Being ahead when you are actually behind

[Litellio]

Extremely Interesting Article from Pokerstove.com website about equity against hand ranges. I take no credit for this, but it is very interesting.


Here's a hand that I played recently which illustrates the magical paradox of poker. Namely, it's possible to simultaneously have the best hand and the worst hand.

It's a fairly tight nine-handed game. I'm in the cutoff with JJ, and the uber-rock raises 2-UTG. I love this position. If he opens there with 99/AQs/AQo or better, then I've got a hand which is just marginally better than his distribution:

equity (%) win (%) / tie (%)

Hand 1: 50.6546 % [ 49.69 00.96 ] { JJ }
Hand 2: 49.3454 % [ 48.38 00.96 ] { AA-99, AKs-AJs, AKo-AQo }

So by raising, I get value AND I can narrow his hand distribution down and find out where I am. I raise, he caps, and now I'm in the ****ter, but I've got odds to hit my set:

equity (%) win (%) / tie (%)

Hand 1: 36.1901 % [ 35.98 00.21 ] { JJ }
Hand 2: 63.8099 % [ 63.60 00.21 ] { AA-QQ, AKs, AKo }

So of course, I flop the set. The board is Ks Js 5s. Uber rock leads out. I'm happy happy happy. I'm nearly 100% certain that he doesn't have a flush. He'd have to have capped with AQs to have a flush, and I just can't give him credit for that. The *only* hand he could have which is better than mine is KK. I push back the irrational fears of set-over-set, and raise for value. I'm ahead of his possible holdings:

Board: 5s Js Ks
equity (%) win (%) / tie (%)

Hand 1: 73.2395 % [ 71.62 01.62 ] { JJ }
Hand 2: 26.7605 % [ 25.14 01.62 ] { AA-KK, AKs, AKo }

Of course, uber-rock three bets me and I cap it. Once he 3-bets me, warning bells start to go off. But I want to make AsAx and AsKx pay for the flush draw:

Board: 5s Js Ks
equity (%) win (%) / tie (%)

Hand 1: 46.8855 % [ 46.13 00.76 ] { JJ }
Hand 2: 53.1145 % [ 52.36 00.76 ] { KdKc, KhKc, AsKc,
AsAc, KhKd, AsKd,
AsAd, AsKh, AsAh }

Unfortunately, I'm behind. Who would'a thunk. Not me. I really thought I was ahead equity-wise when I put in the flop cap. I've got about 65% equity versus AsAx/AsKx and 6.5% equity versus KK. I guess that 65% equity when I was ahead just wasn't quite enough. Maybe he'll give me a free card?

Besides, I have effective odds to call him down. Being the sucker that I am, I'll probably pay him off if the fourth flush card comes. I am the pay-off king!

godisuck

Thankfully all doubt is removed from my mind when the case jack hits on the turn. Uber-rock check-raises me, which is really nice with a 4-bet cap. He gets to put in the last raise, and continue believing he is ahead.

Board: Jh 5s Js Ks
equity (%) win (%) / tie (%)

Hand 1: 97.7273 % [ 97.73 00.00 ] { JJ }
Hand 2: 02.2727 % [ 02.27 00.00 ] { KK }

The river is a blank, uber-rock leads out, and this time I get to cap it.

The uber-rock just happened to have KK. It makes me wonder what he thought *I* had. Maybe he knows about Presto! and put me on 55? Who knows? Silly rock, you go home now.

The point here isn't that I was a huge dog and managed a massive suck-out. Although I do LOVE it when that happens. The point is that I WASN'T a huge dog, and just happened to pull a massive suck-out.

This is a distinction that a lot, and I mean A LOT, of players of all levels can't make. In this hand I was never in big trouble. I was actually leading, or had plenty of odds to continue on in the hand. From a results oriented perspective, I did happen to be royally screwed, but you can't do proper analysis from a results oriented stand point.

You have to take the information that you currently have and make the best decision possible based on that information. That's what poker is all about.

Moral of the story: Always keep 12 big bets at the table when there is a 4 bet cap. You may need them.

- Andrew

[Pates]

Going to the gym now. Will read it when I get back; looks really interesting.

[JB36]

Why did you have to announce you were going to the gym platefish?!?

Interesting article! Love the way he says 'silly rock, you go home now'....yeh what an idiot playing his 2nd nuts like that lol

[Pates]

Limit is poo and this is a perfect example of why. People will chase everything including their 1 outers!

I'm confused like JB36 at the comment "silly rock, you go home now". Is he supposed to be pot controlling with the 2nd nuts when there are hands out there that can pay him?? I don't think so some how.

[ccottis]

Only time I've played limit is in player points freerolls so it is a case of cap every street with anything better than a pair. You can go too far with the maths of hand ranges, your opponent only has one hand so you can never have an exact range.

[Pates]

I was told by someone that in limit, if the pot is heads up then there is no cap to the raises ...

Is this another game that anyone knows about? Because I'm pretty certain that ain't limit.

[bizkit]

I don't play limit but yeah a few things I don't agree with in this article.

"So by raising, I get value AND I can narrow his hand distribution down and find out where I am. I raise, he caps, and now I'm in the ****ter, but I've got odds to hit my set:"

If he's an uber-rock you're not getting value here because some of the hands in the aforementioned range aren't actually in his range. I don't think you're narrowing his range much either cause every hand he raises with from this position he's probably capping it just for principal.

"Of course, uber-rock three bets me and I cap it. Once he 3-bets me, warning bells start to go off. But I want to make AsAx and AsKx pay for the flush draw:"

This is why limit poker is really boring. Your 4bet here doesn't really gain or lose much. Either he has an As and he's priced in to call or he has pocket kings and you're absolutely crushed.

"Silly rock, you go home now."

Actually I kind of agree that its silly to cap both turn and river streets vs an opponent who is decent and capable of perceiving the uber-rock image your presenting. Sure only one exact hand beats you but honestly what else can he play like that? After I check-raise and get 3bet I think I'm just calling then check calling the river. I don't think 55 isolates preflop like this or 3bets the turn after i check raise. AsQs was certainly possible but unlikely to 3bet my turn check raise on a now pair'd board. So JJ is the only hand I really put a decent opponent on.

[Litellio]

Problem is there's only 1 combo of hands, the :Jx :Jx that beats you, everything else in his "range" you crush, except this, so technically given his total range, which i agree is generous, surely this is a standard cap all on all 3 streets?

[thefairy]

not online in most plaes,(think sunpoker plays that rule) platefish but i think what you gota understand bout poker is that east coast america plays it different to west etc, for example lowball rules valry, some ppl wud say the wheel is the best hand in lowball, but if you are saying flushes and straights are high a2346 is best hand, and even some call ace high, so thas why "deuce to seven" lowball exists...house rules are a funny old thing, esp in declare games and draw.

[bizkit]

There's no reason to put the extra 4 big bets in unless you can't eliminate him from isolate 3bet'ing an ep rock raise from co with 55 AND willing to cap with 55 on this board when he's behind every hand in the rocks range...OR him willing to cap streets with AsQs after the board pairs. Most sane opponents don't do either. Yes, there's only one combination that beats you but given what's happened its highly likely he has that one combination.

I was told by someone that in limit, if the pot is heads up then there is no cap to the raises ...

Is this another game that anyone knows about? Because I'm pretty certain that ain't limit.

Most places I've played at online its a 4 bet cap per street. Although its been a while.

[SirJonnyP]

.....anyway.....