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What’s Your Range: Results

by Andrew Brokos |  Published: Feb 14, '11

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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

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.

Andrew Brokos is a professional poker player, writer, and teacher. He is also an avid hiker and traveler and a passionate advocate for urban public education. You can find dozens of his poker strategy articles at www.thinkingpoker.net/articles and more information about group seminars and one-on-one coaching at www.thinkingpoker.net/coaching.

 
Any views or opinions expressed in this blog are solely those of the author and do not necessarily represent those of the ownership or management of CardPlayer.com.
 

Comments

mattrat33
over 11 years ago

I could easily be wrong so forgive my stupidity if I am. IMO there are situations where no positive equity play is possible (positive equity play being defined as one where you profit from the decision). If you had 3 options where each yielded a negative result the best choice would be to pick the negative choice closest to 0 as your decision. I do not consider folding to be a $0 result since I consider folding to be: (your equity against opponent's range*potsize*-1). You essentially lose what's rightfully yours. Also, when your opponents fold I do not consider that a +$221 result. I consider what you gain to be: ((1-opponent equity vs. your range)*potsize). You gain what was rightfully your opponent's portion of the pot. I don't know how the math would change if it does using this logic, but I think always striving to make a "positive decision" is a logical flow. This seems to me to be a spot where you have a hobessian choice and a slightly -ev decision could easily be the correct one.

 
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mattrat33
over 11 years ago

Edit: Opponent fold: ((Oppeonent equity vs. your range)*Potsize)

 
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Foucault82
over 11 years ago

Matt,

I think I get what you're saying. If I'm right, you make an important point, but it is accounted for in the "traditional" EV equation that I use here. As you point out, EV is fundamentally comparitive. In other words, it isn't good enough to show that calling is +EV in a particular and then end your analysis there, as we would have to consider whether raising is MORE +EV before we could determine the correct play.

You're right that in some sense, folding does cost you something. It costs you equity that you have in the current pot. We can treat folding as 0EV, however, because your equity in the pot is reflected in alternative lines that don't involved folding.

In this example, folding Tc9c costs us substantial equity in the pot, but I would argue that the alternatives of calling or raising force us to pay too high a price to realize that equity.

Does that make sense?

 
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LoProPoker
over 11 years ago

I dont mean to boost or brag but i was totally right :)

 
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literation
over 11 years ago

Yes you do mean to boast ;)
Thought I was being a bit tight in my range but from the analysis I can be even more selective.

 
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Foucault82
over 11 years ago

Everything hinges on the raising range that you give BTN in the first place. Hopefully I made a compelling case for why I think he is very strong. If you think there are a lot of hands that he will raise/fold, then you can shove more hands profitably because of this additional fold equity.

 
 

swallsjr
over 11 years ago

Bad reraise imo. You should have played 2nd hand low and let the original bettor shove into you. Calling represents a J with a shitty kicker and a large range of his hands are ahead of that.

 
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Cal3e
over 11 years ago

All 3 players in this hand are online professionals. Nobody is stacking off with worse than KJ or AJ here. Calling looks stronger than shoving.

 
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mattrat33
over 11 years ago

If calling looks stronger than shoving, then that might open up the door for trying to bluff on the turn after cold calling this bet on the flop with some holdings. It may not be enough to make it a profitable play but certainly helps the case.

 
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literation
over 11 years ago

Please more blogs like these with scenarios, comments and later results.

 
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