EV of calling a preflop 3bet with small/medium pairs
 

A recent review session threw up the question - can you profitably call a standard preflop 3bet with 100BB stacks, when you hold a small/medium pair?

This may well have been covered elsewhere - or be obvious to all - but here are my calculations/conclusions. Please let me know if my math(s) is off.



NL100. Hero has 66 in MP, Villain is on the Button. 100BB stacks. Villain is a TAG who CBs 2/3 pot 100% of the time. He never steals or squeezes preflop.

Hero raises to $4 with 66
Villain on the Button re-raises to $14 (he has a big pair or AK)
blinds fold.
Hero calls $10

Is this a +EV move if Hero is playing for set value alone?



Best case scenario – Villain stacks off 100% of his range every time

To do an EV calc, we need to make a few assumptions:-

Villain bets $20 on every flop when checked to.
Hero check/folds without a set; check/calls or check/raises with a set or better.
Hero gets stacked 100% if he hits a set and loses.
When Hero’s set holds up, he wins $18 preflop + $86 post flop = $104
When Hero loses set over set, he loses $96

A set wins 82% vs. AA-JJ
A set wins 95% vs AK
A set wins 87% vs AA-JJ, AK range
(Lets assume the blinds are lost to rake.)

EV when Hero hits a set and Villain (with AA-JJ or AK) goes broke 100% = (0.87 * 104) + (0.13 * -96) = $78

Hero hits a set 11.8% of the time, so

Best case EV of call for set value alone = (0.118 * 78)+(0.882 * -10) = $0.4

Conclusion
With 100BB stacks, calling for set value alone is only +EV if Villain always stacks off with his entire range.



Another way of looking at it.

The chance of losing set over set is very important here. Hero is 7.5:1 (11.8%) to hit a set, but Hero loses with a set 13% of the time vs. an AA-JJ, AK range. You are 7.5:1 to hit a set, but (0.118*0.87 = 0.103) 8.7:1 to hit a set and win. Hero will get stacked ~1.5% of the time. It breaks down like this:

88.2% of the time Hero loses his $10 call
10.3% of the time Hero wins a big pot
1.5% of the time Hero loses his stack

In our typical HU example Hero has 96BB left before his call and the call is 10BB, Hero needs to win the following amount for the call to be 0EV

(0.882 * -10)+(0.103 * X)+(0.015 * -96)=0
X = $100

So Hero needs to win 10 times his call ON AVERAGE to make it +EV for set value alone. With 100BB stacks, he needs to win a further $82 – but Villain only has $86 left.

Hero needs to stack Villain nearly 100% of the time with his entire range, if playing solely for set value.


So what is the EV of a call here for set value alone if we make a more reasonble assumptions of how much Villain will lose with his AA-JJ, AK range?

Let’s say

AA-JJ lose whole stack every time there are no overcards by the turn (optimistic, maybe)
AA loses stack every time
KK only loses 50% of remaining stack on average (after the turn) when an Ace flops/turns
QQ loses 50% of remaining stacks when an A or K flops/turns (QQ is less worried about a K, than KK is of an Ace).
JJ loses 40% of remaining stacks on average when an overcard flops/turns (hates an Ace; K or Q not so bad)
AK loses 30% of remaining stack on average past the turn, when it gets to the turn UI
Villain CBs every flop

When we flop a set, Villain has $66 left on the turn, Hero can win a maximum of (18+20+66)=$104

Average win when Villain has:-

AA (0.82 * 104) + (0.18 * -96) = $68

KK 0.76 * [(0.82 * 104) + (0.18 * -96)] + 0.24[(0.82 * 71) + (0.18 * -96)] = $62

QQ 0.56 * [(0.82 * 104) + (0.18 * -96)] + 0.44 [(0.82 * 71) + (0.18 * -96)] = $56

JJ (0.40 * [(0.82 * 104) + (0.18 * -96)] + 0.60 [(0.82 * 64) + (0.18 * -96)] = $48

AK (0.34 * 104) + (0.66 * 61) = $76

Note:
With AA Hero (only) wins ~82% of the time he flops a set (this fact is important)
With KK there is a 24% chance of an Ace by the turn i.e A6xx board
With QQ there is a 44% chance of an Ace or King by the turn
With JJ there is a 60% chance of an Ace, King or Queen by the turn
With AK there is a 34% chance of AK hitting TP or better by the turn

This gives a weighted average win of $66 when we hit a set vs a range of AA-JJ, AK.

