the hand (iniative ev) & he will fold more often pre-flop or on the flop to a c-bet than is mathematically correct.

The only times I think it is correct to call a 3bet is when you have either positional ev vs someone who folds too much on turn or river or great implied odds ev vs someone who will put there stack in too often with an overpair.
(& Pelions post above is probably ideal to figure out when you have odds to do so.)

Note# with 100bb stacks if you were playing hit to win poker you would be better of calling non-dominated sc's to a tight 3bettor because of the greater implied odds, but as Pelion explained they are rarely there until you get to 135bb+, so I would still prefer calling them to a loose 3bettor (where you have more equity vs his range) if I believed his range or his style was also too weak/tight post flop to stand a raise on alot of board textures. (also taking into account my own image.)


Again take this with a pinch of salt, just been thinking about similar topics these last few weeks while waiting for a proper internet connection to play poker.

Keep in mind that I have a mind of a tourney player and I am usually dealing with situations that involve short bb stacks. So, noble's analagy regarding 12bb stacks makes very good sense. Normally, in a tourney when I have 12bbs, I'm not raising with a hand that I'm not willing to go busto with.

Understanding proper odds to call, dealing with different stack sizes, and ranges is my leak right now. Not to mention post flop skills, which I suck at. Which Sklansky book, TOP or NLHTP regarding optimal bluffing frequency? Great posts guys. Thanks.

This is a link to a website that discusses it

http://www.notedpokerauthority.com/q...frequency.html

& I copied and pasted this from my blog below that sort of explains it.

"At the start of the day I read up on Sklansky's optimal bluffing frequency. He says if your bluff % in a particular spot is the same as the pot odds you are laying your opponent to call your bluff then even if your opponent adjusts perfectly is at worst 0ev.

I'll try explain,

If I bet $10 into a $20 pot on the river when a flush card hits, I am giving my opponent 3-1 on his call. Now if I really have the hand 3/4 times but the 4th time I am bluffing my opponent is in a no win situation. If he calls each time he loses $10 the 3x I have the hand and makes $30 the one time I was bluffing (O). If he folds all the time he loses a $20 pot every 4th time where I was bluffing. "

in a tournament you are very rarely going to have the right implied odds to call with PPs or SCs and play fit or fold.

SCs are interesting because they will partially hit alot more flops. You have a much smaller chance of flopping a made hand (that beats an overpair) than with a set, but you will flop a strong draw (30+% equity) much more often. I think its about 20% of the time. So we could try calling with SCs and going super aggro with a decent draw. The with that is we are still pretty far behind his calling range so we want folds. And if we assume he will fold every time when we go nuclear we are still only going to make a play on 20% of flops.

so 80% of the time we call preflop and check fold the flop for EV of -6.4bb

20% of the time we raise over his cbet and he folds for EV of +6.8bb

So we are only marginally +EV if he ALWAYS folds when we make a play. But in reality we are going to find him folding only say, half the time when we make a play. The rest of the time we are going to be getting it allin as a 30-35% underdog.

so 10% of the time we raise his cbet and he folds. We gain +3.4bb.

10% of the time we are allin with 35% equity. We lose 2.6bb.

So the total EV if we are playing like this is -5.6bbs, which is a pretty hefty loss.

In order to profitably call this 3bet we would need to be deepstacked enough to make him fold overpairs sometimes, or he would need to be fishy and deep enough for us to call and play fit or fold. Thats pretty much never going to happen in a tournament and its unlikely in a cash game.

If hes a light 3bettor, but respects us then it is possible that the gap between his 3 betting range, and his shove-calling range is wide enough that we can profitably shove a hand like 67s/ A5s. e.g. Say he 3bets 22-AA/ATs-AKs/AQ-AK/ KQs or something like that, but he will fold all but QQ+/AK to a shove. Hes 3bettin 9.2% of hands but only calling a shove with 2.6%. That means when we shove he folds 72% of the time. Further, when he calls we still have 31% equity.

So now we have...

72% of the time, we shove, he folds, we pick up 16bbs. EV: +11.52

28% of the time he calls
- 31% of the time we win 104bbs. EV: +9bbs
- 69% of the time we lose 96bbs. EV: -18.5bbs

Our shove has an EV of +2bbs. This gets better as stack sizes get smaller, provided we are no so short that our opponents calling range is not significantly affected.