Quiz of the Week: Small Pocket Pairs

    • awishformore
      awishformore
      Bronze
      Joined: 16.06.2007 Posts: 922
      Hello fellow PokerStrategists!

      Pocket pairs are amongst the strangest hands of poker. Being a favourite even with 22 against AK, you are usually holding the best hand before the flop, but things can turn around in the blink of an eye.

      In the best case scenario, you hit your set on the flop - this will happen in 12% of the cases. You will have an easy time getting to the showdown as it will usually be very hard not to play the hand correctly.

      But what happens if you don't hit your set? You will usually be left with a second pair or worse and your chances to improve will be worse than those of a hand that has hit the flop. A mere two outs coupled with the bad playability turn your pocket pair from favourite into weak made hand and you will hardly ever have the odds to draw.

      There are a lot of concepts applicable to pocket pairs in post-flop play and the hardest aspect of these situations is to correctly assess them and to subsequently put the correct approach to use.

      Depending on your opponent or the board, you might take a completely different road with the exact same hand. As you move past the micro limits, your edge grows increasingly thin, so you will have to be able to use your theoretical knowledge adequately on the tables.

      Do you have what it takes?

  • 18 replies
    • ciRith
      ciRith
      Bronze
      Joined: 25.03.2005 Posts: 18,556
      You have achieved a total 12 of 20 possible points. This corresponds to 60 %!

      Pretty bad but very useful. :)
    • enemaze
      enemaze
      Bronze
      Joined: 06.06.2009 Posts: 608
      15/20
    • taavi1337
      taavi1337
      Bronze
      Joined: 29.05.2009 Posts: 2,920
      14/20
    • Berkstajger
      Berkstajger
      Bronze
      Joined: 19.03.2009 Posts: 878
      "You have achieved a total 15 of 20 possible points. This corresponds to 75 %!#

      And we all beat ciRith... to advanced thinking, ciRith? :)
    • DarthBobo
      DarthBobo
      Bronze
      Joined: 09.09.2007 Posts: 1,134
      16. should've been more I made a really dumb mistake.
    • DarthBobo
      DarthBobo
      Bronze
      Joined: 09.09.2007 Posts: 1,134
      very usefull quiz btw.
    • TerrorBlade
      TerrorBlade
      Black
      Joined: 16.10.2007 Posts: 1,922
      I got 12/20 as well ciRith, I disagree with the general thought process behind deciding whether to VB or not.

      Before I get into this I appreciate the work that goes into these quizzes gj and all that.

      Q2:

      "In this hand, the TAG will bet any ace for value in case you check, but he will check an 8 and his pocket pairs behind. If you bet, you earn at least one more bet against the 8 and the pocket pairs, while still just losing the same BB against an ace. A bet is therefore better than a check/fold in this spot. "

      Firstly it should read "..better than a check/call in this case.."

      This logic doesn't make any sense, we need 50% equity against his calling range to make a value bet EV+ and it assumes that our ONLY alternative is c/c'ing.

      Let's analyse the situation,

      Firstly, I don't think many tags are calling down 55/66 here against a 3-bet but we'll put in 55/66/88/99 and give the quiz the benefit of the doubt.

      Villain is probably putting in a raise at some stage with the strongest aces (and woulda capped anyway probs) so lets say he plays WA/WB with A9 and under and shows down every 8 also.

      We have 37.5% equity against this really speculative TAG calling range and it gets a LOT worse if you remove pocket pairs or some 8s therefore a bet/x is EV- so we can eliminate that.

      I chose c/f cause I didn't want to get into it too deeply and knew we couldn't bet for value and would get value owned by pair Ace every time if we c/c but it really comes down to player tendencies whether we wanna go for a c/c or c/f but against a TAG most of the time c/f will be reasonably safe.


      Q4:

      There is no way we have 50% equity (a bit less if he folds a 4 from time to time) against this guys calling range here, especially against a more passive guy where we can't eliminate even some weak top pairs from his call-call range.

      It's hard to say whether c/f or c/c is better it really depends on reads but against an unknown I'd def c/c.

