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A 30bb stack who you have covered opens {66+, AK} to 4x in EP, and it folds to you in the small blind. You have the options to fold, call, 3-bet to 10x against which he will continue by 4-bet shoving with {QQ+, AK}, or 3-bet to 30x against which he will continue with {KK+}. Which is the best option if you hold AKo?
(I'm going to assume the BB folds here, since no info is given about his range. If you flat-call he may come along, and he may show up with a monster in any scenario, but I can't work these out precisely...)
Fold
EV = 0
3bet 30x
He has 6 combos each of 66-QQ in his range, 3 each of AA-KK (since you hold blockers) and 9 of AK, for 57 total hands, of which 6 call. When called we only have 18.5% equity in a 61BB pot of which we pay 29.5BB. When he folds we win 5.5BB.
EV = 51/57 x 5.5 + 6/57 (-29.5 + 0.185 x 61) = 3.0BB
(Note we're exploiting his fold-to-3bet tendency, shoving over is +EV with zero equity because he folds so much. We should choose to do this with e.g. 87s instead of AKo because it has better equity when called). edit: This isn't true, we have more fold equity with AK because we have blockers to his calling range. Thanks spoon!
3bet 10x
He has the same 57 hands, but this time 21 of them shove. Our equity against his shoving range is 38.8%. We have to call 20BB to win a total pot of 61BB so we only need 32.7% equity, this is a call. So we have 38.8% equity in a 61BB pot of which we pay 29.5BB, and when he folds we again win 5.5BB.
EV = 36/57 x 5.5 + 21/57 (-29.5 + 0.388 x 61) = 1.33BB.
(This isn't great, he doesn't fold nearly so much, and we end up still behind his wider stack-off range but having to call because of pot-odds).
Call
This is obviously fuzzy, it depends on (your opponent's perception of) your calling range, and both players' postflop tendencies.
But the implied odds are likely to be in his favour - if he holds a medium pocket pair he's probably going to be able to get away when an A or K hits. Whereas if you hit and he gets a set or AA, you could lose your stack. You're out of position and he has this initiative.
Overall I suspect you'll struggle to get 'your half' of the pot back, making calling -EV.
So best option seems to be 3-bet shoving, and in fact doing it with ATC until EP or BB adjust.
Couple initial thoughts. It may be possible to make a calculation for AKo in isolation for all of the cases, but the proper approach should be to consider all possible hands I could have been dealt and form sub ranges for each possible action I can take that maximises my equity for the hand as a whole and then as a final act determine in which sub-range AKo belongs.
Initially each hand should end up in the sub-range that maximises the EV of that hand, but if the ranges are very unbalanced and the stack sizes and actions under consideration and the opponent in the hand makes exploitation a concern I may need to balance or merge my ranges.
The actions under consideration are quite different to examine from an EV point of view. 3-bet to 30x is simple, 3-bet to 10x is slightly more complex and calling is heavily affected by lack of information - particularly around post-flop play on the part of the opponent in a raised pot. Folding is simple enough in that folding is always 0 EV.
The elephant in the room is the big blind. This is especially true if the big blind and I both have deep stacks. Any calculation I do is pretty much invalid if it doesn't consider that sometimes BB is dealt a good hand and comes along with either a call or a raise. But in the simple cases I explore I will assume that the big blind folds in this case.
Investigating AKo only. Ignoring rake.
Opponent hand range: AA (3), KK (3), QQ (6), JJ (6), TT (6), 99 (6), 88 (6), 77 (6), 66 (6), AK (9) - total of 57 hand combinations.
