Math Problem with 77 (from the archives)

[hobbsmann]

Ok so I ran across a really interesting hand from the archives that was linked to by somebody in HUSH a couple of weeks ago and I thought it would be an interesting exercise for SS. I will reference the OP after some discussion has taken place and provide a link to his analysis of the hand.

Assume a small to mid stakes party game.

Hero raises 7[img]/images/graemlins/diamond.gif[/img]7[img]/images/graemlins/spade.gif[/img] UTG, TAG in late position 3-bets and it's heads up to the flop.

Hero respects the TAGs play and knows the TAGs range here is 88-AA, AQ/AK. The TAG also respects hero as a player.

Flop (7.5 sb) is K[img]/images/graemlins/heart.gif[/img]9[img]/images/graemlins/heart.gif[/img]6[img]/images/graemlins/club.gif[/img]

Hero check/calls the flop with the plan to check/fold the turn UI.

The question here is given the hand range of villian why is this flop peel correct (or incorrect)?

[TheHammer24]

Chance the Turn will check through?

[newhizzle]

the only hand in that range hero is ahead of is AQ, i think if you are going to fold the turn, you might as well fold the flop, the only reason i could think of to peel the flop is the chance that TAG will check behind on the turn, you are clearly not getting odds to improve

if it didnt come A or K high i might check/raise and see what happens from there, but here i think check/calling and folding turn UI is probably the worst line, if you think your beat and that you cant knock TAG off a hand like 88 or something just check/fold flop

edit: i think i misread the purpose of this post

[hobbsmann]

[ QUOTE ]
Chance the Turn will check through?

[/ QUOTE ]

This is the crux of the flop decision. The frequency of which the turn will be checked through will greatly affect the EV of our flop call.

The questions that need to be asked are about

a) how often does the turn need to be checked through with AQ to make our flop call profitable?

b) how often is the turn checked through when we are behind giving us more chances to spike a set?

[jason_t]

All I have to contribute is that I miss the original poster of this hand tremendously.

[W. Deranged]

This hand smacks of Nate Tha Great... Am I right?

My basic thought here is that when you are drawing in such a situation, you are not just drawing to your obvious outs (the 7s) or the secondary outs (the runner-runner draws), but you are also "drawing" to a couple of other things:

1. Villain checks the turn through for any of a number of reasons, and in that case your 4-5% chance of improving becomes 8-10%, which is very close to EV neutral if you can count some implied odds.

2. You are "drawing" to the fact that when villain checks the turn, you have a high likelihood of being able to get villain to fold unimproved, since the TAG respects your image and may have a hard time calling a river bet with a hand like TT or JJ (I think this is part of it... though I'm a bit unsure).

3. You are drawing to a bunch of potential scare card outs, presumably the As.

I don't know... I guess the idea is that, if we presume that villain will check the turn some reasonable percentage of the time (say 25% of the time) and we will win some reasonable percentage of the time that happens for a number of reasons (say we win like half the time he checks), our equity goes up to like 16-17% or something, and so we can continue on.

[Entity]

[ QUOTE ]
All I have to contribute is that I miss the original poster of this hand tremendously.

[/ QUOTE ]

Me too. [img]/images/graemlins/frown.gif[/img]



[img]/images/graemlins/heart.gif[/img]

[W. Deranged]

[ QUOTE ]
[ QUOTE ]
All I have to contribute is that I miss the original poster of this hand tremendously.

[/ QUOTE ]

Me too. [img]/images/graemlins/frown.gif[/img]



Totally off-topic: I find few things more aesthetically-pleasing than a Barry Zito curveball.
[img]/images/graemlins/heart.gif[/img]

[/ QUOTE ]

[hobbsmann]

[ QUOTE ]
This hand smacks of Nate Tha Great... Am I right?

My basic thought here is that when you are drawing in such a situation, you are not just drawing to your obvious outs (the 7s) or the secondary outs (the runner-runner draws), but you are also "drawing" to a couple of other things:

1. Villain checks the turn through for any of a number of reasons, and in that case your 4-5% chance of improving becomes 8-10%, which is very close to EV neutral if you can count some implied odds.

2. You are "drawing" to the fact that when villain checks the turn, you have a high likelihood of being able to get villain to fold unimproved, since the TAG respects your image and may have a hard time calling a river bet with a hand like TT or JJ (I think this is part of it... though I'm a bit unsure).

3. You are drawing to a bunch of potential scare card outs, presumably the As.

I don't know... I guess the idea is that, if we presume that villain will check the turn some reasonable percentage of the time (say 25% of the time) and we will win some reasonable percentage of the time that happens for a number of reasons (say we win like half the time he checks), our equity goes up to like 16-17% or something, and so we can continue on.

[/ QUOTE ]

As you guesed this was Nate tha' Great laying down some sweet knowledge on us undeserving peons.

In general you're getting at the idea that given villians hand range, AQ is a very distinct possiblity and will be a hand that probably checks the turn. Also that is the only hand we are beating, but on top of that there are a group of his pair hands that will check the turn behind and essentially improving our set drawing odds another porition of the time thus making our flop call +EV. (Brief summary)

So I was hoping we would get a little more response, but oh well. Here is what our resident sabermatrician had to say about the hand....

"
I think this is kind of an important hand. One of the changes I've made recently is to make some seemingly "loose" calls out of position on the flop and on the turn when I think there's a reasonable chance of my opponent checking it behind on the next street. It can help for the board to be a little bit scary in order for me to make these calls.

For example, say that I defend my BB against a CO open-raise with 7 6 , and the flop is T T 5 .