      Q3:

      I'd say call > fold here against an unknown but I'm not sure where a raise fits in the grand scheme here.
    • DukeFreedom
      DukeFreedom
      Black
      Joined: 07.04.2008 Posts: 3,511
      15/20

      TerrorBlade

      Q2: The reasoning is correct and there is no logic of favouring c/c over b/f here. It doesn't matter if our equity against is calling range is smaller than 50%.

      The point is: if you check, an 8 and possibly lower pocket pairs (which I don't really believe either) will usually check behind, while you would get a BB from them if you do bet. If you c/c every ace is going to bet anyway, so you'll loose one BB to them, just like you'd loose one BB to them if you bet yourself. Hence the difference between b/f and c/c here is that you might earn a BB extra if he has an 8. Thus EV(b/f) > EV(c/c) in all cases.

      Looking at the bet on itself isolated like you did, the bet is indeed -EV, but that does not capture the whole story here.

      Ofcourse, if we really know that the opponent will only bet betters hands, then c/f will always be better than b/f. On the limit $1/2 (which the question was about) I would personally never play c/f here though.

      Q3: Well I thought about this question... I knew the right answer was supposed to be raise (and I also answered that) even though I must admit I usually play this call turn, call river myself.

      I'm not so sure whether there really is 'one best' way to play this, as there is something to say for every choice. Raising offers the best protection (which you need even if he's on a bluff). Call(down) against a bluff is the most standard play and offers you the ability to make another decision on the river.

      But folding is not all that bad either actually. The point is, there are no flushdraws. Hence you will only win from some weird bluffs and a few straightdraws. However, I rarely see straightdraws being played like this (call flop, donk turn).

      Nevertheless this is on $1/2 again and I certainly wouldn't choose fold here against unknown.

      Q4: Well I agree that this one's a bit more controversial than Q2, but the same reasoning applies here as well. The point is, a 3 or an ace are usually not going to bet if you check, while any better hand is quite likely to bet on the other side, so even if we're behind in equity, b/f may be better than c/c.

      Now I answered this one with c/c myself, because we have another aspect here and that is that is bluffinduce. There are quite some draws that missed that he might turn in a bluff if checked to.

      Therefore, I personally believe the best course of action in this hand is depending on the exact type of opponent you have here, and it's hard to derive that from his stats. There are many people who will bet most of times with anything if they are checked to on the river, and there are other people who will rarely make such a bluff against your weakness.

      Looking at someone's AF (apart from making notes) is usually the best to determine which kind of player the opponent is, but this guy here has 1.3 AF and that pretty much means he could be both.

      Either way, I would certainly say that c/c > b/c here. B/c is just too extreme IMO, spending so much on a relatively bad hand against an opponent who is not all that agressive.
    • TerrorBlade
      TerrorBlade
      Black
      Joined: 16.10.2007 Posts: 1,922
      No. I didn't say at ALL that c/c was a good option or the best option, I said it was a HUGE MISTAKE to assume that those are the only 2 options, here's why.


      Ok let's say we have 3 options, b/f, c/c and c/f.


      C/C:

      Let's simplify this and assume that every time we c/c villain checks behind with every non-Ace bets with an Ace and we lose 1BB every time so EV of c/c = -1BB.

      B/F:

      Villain calls with all 8s and Aces and some PPs, 37% (best case scenario according to my equilator) of the time we get a BB from those worse hands and 63% of the time we lose a BB to an Ace therefore the EV of betting here is -0.63BB.

      Therefore B/F is more EV+ than C/C which is what the quiz said and I COMPLETELY AGREE!

      Now let's think for a second, we have another option.

      C/F:

      EV of folding is 0.

      0 > -0.63 > -1

      C/F > B/F > C/C

      You didn't mention the possibility of c/f once in your post, why is this :/?
    • DukeFreedom
      DukeFreedom
      Black
      Joined: 07.04.2008 Posts: 3,511
      TerrorBlade wrote:
      but it really comes down to player tendencies whether we wanna go for a c/c or c/f
      This suggested that you considered c/c versus c/f, while the real consideration here is b/f or c/f, because c/c is already shown to be worse than b/f.