Folding: 0 EV
3-bet to 30x: 51 hand combinations fold and I pick up 5.5bb. 6 hand combinations call against which I have 18.474% equity in a 61bb pot of which I have contributed 30bb. EV: 5.5bb*51/57 + 0.18474*31bb*6/57 - 0.81526*30bb*6/57 = 4.921bb + 0.603bb - 2.575bb = + 2.949bb
3-bet to 10x, fold to shove: 21 hand combinations raise and we fold and lose 10bb, 36 hand combinations fold and we win 5.5bb. EV: 5.5bb*36/57 - 10bb*21/57 = 3.474bb - 3.684bb = - 0.210bb
3-bet to 10x, call shove: 21 hand combinations raise against which we have 38.824% equity in a 61bb pot of which we have contributed 30bb, 36 hand combinations fold and we win 5.5bb. EV: 5.5bb*36/57 + 0.38824*31bb*21/57 - 0.61176*30bb*21/57 = 3.474bb + 4.434bb - 6.762bb = + 1.146bb
Call: The above 3-betting EV calculations underline that equity realised by making the opponent fold once there is money in the pot is pretty big. Calling has no such equity pre-flop. Since it's late for me I won't go into setting assumptions for opponent tendencies and outline how for some flop types I'd be stacking off regardless and why and how likely those flops are considering the opponent range and my holdings and considering how likely it is for the opponent to stack off with a hand worse than mine etc. Generally speaking, AK is a premium hand that is worth playing, but calling here is only really good if we read our opponent well, and being OOP for the rest of the hand makes that pretty difficult. The opponent range makes life even more difficult for us. As an example, let me consider a Q96 flop.
Opponent hand range: AA (3), KK (3), QQ (3), JJ (6), TT (6), 99 (3), 88 (6), 77 (6), 66 (3), AK (9) - total of 48 hand combinations.
Now there are more blockers to his hand range - and some of his range improves to become sets. Against fully 15 of the 48 hand combinations we are crushed, and we are splitting against 9. We beat 24 hand combinations of JJ, TT, 88, 77 all of which are unlikely to pay us any great amount of money. So if the money goes in here we are probably crushed. A flop that contains one or more cards below 6 look better for us because there are fewer opponent sets in it. A flop containing A, K or both is ideal for us but we're never a lock to win. A K-high flop with lowest card above 5 only gives us 65% equity against the whole hand range - and the opponent surely will not stack off with his whole range. So my call EV is inconclusive except to say that against certain opponent playing tendencies it is most profitable to call, but against others - and this is probably most and goes for unknowns also - calling is risky.
Additionally to consider with calling is that BB is that more likely to come along. This may be an argument for or against calling depending on stack sizes and how well we know this opponent and in exactly which ways we know he is bad.
Even if 3-betting to 10x and 3-betting to 30x was about similar in EV I would still advocate betting to 30x to elicit more folds from the big blind. As it is, 3-betting to 30x seems the clearly better play. The main value of the play seems not to be realised by the hand we are actually holding but rather by the opponent playing an exploitable pre-flop strategy that folds too often to 3-bets.
Think you're looking at a K96 flop there Erpel, not Q96, if we're beating JJ,TT,88,77 (we also beat QQ). I think the most difficult part of calling is you miss the flop 2/3 of the time and if you do you're behind or tying every single hand in his range. This means you *have* to get paid if you hit, and it's hard to see how you do.
The discrepancies in EV seem to be because you're charging us 30BB when we stack off - since we've already paid the SB, I think this should be 29.5.
Good analysis. Just want to point out that the bold isn't necessarily true because he folds more often when we have AK.Quote:
Originally Posted by tunah
did all the math in my head while i was at work so no pokerstove/answers are rounded/answers are bound to be wrong 'cause there were a lot of numbers flying around without nary pen and paper.
EDIT: After reading the other answers i also realize that i misremembered the question, so everything's based off of the falsehood that nitty SS raised 3bb's instead of 4. maybe my answer's still worth reading just to see how the power of FE even if there is a smaller PFR
push > 3bet 10bb/call a shove > fold > 3bet 10bb/fold to a shove
shoving: we win 229.5bb's : losing 120bb's over 57 hands, meaning you win about 2bb's/hand (the 120bb number is based on the complete guess that we have 16.7% equity against KK+, but honestly that number stays consistent enough that it isn't really important that it's more or less arbitrary)
3bet 100bb/call: we win 162bb's : losing 120bb's over 57 hands, meaning you win <1bb/hand.