Hero flops a set 11.8% of the time; so

EV of call for set value alone = (0.118 * 66)+(0.882 * -10) = -$1.0

I did some algebra which indicates that Hero can only profitably call a 3bet to 12.7BB, under the above assumptions. Of course, as soon as we give Villain a wider range than AA-JJ, AK, the situation for Hero is worse, as Villain is going to pay off a smaller proportion of his stack on average with worse hands. Also, we cannot expect to take 100% of Villain’s stack every time he has JJ and no overs come. Some players will be able to get way from this vs. a TAG who calls a preflop 3bet and a big CB.

Conclusion
If you have a small/mid pair and are facing a standard sized 3bet by an aggressive Villain, you cannot profitably call for set value alone with 100BB stacks – whether he has a tight or loose 3bet range – even if he CBs 100% of the time. If you do call, you will need to find some +EV spots postflop without a set.

Re: EV of calling a preflop 3bet with small/medium pairs
 

"did some algebra which indicates that Hero can only profitably call a 3bet to 12.7BB"


I think you meant 127BB, yes?

This is about what I would say as I follow a 15:1 stack size rule. It's $10 more to call, but there is already $19 in the pot for overlay. So $150 - $19 = $131.

So I would want $135BB at the start of this hand to make this call.


Here's a link to a good thread of a similiar vein.

http://forumserver.twoplustwo.com/showfl...part=1&vc=1

Re: EV of calling a preflop 3bet with small/medium pairs
 

so many of those 6 max guys are complete moron idiots.

you flop a set 1 in 8.5

no no floppping a set is 7.5 to 1

yeah i think hes right
lol

Re: EV of calling a preflop 3bet with small/medium pairs
 

[ QUOTE ]
so many of those 6 max guys are complete moron idiots.

you flop a set 1 in 8.5

no no floppping a set is 7.5 to 1

yeah i think hes right
lol

[/ QUOTE ]

lol I had to check that twice

Re: EV of calling a preflop 3bet with small/medium pairs
 

[ QUOTE ]
"did some algebra which indicates that Hero can only profitably call a 3bet to 12.7BB"


I think you meant 127BB, yes?



[/ QUOTE ]

No. If we raise to 4BB, we can only call if Villain 3bets to no more than 12.7BB (under my scenario). If the 3bet is to 14BB (as is frequently the case), it's -EV to call for set value alone, regardless of Villain's range, unless he goes broke with every hand he can have 100% of the time.

In reality i.e Villain plays more normally and loses as much as they usually would with each hand in their range; we should not be calling a 3bet to more than ~10BB - for set value alone.

In my opinion, if you plan to call 3bets with the likes of 66 (with 100BB stacks), you had better be good enough post flop in a 3bet pot to win sometimes without a set.

Re: EV of calling a preflop 3bet with small/medium pairs
 

I bet the Hero wishes he limped now. [img]/images/graemlins/smile.gif[/img]

Re: EV of calling a preflop 3bet with small/medium pairs
 

So, the 12.7BB out of 100BBs is completely in line w/ the 5-10 rule, or at least close enough for table use. The size of the 3 bet is the key here, >10% of yours and/or villain's stack is a fold and <10% of yours and/or villain's stack is a call, sometimes...

Re: EV of calling a preflop 3bet with small/medium pairs
 

Shouldn't a TAG be limping with small pairs? IOW, wouldn't it be more profitable to limp/call to see flop rather than raising?