      DukeFreedom wrote:
      Ofcourse, if we really know that the opponent will only bet betters hands, then c/f will always be better than b/f. On the limit $1/2 (which the question was about) I would personally never play c/f here though.
      And I did write about c/f.

      Using the pot size, and your equity of 37% we have the complete situation described by:

      EV(c/c | he never bluffs when behind) = 37%*6.5 - 63%*1 = 1.78
      EV(c/f | he bluffs 20% when behind) = 37%*80%*6.5 = 1.92
      EV(b/f) = 37%*7.5 - 63%*1 = 2.15
      EV(c/f | he bluffs 10% when behind) = 37%*90%*6.5 = 2.16
      EV(c/f | he never bluffs when behind) = 37%*6.5 = 2.41

      Like I already said, I personally prefer not to play c/f at $1/2 here, but if you are certain that he'll never bluff then be my guest: I certainly won't dispute that as being wrong.
    • TerrorBlade
      TerrorBlade
      Black
      Joined: 16.10.2007 Posts: 1,922
      Sorry, my mistake that I missed that.

      It's just you said we don't need 50% equity to VB here against his calling range which is actually what we need to make betting EV+ and thus better than folding.

      Also as I have demonstrated, the quiz explanation is pretty bad in explaining the reason for VBetting here and is putting the wrong ideas in new players minds.

      Some straight up facts:

      -The universal constant EV of c/f is 0

      -If we don't have 50% or more equity against an opponents calling range assuming no better hands fold then a bet is EV- and thus WORSE than folding.

      Also regarding c/c in that question, it could be a possible option against some opponents, some TAGs will even bet the river with their 8s and small pairs mindlessly but this really isn't the point.

      The main thing that disturbed me was that you said we didn't need 50% equity to make a VBet here and it wasn't mentioned in the quiz explanation whereas it's an extremely fundamental concept in deciding between different options here.
    • DukeFreedom
      DukeFreedom
      Black
      Joined: 07.04.2008 Posts: 3,511
      Updated my post see above ^^

      And no we don't need 50% to bet here but VB is not really a correct name for such a bet... It's more an anti-bluff bet in comparsion to just c/f. And it is in fact somewhat of a VB in comparison to c/c, because the EV of b/f is higher than of c/c.

      In your EV calculations you are totally ignoring the pot size (not too relevant here really), but more important: the fact that the opponent might bluff if checked to, which you did mention in defense of c/c.

      If he only "bluffs" with a worse hand 10% or more of the time then the calculations above show that b/f is better than c/f.
    • TerrorBlade
      TerrorBlade
      Black
      Joined: 16.10.2007 Posts: 1,922
      Disclaimer: I've been known to make mistakes in the past so if I'm wrong here, please don't "LOLOLOL" too loud at me ;(

      I'm not sure I understand your calculations, but this is interesting so I want to delve into it further!

      Btw my calc before with the EV of the bet/fold was incorrect, I do a better one here.

      Fyi 37% equity is against the range he's going to call with including all the worse hands and Aces. In a lot of these situations potsize is irrelevant unless you are planning on calling.

      EV(c/c | he never bluffs when behind) = 37%*6.5 - 63%*1 = 1.78

      We actually have 0% equity against his betting range if we decide to call and thus own 0% of the pot therefore the EV is -100%*1=-1BB.

      EV(c/f | he bluffs 20% when behind) = 37%*80%*6.5 = 1.92

      EV of c/f is always 0 even if he has 100% bluffs in his range and you beat it all. It's just that the EV of c/c will be huge +++ in that case and thus will be much better than c/f.

      EV(b/f) = 37%*7.5 - 63%*1 = 2.15

      Again, we're not interested in the potsize at all because the pot is never at risk of being lost so the only consideration is if this last bet goes in good or bad and will go in bad 63% of the time.


      There's a far better way to approach this.

      Imo this guy is probably ALWAYS checking behind the river when checked to with anything worse than an Ace but lets say he bluffs the river with the bottom part of his range (55-77) to try and make better pairs fold, say 10% of the time.

