What’s Your Range? Results

Sorry that I was slow in posting results and lax about responding to comments. Not only was I moving over the weekend (got a place in Boston for a few months- more on this soon), but I also took ill. In retrospect eating a pre-made tuna sandwich from a rest stop Starbucks may not have been a great idea.

Anyway, I’ll go ahead and reveal my cards and the results, then I’ll get into my thoughts on what my range ought to be here:

PokerStars No-Limit Hold’em, $6 BB (9 handed) Hand History converter Courtesy of PokerZion.com

Button ($605.25)
Hero ($1134.25)
BB ($609)
UTG ($1229)
UTG+1 ($668.20)
MP1 ($591)
MP2 ($702.15)
MP3 ($216.50)
CO ($726)

Preflop: Hero is SB with 8h, 8s.
3 folds, MP2 raises to $12, 2 folds, Button calls $12, Hero calls $9, BB calls $6.

Flop: ($48) Jc, 8c, Jd (4 players)
Hero checks, BB checks, MP2 bets $42, Button raises to $131, Hero raises to $1122.25, BB folds, MP2 folds, Button folds.

Final Pot: $1343.25

Results in white below:

No showdown. Hero wins $1343.25.

Villain begged me to tell him what I had, and I told him that I would if he would tell me what’s the worst hand he calls with. He agreed, I answered him truthfully, and he fold me AJ is the worst hand he’d call with. He also told me that he folded KJ.

He spent a lot of time in the tank before folding, and I do believe that he folded a J. I’d say it’s more likely than not that he’s telling the truth about his actual hand, but I wouldn’t be shocked if he were lying about the strength of his kicker.

What’s My Range?

If Villain is really folding KJ here, my answer would change, and we’ll come back to that in a moment. I do think BTN has a J just about always when he makes this raise. MP2 has made a very large continuation bet into three players, and BTN’s raise is also quite large. If he wanted to raise as a bluff, I believe he would have chosen a smaller amount. I doubt this is a play he would make against someone he considered very good. In this case, he probably just assumed that MP2 had hand he liked and would have difficult letting it go, and consequently made an exploitable raise that he would only make with a hand with which he’s willing to stack off to MP2.

With 88, there was no question that I wanted to shove. I don’t think there is any hand that I would cold-call here except maybe JJ just because even though it would look suspicious as hell the only hand that could call a shove (88) probably wouldn’t get away anyway. I’d never cold-call a draw here, and consequently cold calling is going to look even stronger than shoving, which is something I could conceivably do with good draws.

There are a few really key points to recognize about my shoving range: (1) When I have trips, my kicker matters; and (2) It should be unbalanced and should not contain any draws. Because of the size of the pot and the number of players involved, everyone’s ranges must be very strong. Consequently, balance is not really a consideration. Given how much we are risking relative to the pot and how many players are left to act behind us, anything resembling a bluff is out of the question. It’s just a question of which hands are strong enough to stack off with here, and that boils down to equity vs. Villain’s calling range.

Kickers Matter

Let’s assume that Villains raising range consists of JTs, QJs, KJs, AJs, KJo, AJo, and 88. This assumes that he folds JTo and QJ pre-flop and that he slowplays quads and J8 (if he has this in his range). Likewise if he happens to have something like J9 where his kicker is very weak, we’ll assume that he doesn’t raise that either. Combinatorically, he has

(2) JTs
(2) QJs
(2) KJs
(2) AJs
(8) KJo
(8) AJo
(3) 88

If he calls only with AJ and 88, then he folds 14 combos and calls with 11 combos. This means that we win a $221 pot slightly over half the time when we shove. We are risking $600 to make this play, though, so our equity when called is going to matter a great deal.

Against a calling range of {AJo,AJs,88}, JTs has 23% equity, and QJs and KJs have slightly less than that (because they will make fewer running straights). Ordinarily, the card removal effect of our holding trips would be quite significant, but in this case his calling range includes 88 but his folding range consists entirely of J’s, so holding a J actually increases the likelihood that we’ll be called.

