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the brutal math of big unpaired cards in multiway pots

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LawDude

03-02-2010, 09:52 PM Post subject: the brutal math of big unpaired cards in multiway pots

#1 (permalink)

Full House

Join Date: Feb 2009

Posts: 940

During downswings, I always think about what I might be doing wrong. Of course, that can result in tilt (bad) but it can also result in new ways to think about the game (good). I have had a downswing lately where I have been losing a lot of money at tables with, say, 5 calling stations, as opposed to a table with maybe 2 of them and the balance of players being nits or decent players. Now, of course, most of this is just variance-- those calling stations would be paying me off if I were hitting big hands! But it's not all variance. I was reflecting on how hard it is to win with a hand like AK when you raise and get 5 or 6 callers. First of all, you need to hit the flop-- you aren't going to have the best hand with AK unimproved very much, and you aren't going to be able to get to showdown without spewing a bunch of chips at bad odds if you do.

Second, when you are up against a bunch of players, even top pair top kicker seems like it loses a lot of the time on all but the driest boards, because someone is often out there with 2 pair, trips, a flush, or a straight. Again, you get paid off well when your hand holds up or you make a bigger hand, but the latter doesn't happen that often with a big ace and the former has to be balanced against all the chips you spew when you hit the flop and nonetheless lose.

This got me to wondering exactly what happens to your equity with a big ace in a multiway pot. Well, the answer is depressing.

Here's a typical sort of hand from last night, where I lost a ton at a very fishy 8-16 table, most of it on AK-AT:

Kd Ah 131361 19.96 521553 79.26 5094 0.77 0.203
Qh 4h 120338 18.29 537011 81.61 659 0.10 0.183
7c 6c 139648 21.22 517701 78.68 659 0.10 0.212
2s 2d 107178 16.29 550171 83.61 659 0.10 0.163
Js 9d 111609 16.96 545740 82.94 659 0.10 0.170
8s Kc 42780 6.50 610134 92.72 5094 0.77 0.069

Now, notice, I do have enough of an equity advantage to justify a pre-flop raise-- the chances of winning a six-way pot with a random hand are 16.67 percent, and I have 20 percent equity. But I have less equity than suited connectors (the favorite here!) and barely more equity than Q4 suited!

And here's the problem-- am I really capturing that 20 percent equity here, and at what cost? I suspect that our friend with 76 IS capturing most of his or her equity-- basically the flop comes and the hand is dumped if it misses, called or raised for value or free cards if it hits a pair or a draw, folded if the pot odds don't justify a call on a speculative draw, and bet for value if it makes two pair or better.

Similarly, I suspect that our villain with deuces is capturing a lot of his or her equity-- very little of that equity is unimproved, and basically if the villain flops a set, he or she will collect enough additional bets from players chasing hands to make up for the possibility that the hand is folded where it would have made a set on the turn or river.

But with AK, when I hit, I am in a classic reverse implied odds situation, where I may well be pouring lots of money into a pot I won't win. And if I miss, I have to decide whether to call with respect to outs that may not be good.

And this, of course, is with AK. Here's one with AJ:

Jd Ah 130090 19.77 527692 80.20 226 0.03 0.198
Qs 6s 116864 17.76 540918 82.21 226 0.03 0.178
9d 7d 95001 14.44 558023 84.80 4984 0.76 0.148
4s 4c 118014 17.94 539768 82.03 226 0.03 0.179
8s Kh 83627 12.71 574155 87.26 226 0.03 0.127
Tc 7c 109428 16.63 543596 82.61 4984 0.76 0.170

Here I am at least a slight favorite. But the equity capture problem is even worse here. If my ace hits, fair enough. If my jack hits, I have to sweat out possible overcards. And that's fine in decent games where players will fold if they don't have correct pot odds to chase to 3 outs. But it's terrible in games against calling stations, because even though neither villain 2 nor villain 5 is likely getting correct pot odds to call to the river to hit a 15 to 1 shot on each street, if they both call (incorrectly), it doubles the number of cards in the deck that can hurt me. And, again, the problem is one of reverse implied odds-- if they DO hit, I am likely going to have to pay them off on the river, whereas if they DON'T hit, they get to fold the river.

But where it gets really bad is when you open the pot in late position. All you need is some people behind you who think one of three things:

1. I'm in position in that guy on the button, so I better call to protect my position.
2. I've already put my blind in, I better protect it.
3. I read in a poker book somewhere that players steal blinds from late position, so I should call a late position raise as I may be ahead.

So, let's say that I'm in the cut-off with A7o and everyone calls me. Look at this:

7c Ah 282777 26.04 801369 73.79 1862 0.17 0.261
Kc 4c 290110 26.71 794036 73.12 1862 0.17 0.268
8d 6d 290971 26.79 793175 73.04 1862 0.17 0.268
Qs 5d 220288 20.28 863858 79.54 1862 0.17 0.203

Yuck! I would be a big favorite against any of these three hands heads up. Instead, I am 3rd favorite to win the hand and am barely getting any equity advantage at all with my hand.