Re: EV of calling a preflop 3bet with small/medium pairs
 

Yes, limp call would be the more "perfect" play in this situation, but apparently the OP left his crystal ball at home and didn't have it at the poka table with him...

Re: EV of calling a preflop 3bet with small/medium pairs
 

Is it necessary a crystal ball to limp small pairs?

Re: EV of calling a preflop 3bet with small/medium pairs
 

[ QUOTE ]
Is it necessary a crystal ball to limp small pairs?

[/ QUOTE ]

Haha, no.

I shouldn't have said anything. I should have known it would start the age old debate. [img]/images/graemlins/smile.gif[/img]

A limp is fine here, a raise is fine here. A limp is better here, a raise is better here. We don't have any idea of the table dynamics that would swing in into "usually raise land", therefore the whole thing is open to debate.

Let's not debate though... [img]/images/graemlins/smile.gif[/img]

Re: EV of calling a preflop 3bet with small/medium pairs
 

Open limp- BOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!

Re: EV of calling a preflop 3bet with small/medium pairs
 

Re: open limping v. raising, the issue driving every debate IMO is style. If you open limp hands including SCs, small/med pp's then it's fine, if you don't open limp other hands don't open limp small/medium pp's. In this case, if we KNOW that this villian will r/r our raise and will have AK or a big pp, obv we open limp. Even the guys that open raise all the time (myself included) would probably open limp if we KNEW that this villian would be reraising his AK/big pp.

The point here is addressed by Mack when he says you need to be good enough post flop to play people off their hands occasionally w/o a set. IMO most of the guys that do favor open raising pf as opposed to open limping have enough experience with 3 bet pots (as they tend to be the same players 3 betting light in position) that they can play proficiently post flop.

That isn't me saying those favoring open raising pf are better players. I do feel that it is a better strategy in general and that's why I use it, but I see the other side of the argument and one's style should be more dictated by the dynamics of the table than anything else.

Re: EV of calling a preflop 3bet with small/medium pairs
 

I agree with everything DougieG wrote

I think sometimes we get caught up analyzing hands in a vacuum and not looking at the style, or system, we play

I might due a carpal/tunnel post on playing poker as a system instead of independent hands

Re: EV of calling a preflop 3bet with small/medium pairs
 

often times, tinkering with how you approach a specific situation might have a chaotic effect on the rest of your game

think of a butterfly wings causing a hurricane

Re: EV of calling a preflop 3bet with small/medium pairs
 

You guys make poker way to hard.

Re: EV of calling a preflop 3bet with small/medium pairs
 

poker is easy

optimal play is hard

Re: EV of calling a preflop 3bet with small/medium pairs
 

[ QUOTE ]
I might due a carpal/tunnel post on playing poker as a system instead of independent hands

[/ QUOTE ]

Would love to see this since that's been the major difference in my play/approach to the game in the last 3-5 months.

Re: EV of calling a preflop 3bet with small/medium pairs
 

[ QUOTE ]
I bet the Hero wishes he limped now. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]


Even small pair limpers surely open raise them if it is folded to them in the Hijack or CO, no? If they do and the button or blinds 3bet, this this theory applies.

As I said in the original post, this came from a session review I did, where a good player at the $200 level called a 3bet thinking that he had odds for set value. I disagreed, he disagreed with me - and so I did the math.

Re: EV of calling a preflop 3bet with small/medium pairs
 

[ QUOTE ]
[ QUOTE ]
I bet the Hero wishes he limped now. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]


Even small pair limpers surely open raise them if it is folded to them in the Hijack or CO, no?

[/ QUOTE ]

I hate to go cliche on ya, but it really does depend.

Re: EV of calling a preflop 3bet with small/medium pairs
 

If you were going to open limp a small pair the button could be the best place to do it. It would defiantly be better to open limp the button situationally than to auto limp under the gun.