Note that I have some legitimate outs here: a backdoor flush, a backdoor straight, and probable pairing outs. You can make an argument for a call on this basis alone, even if you knew that your opponent was going to bet the turn, regardless of what he held. However, you should almost certainly peel here, because your opponent will often check behind on the turn, fearing a check-raise from trips. That is, I'll often be getting two cards for the price of one, making the call quite profitable.

More often, this will involve a situation in which there is some chance that you have the best hand, and also some chance that you will improve if you do not have the best hand.

For example, let's say that I'm again in the BB, defending against a Cutoff open-raise from a solid, thinking player. My hand is 9 8 and the flop is 8 5 3 .

I check-raise the flop and my opponent calls.

The turn is the K . I bet and my opponent raises. There are around 7 BB in the pot at this point.

If my opponent does in fact have the King, I will usually have five outs to beat him, which is not quite enough to call with getting 7:1. However, I also believe that my opponent is capable making this play with some other overcard hand like AQ. When he does this, he will usually check behind on the river, especially since the flop contains some draws and his hand would beat a busted draw at showdown. If he checks behind the river even a small percentage of the time, calling the turn goes from slightly unprofitable to highly profitable. So I should almost certainly make this call on the turn. Against a particularly aggressive opponent, of course, I would want to call down on the river anyway, especially if another big card does not come off, but there are lots of folks against whom I suspect calling the turn and folding to a river bet is the correct play.

This 77 hand is another, somewhat more complicated example of this principle. Suppose that I've pegged my opponent's hand range correctly. The only hand that I beat is

AQ (16 combos)

Whereas I lose to

AK (12 combos)
AA (6)
KK (3)
QQ (6)
JJ (6)
TT (6)
99 (3)
88 (6)

Or 48 total combos. That is, I believe my sevens are the best hand about 16/64 or 1/4 times.

I also will usually have around 3 outs to improve if I do not have the best hand, between spiking a set and backdoor straight possibilities. Of course, sometimes I will hit a 7 and lose to a set of kings or nines, or a flush. On the other hand, if I do spike a 7, and my opponent has something like AK or AA, the implied odds situation is pretty favorable. I think 3 outs is a reasonable working estimate.

How many outs to I need to make a correct call here on the flop?

There are around 8.25 SB in the pot once my opponent bets. As it works out, I need almost exactly 5 outs worth of equity in order to make the call profitable.

As we've discussed, I have about 3 "legitimate" outs here that come from spiking a seven or making a backdoor straight, meaning that I have to make up 2 outs somehow in order for the call to be correct.

The question I posed earlier was: how often does my opponent need to check behind AQ on the turn in order for my call to be profitable? As I hope you will see, the answer is: not very often. For example, suppose that my guess is that my opponent will check behind AQ on the turn just 1/4 of the time here. How much is this worth in terms of outs?

We're looking at a parlay here: my opponent needs to have AQ (1/4 of the time) *and* she needs to check it behind (1/4 of the time). All told, this will happen just 1/16 of the time.

This seems like a longshot, but it is actually worth a little something. A 1/16 shot is equivalent to 3/48, or about a 3-"out" draw with 47 unseen cards to come. So now I have 3 legitimate drawing outs, plus about 3 checking behind outs, for a total of 6, which is more than I need to make the call profitable. In practice, I believed that my opponent would check behind with AQ more often than one in four times here, as this is one of the worst conceivable boards for AQ against a tightish UTG raiser. If she checked behind with AQ say half the time here, then folding would be a huge mistake.

Of course, sometimes my opponent will take her free card, and spike an A or a Q on the river to win her the pot. This is one of the things that I just have to live with, as I will not be ahead often enough to justify making a play at the pot and preventing free cards. On the other hand, there are a couple of other devlopments that could work out favorably for me:

1) My opponent could check behind with something like TT on the turn, hoping to see a cheap showdown, doubling my chances to spike a 7 and making it cheaper for me to draw to a straight.

2) I could pick up a gutshot or OSED on the turn and call a bet from my opponent, and win some additional percentage of the time if I don't improve, but she decides to check behind her AQ on the river.

I'd guess that these scenarios are worth an additional 1.5 or 2 outs all on their own.

There is also an important point to be considered here from the standpoint of the villian. Note that I am willing to be bluffed off the pot on the turn, if she's prepared to follow through and again bet her AQ. However, because my sense based on her previous play was that she'd often check behind this board with her AQ, she made it correct for me to make a loose peel on the flop. That is, if my opponent were more relentlessly aggressive, I would probably not have peeled on the flop, even though against an extremely aggressive opponent with a wider 3-betting range, there would be more chance that I had the best hand at present.

In poker, there are a certain set of plays that are made frequently by very good opponents, and are also made frequently by very bad opponents, but are not made as frequently by average-good opponents. Making a loose peel on the flop is one such play. A fish will call your bet on the flop with a wide range of hands because he isn't thinking about pot odds and doesn't put any stock in your "automatic" flop bet, but a very tough player may make some loose peels as well because he recognizes that the aggression he's shown you in other hands will frequently intimidate you into checking behind on the turn, giving him a free card, a cheap showdown, or possibly even a profitable bluffing opportunity.

Against both of these types of opponents, you should be more inclined to bet the turn rather than take a free card or cheaply pick off a bluff at showdown, even if you believe that there's a good chance that you're drawing. Of course, you will get check-raised sometimes by a hand that you're drawing live against, or even get check-raised occasionally by a worse hand that has picked up some sort of semibluff or otherwise senses weakness. But over the long run, you will probably give away more pots by playing the turn too meekly than by playing it too strong. "

-Nate tha' Great
And the link to the whole hand

[W. Deranged]

I'm bumping this, and may well continue to do this a few times a day for the next... oh... 3 months or so...

This is awesome. Everyone should read this. And then read it again when I bump it again.