Note that it only gets a little better if I have a stronger ace:

Jc Ah 322765 29.72 761378 70.11 1865 0.17 0.298
Kc 4c 276659 25.47 807484 74.35 1865 0.17 0.255
8d 6d 279537 25.74 804606 74.09 1865 0.17 0.258
Qs 5d 205182 18.89 878961 80.94 1865 0.17 0.189

That's an advantage, sure, but I still have to worry about overcards if I pair my jack, so I am probably not going to be able to capture all of my equity even in this situation (though obviously the fewer opponents I have in the hand, the better off I am).

What's the point of all this? I'm not really sure. I've thought about whether it might be better to limp strong aces and see what happens, but that, if anything, makes the reverse implied odds problem worse. We could limp re-raise, but the same types of players who call 2 bets willy-nilly call 3 or 4 willy-nilly too. I'm not folding ace-king or ace-queen either.

But basically leaves me back to pushing a small equity edge that often puts me in big-time reverse implied odds situations. It's less than ideal, but I see no better way.

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Sl4y3r

03-02-2010, 11:52 PM

#2 (permalink)

3-of-a-Kind

Join Date: May 2008

Location: Adelaide, Australia

Posts: 59

Good read thanks!

Been playing on cake and was owned by stations last session, ill be playing with stove before i have my next.

swiggidy

03-03-2010, 02:22 AM

#3 (permalink)

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Join Date: Sep 2005

Location: Waiting in the shadows ...

Posts: 3,777

Why would you even include A7o example? If they're calling with ATC don't raise mediocre hands. Don't bluff multi-way, and don't be excited to stack off with an overpair on a 5 way flop. If too many people call raise more pre and find your own sweet spot. 3-4bb is just a guideline for a reasonable table.

This is a really long post to say "I don't know how to play TPTK in a 5way pot"

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KoRnholio

03-03-2010, 04:34 AM

#4 (permalink)

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Posts: 2,165

KoRnholio will become famous soon enough

I think basically it boils down to the fact that some hands just play much better in multiway pots. Suited connectors and small pairs are easy to determine your pot odds on and make profitable calls.

Hands like AKo are still strong and can peel, but will frequently lose even after hitting tptk. It's still +EV to play, just more difficult and (possibly) less profitable when going 5ways rather than heads up against a fish/station.

I've always had a problem with using preflop equities based on all hands getting to the river for analysis of LHE, but I don't have any better way. What I do know is that for post flop play in Loose/Passive LHE, it's generally the draws that have the edge over the long run.

Some days it feels like I've been standing forever, waiting for the bank teller to return so I can cash in all these Sklansky Bucks.

LawDude

03-03-2010, 06:57 AM

#5 (permalink)

Full House

Join Date: Feb 2009

Posts: 940

Quote:

Originally Posted by swiggidy

No. It's actually partly that there IS no correct way to play it against stations in multiway pots, because you are either WA/WB or susceptible to lots of draws and both need to protect your hand and extract value and are vulnerable to RIO's.

As for A7, I used that as a lead-in for AJ. We know about A7, but AJ is not much better.

But the main point is that stations kill the value of big unpaired cards.

Coop56

03-03-2010, 05:45 PM

#6 (permalink)

High Card

Join Date: Mar 2010

Posts: 6

I can't stand too many call stations at one table. Playing small ball poker, it's tough to avoid the call stations beating you on some insane river card. You just have to get past it though, because even though it seems like it happens all the time you'll win with the better hand more often then not.

I don't like coin flip hands like AK myself, and if the heat comes on after I miss the flop I typically just muck them and save my chips.

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drmcboy

03-04-2010, 02:53 AM

#7 (permalink)

DrButtInski
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i play small ball limit holdem 2

JWalker

05-15-2010, 03:45 PM

#8 (permalink)

High Card

Join Date: May 2010

Posts: 10

Very good analysis. Thanks. I'm amazed 76s has better hot/cold here. Perhaps some pot size manipulation is in order, even with AK. If you overlimp instead of raise you lose little in terms of equity as you have pointed out. Then the pot is small enough that you may be able to price out the weak draws at some point on the flop or turn with a raise.

Also with AK remember that though you have some reverse implied odds going on, poker is very complex, and you have some positive implied odds situations as well (ex: KK3 board in which you dominate K8).

Ragnar4

06-17-2010, 05:52 AM

#9 (permalink)

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Join Date: Sep 2005

Location: Billings, Montana

Posts: 1,284

Thank you very much for the analysis.

Perhaps I play my AK-AT KQ KJ et al too simply.
But:
If I'm not the one raising with them, I'm probably not playing them.
If I'm contemplating calling a raise with them, I'm probably incorrect.
If I'm contemplating calling a 3-bet, again, I'm probably incorrect.

At least then on the flop the math helps me peel when I'm behind if it's HU, and it helps me push my edge when I'm ahead.

All too often, you're right though, you end up 3 or 4 way where it's just about impossible to identify what your correct play is, because you have no idea where you're at. At least when you miss. When you catch, you're just about always showing down, unless people go bet-style-retarded on the flop or turn.

Also: Something interesting about all of your hands: In every situation, you are winning more than your fair share. Every time. So ideally you should be capping pre-flop in every situation.

Example #2, though, 4 way with A7o may be a total wash, because even if you cap pre-flop I don't think you can beat the rake.

The older I get, the more I start wondering; Just what in the hell is going on here?

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the brutal math of big unpaired cards in multiway pots

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