When we hold AJs, his combos change to

(1) JTs
(1) QJs
(1) KJs
(1) AJs
(4) KJo
(2) AJo
(3) 88

Assuming a calling range of {AJo,AJs,88}, he folds 7/13. Given that the pot is $221 when he folds, we have $119 in fold equity.

AJs has 36.086% equity against that calling range. If only BTN calls our shove, the pot is $1343.25, giving us $484.73 in showdown equity.

Adding our showdown equity and our fold equity gives us $603.73, whereas we are risking $594 when only the BTN calls, making this very marginally +EV. The possibility of BTN calling with KJ or having a few random lighter hands in his raising range that he folds is probably enough to compensate for the risk of BB or MP2 waking up with 88, making this a shove with AJs.

AJo actually has about .5% more equity than AJs because of the possibility of backdoor club draws, making that a shove as well, but shoving KJ or worse would be a losing play when our opponents fold trips with a worse kicker. Even if we put KJs and KJo in BTN’s calling range, we don’t have enough equity to shove KJs profitably, and the other Villains are even less likely to call with these hands than is BTN.

In fact, our equity with KJ is so poor that even adding a few hands to Villain’s raise-folding range and thus increasing our fold equity isn’t enough to make it profitable.

Semi-Bluffing is Not Profitable

Against a calling range of {AJo,AJs,88}, Tc9c has 33%, making a shove slightly -EV. Adding KJs and KJo to Villains’ range gives Tc9c 36% equity when called, but it drastically lowers our fold equity, meaning that we still can’t shove it profitably. All other draws have much worse equity when called and thus will not be profitable, either.

This actually came as a surprise to me. My instinct was to shove Tc9c here, and I told Villain that I would have. It feels weird to shove only value hands in a spot where Villain is able to make some big folds, but it’s nonetheless correct in this case.

What if BTN Has a Draw?

BTN needs 36% equity to call this shove. Even if he has Tc9c, which is his highest equity draw vs. our shoving range, he has only 33% equity against {AJs,AJo,88}. Even if he were to raise with this hand, which isn’t a guarantee, he can’t call our shove.

If you include KJs and KJo in our shoving range, then he has the equity to call with Tc9c, but we’ve already seen why we can’t profitably shove those hands. Even putting Tc9c into his calling range doesn’t make it profitable for us to shove KcJ, which is our highest-equity KJ.

Conclusion

I’m shoving only {AJo,AJs,88} here. I’d cold call exactly JJ, and I’d fold everything else.

Since When is it Correct to Be Unbalanced?

MP2 and BTN started it. They both presumably have ranges that are really unbalanced. If I thought that they were both bluffing with optimal frequency, then I wouldn’t be folding KJ or Tc9c here. However, my reads and their betsizing suggest otherwise. Assuming BTN is correct that MP2 will not fold as often as he should to a raise, then he is correct to exploit that with an unbalanced raising range. The risk of me “exploiting” him by folding Tc9c isn’t a reason not to do it, it’s just something that’s going to make his raise slightly less profitable. BB and I will wake up with hands so infrequently that BTN is correct to focus on exploiting MP2, if he believes that he can.

24 thoughts on “What’s Your Range? Results

  1. I like your comments on being unbalanced here. It’s good to know when your actions should be balanced and when they should be unbalanced.
    It seems like one set of times to be unbalanced is when relative stacks are shallow. Here the raise by villian was large enough relative to his stack that it forced your decision to be unbalanced.
    In general is that one of the things you consider when playing? For example, if you are up against a player pre-flop that has <40 BB, do you automatically change to an unbalanced playing style and only play a range stronger than his perceived range?