      Let's also say that he just folds those pairs that he is using to try and bluff 55-66 if we bet which is completely reasonable, now our equity is 29% btw if he doesn't fold 77 so I already know the outcome of this simulation but lets do it anyway.

      EV of each option:

      C/f = 0

      Note with B/f below we have ~30% equity vs his calling range.

      B/f = -1BB*.70 + 1BB*.30 = -0.40BB


      C/c = [EV of the last bet that goes in](-1BB*0.90 +1BB*0.1) +[EV of the previous 6.5 pot](6.5*.1) = -0.15BB


      The drastic difference in the C/C equity-wise is because once he has bet the river after we check to him, we now have 10% equity against his range (10% bluffs, 90% Aces).

      c/f > c/c > b/f now apparently

      I'm dakrynveii on skype if you want to discuss this further.

      Epic fixed limit battle imo.
    • DukeFreedom
      DukeFreedom
      Black
      Joined: 07.04.2008 Posts: 3,511
      First my reaction to some things you replied on my post:

      We actually have 0% equity against his betting range if we decide to call and thus own 0% of the pot therefore the EV is -100%*1=-1BB.
      Incorrect. We still have our original 37% equity, and if he never bets with worse hands then that means he only bets 63% of the time and not 100%, for which the EV would be -1*63% = -0.63.

      Again, we're not interested in the potsize at all because the pot is never at risk of being lost so the only consideration is if this last bet goes in good or bad and will go in bad 63% of the time.
      The pot is always at risk of being lost if he ever bluffs.

      EV of c/f is always 0 even if he has 100% bluffs in his range and you beat it all. It's just that the EV of c/c will be huge +++ in that case and thus will be much better than c/f.
      I understand that in your point of view the EV of c/f is always 0, but that is heavily ignoring the situation and looking far too much at the "value of the line" as an isolated case, while we're actually having a 37% equity of a 6.5 BB pot = 2.4 BB. If he always bluffs, you're effectively loosing that 2.4 BB.

      But it's how you want to look at it. Correct calculations get troublesome quickly in the model you use though, and therefore it is far easier to calculate with the complete situation IMO.

      -----------------------------

      Either way, the example you came with shows this once again, as your calculation for b/f is off, because the situation is more complex than you describe. Nevertheless I'll keep to the EV(c/f) = 0 model now to explain this...

      The point is, by playing c/f you are going to let him bluff you out of a pot you'd normally win 10% of the time. Hence, it logically follows that we already win 10% more pots just by betting ourselves, because he can't bluff us out of the pot then. This is also why I said earlier that it is better to view the bet as an anti-bluff bet, rather than a VB!.

      The calculation for b/f now becomes:

      B/f = %ofpotswewinmore * $potsize + 1 BB * %winfromworsehand - 1 BB * %looseextraBBtobetterhand + 0 * %worsehandshefolds

      B/f = 10% * 6.5 + 1 * 30% - 1 * 63% + 0 * 7%= +0.32 BB

      Hence, b/f is clearly better than c/f if you do the math well. And the conclusion is that b/f > c/f > c/c.
    • ciRith
      ciRith
      Bronze
      Joined: 25.03.2005 Posts: 18,556
      Woa nice discussion going on here. :D

      Well F has an EV of 0. To make it easier I say he bluffs with 10% of his worse hands (we beat them all) and he valuebets all better hands.
      So the move of C/F is: 27% * 6,5 BB (37% - 10% bluff) = 1,755 BB

      C/C:
      27% * 6,5 BB (he checks behind a worse hand)
      + 10% * 7,5 BB (he bluffbets)
      - 73% * 1 BB (the times he bet where we call)
      = 1,757 BB

      Slighlty better than C/F.

      B/F:
      I don't think that he will call more than 20% of the time with a worse hand but with all better ones.

      20% * 7,5 BB (he calls with a worse hand)
      + 17% * 6,5 (he folds a worse hand)
      - 63% * 1 BB (he raises/calls with a better hand)
      = 1,5 + 1,105 - 0,63
      = 1,975 BB

      He never bluffraises?
      Well that has to be reduced from the 20% and added to the 63%. :) (Not 100% sure here.)


      So B/F is the best move.

