A Pure Math Situation

[gaming_mouse]

Villain is a TAG on the less agressive side. After the flop action, we can safely put him on the typical PF capping range, excluding TT.

I'll put my analysis in a separate post, so people can vote first without being influenced.

Party Poker 5/10 Hold'em (6 max, 6 handed) pokerhand.org hand converter (http://www.pokerhand.org)

Preflop: Hero is MP with A/images/graemlins/heart.gif, K/images/graemlins/diamond.gif.
UTG calls, <font color="#CC3333">Hero raises</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">Button 3-bets</font>, <font color="#666666">2 folds</font>, UTG calls, <font color="#CC3333">Hero caps</font>, Button calls, UTG calls.

Flop: (13.40 SB) 7/images/graemlins/diamond.gif, 6/images/graemlins/diamond.gif, 6/images/graemlins/club.gif <font color="#0000FF">(3 players)</font>
UTG checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">Button raises</font>, UTG folds, Hero calls.

Turn: (8.70 BB) J/images/graemlins/heart.gif <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets</font>

[gaming_mouse]

I thought this situation was interesting because the correct play was precisely calculable, although it also depends also on our read of villains agression.

AK - 9
AA - 3
KK - 3
QQ - 6
JJ - 3

Giving all hands equal weight, we have clear calldown:

(9/24)*5.3 + (6/24)( (6/44)*10.7 + (38/44)*-2) + (9/24)(-2) = 1.17

But it might be more realistic to discount AK and QQ about 50%, in which case it becomes much closer:

(4/17)*5.3 + (3/17)( (6/44)*10.7 + (38/44)*-2) + (9/17)(-2) = .14

And one could argue that, given my description of villain, we should discount AK even further, and that would swing our decision to a fold.

On a related note, does anyone have any tricks that would allow one to make EV calculations like these in your head anywhere close to possible?

[Nick C]

[ QUOTE ]
I thought this situation was interesting because the correct play was precisely calculable, although it also depends also on our read of villains agression.

AK - 9
AA - 3
KK - 3
QQ - 6
JJ - 3

Giving all hands equal weight, we have clear calldown:

(9/24)*5.3 + (6/24)( (6/44)*10.7 + (38/44)*-2) + (9/24)(-2) = 1.17

[/ QUOTE ]

I was glad to read this, because based on the premises as I understood them, the calldown seemed easy to me, even without taking into account our chances of improving on the river to overtake KK/QQ.

[ QUOTE ]
But it might be more realistic to discount AK and QQ about 50%, in which case it becomes much closer:

(4/17)*5.3 + (3/17)( (6/44)*10.7 + (38/44)*-2) + (9/17)(-2) = .14

And one could argue that, given my description of villain, we should discount AK even further, and that would swing our decision to a fold.

[/ QUOTE ]

Yeah, if our read regarding how Villain will play his various possible holdings isn't so certain (and, at the table, it usually isn't), then the decisions become more complicated.

[gaming_mouse]

[ QUOTE ]

Yeah, if our read regarding how Villain will play his various possible holdings isn't so certain (and, at the table, it usually isn't), then the decisions become more complicated.

[/ QUOTE ]

Yeah, in the heat of battle I could not do the calculation, and I folded. But I actually think that now, even having done it, I would still fold. It seems to me that players like the one I described will not raise the flop here with AK nearly as much as 50% of the time.

[SackUp]

Where is the option for peel the turn and fold the river UI?

I think a lot of players will raise AK on the flop and continue through on the turn, but then check behind on the river.

I don't think a TAG is betting AK on the river UI too often, so we can safely fold for that bet.

[SackUp]

[ QUOTE ]
we can safely put him on the typical PF capping range, excluding TT

[/ QUOTE ]

I don't know if I agree with this. I think 99 and 1010 are playing this flop and turn the exact same way.

[Shillx]

Sorry if this post is super confusing.

I don't know what a typical hand range is here, but this is what I'm thinking when he raises the flop.

AA - KK &gt; AQ - Ax /images/graemlins/diamond.gif (dunno what x is) &gt; QQ &gt; JJ &gt;&gt; AK and TT

So if TT isn't an option for his range here, I don't really think that AK should be included either. I don't really like just calling the turn and folding the river UI because we will sometimes be folding the best hand. If he can have JJ+/AQ-AT /images/graemlins/diamond.gif, we are making a mistake should we fold it on a brick.