    • The really key factors are when you are moving all-in before the river (equity when called matters more than balance, which is relevant primarily when folding is still an option for you) and when your opponents are themselves unbalanced. Both of these are more likely to be true when the stack:pot ratio is small, but there are also cases where stacks are shallow but balance still matters. Check-raising a continuation bet on a J77r flop comes to mind.

  2. Still not sure why you didn’t cold-call here. If there’s a flush/straight draw out there, you want it to get there as you may have a 3-way all-in. And any J only has 4 outs with an additional one if the turn checks through. Thanx!

    • Hey Gary,

      I’m not andrew but..

      Assuming your opponents aren’t weak players, cold calling here looks incredibly strong. Cold calling runs two risks:

      1) If your opponent has a hand like AJ or KJ, he might not put any more $ in the pot if a club hits
      2) If your opponent has a hand like AcTc and does make his flush, he still might not stack off on some turn/river combinations because he’s pretty convinced you have 88.
      3) You don’t give someone with AJ/KJ, or AcTc a chance to put in a ton of $ in bad shape on the flop, which he may do.

      In such a spot against good players, you goal should be to keep your perceived range as wide as possible. We don’t need to ‘trap’ someone who has AJ or KJ – we expect those hands to stack-off on the flop already. Given we have 88, and our opponents aren’t fish – there’s pretty much no way we get a 3 way all-in on a later street, unless we’re beat.

        • I’ve made some videos on the subject. It’s really a game theory concept more than anything, so I guess Mathematics of Poker would be a good resource, but it doesn’t come out and say, “Here’s what a balanced range is and how to do it.”

    • Pretty much what Chris said. A good player with a flush draw isn’t going to try to value bet a flush against a cold caller, and can probably even find a fold if I try to put money in the pot after such an obvious draw has hit. And the one clearly worse hand that can call a shove, AJ, may well slow down whether or not a club hits once I cold call. Think about it: with what hands would I cold call here that AJ can beat?

  3. I think there’s a small flaw in your logic in saying semi-bluffing isn’t profitable.

    You have 33% equity when called, but you haven’t factored in the EV gained through FE. If you have FE vs 50% of his flop raising range (he did fold KJ), you have to do the math and see if the FE + 33% equity > 50% pot equity.

    Unless you skipped this by implying that in no way will FE + 33% > %50?

    I also wouldn’t have jammed a draw here vs a villain who I don’t think raises flop light / folds often – but there are villains who will. If he’s raising with QJ/KJ, and then folding them to jams, I actually think the math would be really close on whether jamming T9cc is profitable given you win the pot more than 50% of the time uncontested.

    • I guess I wasn’t as clear as I should have been. I already did the math, including FE, to show that shoving AJ was barely profitable against a calling range that doesn’t include KJ. KJ obviously has substantially less equity against that same calling range. It’s equity is better against a calling range that includes KJ, but once we put that in Villain’s range, our FE goes out the window.

  4. I just have one question. Isn’t it kind of a disaster that you got KJ (or any J for that matter) to fold when you shove all-in holding 88? What are your thoughts on just raising to something like $350-$400 range, allowing your opponents to possibly shove over the top, or just flat call which would make them pretty committed to calling a shove on turn. Thanks.

    • It is, but part of what I meant to say in the post is that there’s not anything I can do about that. If Villain is a good hand reader and capable of disciplined folds, there’s nothing I can do to conceal the strength of my hand with this action in front of me.

    • Sorry, meant to add that a smaller raise isn’t going to look any weaker than a shove to a good player. There are no hands with which it would be correct for me to raise-fold, so a small raise really shouldn’t create any perceived fold equity.

  5. I like the cold call better. Make him think you want him to think that you are strong so you can bluff the turn. Plus you may get the MP2 to shove/squeeze.

    • I am actually curious to test the idea of cold calling as a “semi-bluff” or float on the assumption that it would look really strong. I have my doubts, but I do want to investigate it further. The problem is that when it comes to calling vs. raising, it’s not purely a matter of perception. There are objective, mathematical reasons why calling ranges generally have to be stronger than raising ranges, the primary one being that you have no immediate fold equity when you call.