fold: well...um...yeah
3bet 10bb/fold to a shove: we still win 162bb's but we lose 210 bb's over 57 hands because we lose EVERY TIME villain has QQ+, AK. so EV is almost -1bb/hand
so there you have it. in short, FE pwns risk:reward ratio when effective stacks is 30bb's. this was easily my initial instinct when i read the question due to SnG experience where FE pwns everything because there are small stacks
EDIT: i forgot to mention that the EV for the 3bet 10bb/call is actually thinner than the numbers i came up with in my head because i assumed 50% equity against QQ and AK when we actually have slightly less than that against both of them. also rake is going to be bigger here because we're going to get past the flop and be all in more times so the poker site gets more of our EV (full tilt especially since they have a no flop/no drop policy and no cap on their rake)
Nicely done. Tunah's point about doing this with 87s got me thinking about doing this w/ ATC against this opponent. I know this is going beyond the quiz where we're supposed to analyze AKo, but is this profitable with a wider range?Quote:
Originally Posted by tunah
Running this with a variety of hands we see the overbet shove is indeed the best option with ATC with only 2 exceptions (although we do need some equity when we don't have blockers since w/o a blocker the total number of hand combinations increases to 70 and 12 will continue to the overbet shove so w/o any equity we'd be -EV, but even the modest 11.9% equity w/ 27o is enough to make it +EV, or if you don't want any blockers on any hands the 14.4% equity of 25o works too). The exceptions are AA and KK. AA and KK do better w/ the 10x 3-bet due to the huge equity advantage we'd hold over our opponent's continuing range. With AA and KK, the total hand combinations stay constant (57), but now 7 will continue instead of 6 with the overbet shove.
Unless I made a mistake (entirely possible), the analysis leads us to conclude the best option here is:
Shove ATC other than AA, KK.
3 bet 10x w/ AA, KK.
Of course thinking opponents would quickly adjust and this strategy is unbelievably exploitable, but it does show the power of 3-betting. It also shows the importance of having at least one blocker when doing so.
Here's a hint: This edition isn't really about 3-betting.
well that's a pretty damned big hint. looking forward to hering the justifications and all 'cause AK OOP is a leak for me
There are a couple of ways to interpret that "this edition isn't really about 3-betting."
1) It's not about 3-betting.
1a) Given we know overbet shove > 10x 3-bet > fold, that means calling would need to be better than shoving on average. We've got a couple of factors working for us to help us extract value. First, we know we are almost always up against pp's. Meaning most A and/or K flops will often win the pot for us and we don't need to worry about 3 card straights or flushes beating us. Also, A and/or K flops would be good for our opponent to bluff at (but he doesn't often need to bluff to push out better hands given the amount of pp's in his opening range). It'd also be unlikely he'd be willing to stack off on an A/K high board w/o a set or an overpair. I see a lot of checking down for pot control, what we want to avoid.
1b) How about exploiting post flop the same way we can pf? We could open shove the flop (this can't be better than shoving preflop since his odds to hit a set are better than his continuing range and our equity would have dropped significantly if he hits a set so we'd be doing worse here).
1c) How about c/shoving any flop? Again, for the same reasons listed above, this isn't going to do it unless he's putting quite a bit into the pot on the flop ui.
I don't see how we'd be able to extract enough value oop when we hit to make up for the 3.5 bb we put into the pot plus the 3 bb EV we'd get from shoving. I'm with surviva here. I must be missing something if this is the case.
OR
2) It's not "really" about 3-betting (aka - it's about playing against thinking opponents).
A thinking opponent would be able to exploit this player by 3 betting wide. When playing against thinking opponents we need to think about the game-theoretic strategy, the least exploitable. This player's choice to short stack combined with choosing to raise far wider than he is willing to stack off with makes him very exploitable. Precisely what we need to avoid doing as players - being exploitable.
OR
3) The most likely case - I've missed something that is very important here.