      Now you can start changing all variables. 20% bluffs, 30% call with a worse etc..
    • TerrorBlade
      TerrorBlade
      Black
      Joined: 16.10.2007 Posts: 1,922
      Wait, wait, wait.

      If we put in potsize into the c/f then wouldn't it be 10%*37%*6.5BB that we "lose" from that line instead of 37%*6.5?
    • TerrorBlade
      TerrorBlade
      Black
      Joined: 16.10.2007 Posts: 1,922
      OK I really like how ciRith lays it out, it's easy to understand that way and tbh, this is the first time I've ever done an "EV calculation", ty!

      I think that 73% in the C/C part is wrong though, it should be 63% (times he bets where we lose a bet) so it will make c/c a bit better.

      Also I'd like to invalidate everything thus far with something I didn't think about before.

      It's not that likely he's calling the turn or sometimes even the flop with 55-77 therefore will have little to no hands to bluff with on the river, in my experience most tags will just check every 8 behind tbh so yeah.

      :D

      Let me try this again:

      C/f :

      [He checks behind]34%*6.5 = 2.21BB

      C/c:

      [He checks behind]2.21BB

      -[He bets and we call]66%*1BB = 1.55BB

      B/f:

      [He calls with worse]34%*7.5BB
      -[He calls with better]66%*1BB = 1.89BB

      I fiddled around with the numbers and with 50% equity against his calling range to break even on a bet which was obviously expected if he doesn't bluff here.

      Thanks DukeFreedom & ciRith for helping me out with this!
      EDIT AGAIN: We have 26% equity if he doesn't raise with AT postflop, GG
    • ciRith
      ciRith
      Bronze
      Joined: 25.03.2005 Posts: 18,556
      Originally posted by TerrorBlade
      Wait, wait, wait.

      If we put in potsize into the c/f then wouldn't it be 10%*37%*6.5BB that we "lose" from that line instead of 37%*6.5?
      Hmm? No I did this pretty "easyway". I just assumed that out of the 37% equity we have we lose 10% by his bluffbets. That may be too much but it's easier than saying he has a bluffrange of 27% (37% * 28% = my 10%).

      Now that I see that this is pretty much I think 37% * 10% = 3,7% or as you choose 34% total for you should be more accurate.

      I think my whole C/C calculation is wrong.
      Here's the Call calculation:

      EV(Call) = (P + V + V) * EQ - V
      P = Potsize = 6,5 BB
      V = Betsize = 1 BB
      EQ = our Equity when we call. So what is this? He is only bluffbetting 10% out of the range we beat. We beat 37% so 10% out of that is 3,6%. I go with 4% now.

      EV(C/F) = 33% * 6,5 BB = 2,145 BB
      EV (C/C) = EV(C/F) + (6,5 BB + 1 BB + 1 BB) * 4% - 1 BB = 1,485 BB

      When will C/C be better than C/F?
      8,5 BB * x% = 1 BB | : 8,5 BB
      x% = 1 BB : 8,5 BB
      x% = ~12%

      So we need 12% equity when we call to make this play break even. Does that mean he has to bluffbet 30% of the time? 37% * 32% = ~12%?

      EV(B/F) is just a matter how you like to define the variables.
      But when will it be beter than EV(C/F)?
      If he calls any better hand? --> Never.

      I go with your calculation as it's easier. ;)

      34% * 7,5 BB - x% * 1 BB = 2,145 BB
      x% * 1 BB = 34% * 7,5 BB - 2,145 BB
      x% * 1 BB = 2,55 BB - 2,145 BB
      x% = 0,405

      So he has to fold 66% - 40,5% = 25,5% or more better hands to make EV(B/F) better than EV(C/F).

      Alternatively we can argue that he just bluffbets more when we check to him.

      EV(C/F) = x% * 6,5 BB = 1,89 BB
      x% = 1,89 BB : 6,5 BB
      x% = ~0,29

      That equals a 20% bluffbettingrange if I'm correct. So it highly depends on the opponent what line is bet.

      If he bluffsbet a lot when we check to him then C/C should be best. If he is reasonable I like C/F the most. If he is a callingstation then B/F should be our best choice.