  6. It seems a little odd to me your reason for not cold calling include the possibility of Villain having A10cc/910cc but you don’t include it in your calculations.

    If you cold call I think villain can put you on another jack (j9,j10,QJ) thinking you might fold to a bet on the turn. I certainly can see how he can get away with anything but AJ on the flop but it is not like he is going to get away every time you cold call. Plus MP might spazz and shove. Plus doesn’t button raise AJs pre against a loose player at least some of the time thereby discounting it a little on the flop.

    I do think this whole example shows just how significant one’s assumptions are when figuring out the best play to make.

    For what it is worth I still think your instinct/intuition to shove 910cc was right. Though I see based on your explicit assumptions why it was wrong. I guess I feel like you need to include a few semi-bluffs (10%-20%) in your calculations, maybe add J9 to villains range)

    I do appreciate you making such a complete post. Good work.

    • “It seems a little odd to me your reason for not cold calling include the possibility of Villain having A10cc/910cc but you don’t include it in your calculations.”

      I mentioned them to address your argument about wanting to let a flush draw get there, not because I necessarily put them in Villain’s range myself.

      “Plus doesn’t button raise AJs pre against a loose player at least some of the time thereby discounting it a little on the flop.”

      FWIW though MP2 was both slightly loose and slightly passive, so while his calling range might be wider than it should, his range for open raising may be tighter than it should be.

      “I do think this whole example shows just how significant one’s assumptions are when figuring out the best play to make.”

      Agreed. I’m actually curious to do some more in-depth analysis of this situation and play around with just how sensitive the results are to various assumptions. Hopefully I’ll have an even more thorough follow-up soon.

      Thanks for the good questions/feedback.

  7. Using your numbers, holding AJ

    EV = P(fold)*pot + P(call)* (P(win)*(win amount) + (P loose) *(-loose amount))
    Button has 462 131 to call

    Pot = 221
    Win amount = 221+462 = 683
    Loose amount = 462 + 131 = 593

    EV = 7/13 (221) + 6/13 (.36 *(683) + .64 *(- 593)) = $57

    I wouldn’t call this marginal. None of this analysis is particularly meaningful though since Button almost never has 88. 88 invariably smooth calls this flop. I would not even call this a slow play. The advantage of allowing a draw in cheaply vastly outweighs the risk of a suckout. Furthermore, most if not all Jx shove to protect against button’s ‘obvious’ FD.

    And what does button do with 109cc, Q10cc, Q9cc, Axcc, etc. I don’t think he folds them. Raise, shove, call? Villain turns up with these hands at least some of time. It’s a major assumption to assume villain is completely unbalanced here.

    Also, against a range of AJ, 88, villains call with even AJ is $-49 EV

    So If these relatively modest assumptions hold: KJ folds and no 88, Axcc and J10cc become profitable pushes.

  8. Perhaps an over simplified way of looking at it might help.
    I am not sure if I butchered the math here but this might be a way of looking at.
    If we assume Button raises and folds everything but 88,AJ (ignore JJ and J8 for the moment)
    Every time button folds Hero makes 200
    Every time button calls Hero loses 600 (of course sometimes Hero sucks out with a straight flush draw…etc)
    6:2
    So break even is…
    75% of the time 0.75(200)- Hero makes 150$
    25% of the time 0.25(600)- Hero loses 150$
    So basically if we think Button has AJ or 88 more than 25% of the time Hero should fold.
    I really think Button would make a more standard raise or flat call with AJ or 88 a bunch but I don’t think I would be confident enough to say that Button doesn’t have AJ or 88 close to 25% of the time.
    One could certainly think there is more room to be wrong then right and justify a fold with everything but AJ/88 that way.
    (Of course that doesn’t include the times Hero has AJ and button has 88 but that’s just a huge cooler I guess.)

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