Or maybe you just overlooked it when it was in plain sight. There are two cases where we 3-bet with only one real difference. What's that difference? Hint: It's not the bet size.Quote:
Originally Posted by okiman
The difference is in one case we allow our opponent to push all in while in the other we push (we commit or he commits). We're removing our opponent's fold equity and maximizing our fold equity.Quote:
Originally Posted by spoonitnow
well my original answer to the original question was going to be a completely non-mathematic answer until i realized that 3b 10bb/fold to 4b was an option so i actually had to do EV calculations.
i was just gonna flatly point out that the only difference between the two is that in the 3b pushing option we beat QQ and AK 100% of the time well we are less than break even against those hands in the 3b 10x's option.
sooo are you getting at the fact that this question is really all about FE? the more hands we can fold out of his range the better w/o having to run calculations or any of that crap
Just some ramblings about applying this concept to a wider range of hands and more situations (trying to apply what we've learned):Quote:
Originally Posted by surviva316
For this specific case, with this specific hand, being behind those two hands in terms of equity which we can fold out (here any of the pocket pairs since they all have an equity advantage against AKo), yes. In general, no. Again, the calculations are important as our 3-betting range gets expanded beyond AKo in either direction. With an opponent who's deep(er), with trash hands (against a deeper opponent), or with the top end of our range (here AA, KK), it's not always true. The trash hands would have too little equity with a push (deep enough, so will AKo). AA, KK would be giving up too much value by pushing out hands they dominate.
no i know that if he calls with AQ-, then equity calculations are necessary. i did mean in this specific case. i was wondering if spoonit was trying to get us thinking about FE and how it's always better to fold out hands that we are B/E against (or at least, in all in situations). i wasn't actually making a statement on poker theory as a greater wholeQuote:
Originally Posted by okiman
And I wasn't attacking your post either. I'm trying to apply this to other situations.Quote:
Originally Posted by surviva316
And I sure hope spoon was trying to get us to think about FE. Otherwise, I'm truly lost here.
Nope, it's not fold equity, but you're really close.Quote:
Originally Posted by okiman
Here's a hint: The underlined portion isn't completely true. Our opponent doesn't have fold equity in this situation.
The amount he folds changes, so the amount he ______________ changes. Why does that change, and why is it important?
Edit: Actually fold equity *is* important here, and is very much related to what I'm hoping you get at eventually, but now I see it might be a little too hidden in this example, so I'm going to spit it out.
This hand is a very basic example of range manipulation.
I would not have said range manipulation. I would have come back with another weak-ass convoluted description of it as before - dancing around it without ever stating it correctly, such as:Quote:
Originally Posted by spoonitnow
But this is really about 2 things, right? First, manipulating our opponent's ranges and, second, making it as difficult as possible to manipulate ours.Quote:
Originally Posted by okiman
We aren't worried too much about our range in this example.
No, not in this example, but when we are thinking about how to best play. I'm trying to take this example and learn as much as I can from it.Quote:
Originally Posted by spoonitnow
Yeah, I was just throwing that out there so anyone who comes along later and reads the thread won't get confused.Quote:
Originally Posted by okiman
Fuck. Maybe a slightly less coy teaching method would have a little more impact on the BC.Quote:
Originally Posted by spoonitnow
folding is incorrect obv..Quote:
Originally Posted by spoonitnow
we're holding a strong hand and want action, and we're not going to get action from enough hands that we beat if we 3bet either amount.
call and re-evaluate flop.
even if we were after fold equity, there's not enough. he's only folding 50% of his range.
My calculations on the 3bet EVs are different than everyone's above.
3bet shove has EV = 3.074 BB
3bet 10x / call shove has EV = 2.373 BB
Oh, yeah, folding is NOT EV = 0. We lose our 0.5 BB when we fold the SB.
The EV question boils down to whether we can earn more than ~3BB's on average playing AK for a flat call oop against a nit. Seems unlikely given poor implied odds and big reverse implied odds.
Be interesting to see what spoony has in mind for further discussion.
KK+ is 9% of his rangeQuote:
Originally Posted by langaan
I was drunk when I wrote that. Please disregard. At least you're posting and trying to help. :oops:Quote:
Originally Posted by PlayToWin
in the first scenario qq+ ak is closer to 50Quote:
Originally Posted by surviva316
so how does this relate to your other thread:
http://www.flopturnriver.com/phpBB2/...ns-t75339.html
Is this scenario we can 3 bet 10x folding out 63% of his range or 3 bet all in folding out almost 90% of his range.Quote:
Originally Posted by langaan
I'll take a first stab. Spoon can correct me if I'm wrong.Quote:
Originally Posted by surviva316
Since the player in the other post is deeper and is willing to stack off with a wider range, he is greatly reducing our ability to manipulate his range (unless his opening range is outrageously wide). Plus, being UTG+1 we have the advantage of position and the disadvantage of several players behind us yet to act.
I fergot blockers....Quote:
Originally Posted by okiman
Could you show the calculation for these? Entirely possible I messed up the EV calcs but would be curious to know how.Quote:
Originally Posted by Robb
Depends where you set your baseline. I was using the convention the convention that 0EV = keeping the money you have at the point where you have to make the decision. Once the money is in the middle and has been called it's not yours in any meaningful sense.Quote:
Oh, yeah, folding is NOT EV = 0. We lose our 0.5 BB when we fold the SB.
But you can equally well use 0EV = finish the hand with the same stack you started with. EV for all the options will be 0.5BB less (when you win the hand, you can't count the 0.5 in your winnings, and when you lose the hand you count the 0.5 as your losses) but the order and difference between them will be unchanged.
3b shove EV
Villain folds to Hero shove: 5.5 BB * (51/57) = 4.921
Villains calls, Hero wins: 31.5 BB * (6/57) * .196 = .650
Villain calls, Villain wins: -29.5 BB * (6/57) * .804 = -2.497
EV = 4.921 + .65 - 2.497 = 3.074 BB
3b 10BB EV
Villain folds to Hero 3b: 5.5 BB * (42/57) = 4.052
Villains shoves, Hero calls/wins: 31.5 BB * (15/57) * .379 = 3.142
Villain shoves, Villain wins: -29.5 BB * (15/57) * .621 = -4.821
EV = 4.052 + 3.142 - 4.821 = 2.373 BB
The differences I saw were in how to "count" the posted SB and in small differences in equity (I used poker stove to get mine). I was pretty tired when I did it, so I may have screwed up somewhere.
The bigger difference is you've got villain shoving 15 hand combos to a 10x, I make it 3 AA, 3 KK, 6 QQ, 9 AK = 21.
(FWIW, I think the 19.6% equity for 3bet shove comes from using {AKs,AKo} instead of {AKo} for hero. I'm not sure about the 37.9% unless you're using {QQ+,AKo} for villain instead of {QQ+,AKo,AKs}. Doesn't make a big difference anyhow)
are we supposed to assume the BB never waffle-crushes us?
I know I did.Quote:
Originally Posted by Erpel
Oops - guess I misread it.Quote:
Originally Posted by tunah
@ spenda - yeah, think we're assuming BB never has a hand he'll continue with.
I've been thinking about the implications of this thread, because spenda and others have pointed out that I used to raise way too often with good-but-not-great hands like JJ/TT/AQ when flatting actually earns more. If villain's folding to 3b's too often, we should 3b more - certainly - but pick hands that don't play as well when we flat. Of course, position matters, so it's a slightly different batch of hands oop than ip.
The game is to be sold, not told. I'm not going to hold your hand while you learn poker just like I'm not going to hold your dick while you take a piss.Quote:
Originally Posted by PlayToWin
That post is really a history lesson. About 9 months after I first beat 200nl I realized I could 3-bet bluff.Quote:
Originally Posted by surviva316
I know, I know.......I was drunk. Some teaching methods work better for some than for others. I had no right to criticize you.Quote:
Originally Posted by spoonitnow
Sure you do. You have every right in the world to criticize me. Doesn't mean it does either of us any good. :]Quote:
Originally Posted by PlayToWin