A good player should be playing this hand really carefully with soemthing like JJ or TT imo. If he has JJ, he is behind when you have a better overpair and he has the 3rd player drawing really thin when you have overcards. If JJ is actually the best hand on this board, it does him no good to knock out any potential losses in the deck (namely aces through queens) that the 3rd player might hold since you are holding them too when the jacks are good. Let the guy put bets in with KT when he is drawing to running tens or a running 9+8.

So when a very good player raises the flop, I start worrying that he has AA or KK and don't really fear QQ down. Then to mix it up he should also raise big flush draws (say AQs and AJs). So in that case you will be somewhere in the range of a 9:1 dog and you are getting 9.7:1 to call the turn. You can see why this would put you in a quagmire.

Against someone who plays a bit worse I would probably calldown because you will see lower overpairs more. And if I don't outdraw them, I'm getting such a good price to call the river and hope that they are on a flush draw or AK. I'm sure it will win $$$ net but if he can't have TT (and therefore can't have AK) when he raises the flop (but can have JJ) I would fold the turn.

Brad

I lay this down. You're not getting the odds to call to more bets to win &gt;11 (minus whatever they would rake from there).

Seperately, do you guys cap this preflop? Esp given the read, I think just calling the 3 bet is okay, though with UTG in there to pad the pot I'm not saying it's a mistake or anything to cap. HU I just call down the 3 bet for sure given your read. (Comments despite my low post count?)

[gaming_mouse]

[ QUOTE ]
Where is the option for peel the turn and fold the river UI?

I think a lot of players will raise AK on the flop and continue through on the turn, but then check behind on the river.

I don't think a TAG is betting AK on the river UI too often, so we can safely fold for that bet.

[/ QUOTE ]

This is interesting. However, think of it from his POV. After peeling the turn, we have an AK sticker on our forehead. If he has AK too, folding our AK is a pretty nice proposition, especially since a raise is unlikely and he could safely fold to one.

[gaming_mouse]

[ QUOTE ]
[ QUOTE ]
we can safely put him on the typical PF capping range, excluding TT

[/ QUOTE ]

I don't know if I agree with this. I think 99 and 1010 are playing this flop and turn the exact same way.

[/ QUOTE ]

He was on the timid side of TAG, so I didn't that he would. You are right that these a possibilities though, and a more thorough analysis would include them, discounted appropriately.

[gaming_mouse]

Brad,

Thanks for that excellent analysis.

[gaming_mouse]

[ QUOTE ]

So when a very good player raises the flop, I start worrying that he has AA or KK and don't really fear QQ down. Then to mix it up he should also raise big flush draws (say AQs and AJs). So in that case you will be somewhere in the range of a 9:1 dog and you are getting 9.7:1 to call the turn. You can see why this would put you in a quagmire.

[/ QUOTE ]

One thing though. How did you come up with 9:1 dog. There are 2 big flush draw combos, and 6 ways to make either AA or KK. So we are a 6:2 or 3:1 dog, no? And now calling down seems much more attractive versus a good player. What am I missing?

[Shillx]

AJ /images/graemlins/diamond.gif just passed us on the turn. AQ /images/graemlins/diamond.gif has 12 outs against us and another 5 outs to chop.


3,960 games 0.005 secs 792,000 games/sec

Board: 7d 6d 7h Js
Dead:

equity (%) win (%) tie (%)
Hand 1: 10.0379 % 09.47% 00.57% { AKo }
Hand 2: 89.9621 % 89.39% 00.57% { KK+, AdQd, AdJd }

Now for a river blank...

Text results appended to pokerstove.txt

90 games 0.005 secs 18,000 games/sec

Board: 7d 6d 7h Js 2c
Dead:

equity (%) win (%) tie (%)
Hand 1: 10.0000 % 10.00% 00.00% { AKo }
Hand 2: 90.0000 % 90.00% 00.00% { KK+, AdQd, AdJd }

So against this range we either have to fold the turn or calldown. Notice how the equity doesn't change when the river bricks.

[gaming_mouse]

Oh, thank you. I really wasn't thinking.

[BWebb]

In your math, isn't it incorrect to include bets you put in on later streets? Calling down from the turn you against AK it is (9/24)*(4.3) since you are making the decision on the turn. Same with QQ, (6/24)((6/44*8.7)+(38/44*-2) and so on. It still is a calldown, but I'm getting about +0.82 in my calculations.

[gaming_mouse]

[ QUOTE ]
In your math, isn't it incorrect to include bets you put in on later streets? Calling down from the turn you against AK it is (9/24)*(4.3) since you are making the decision on the turn. Same with QQ, (6/24)((6/44*8.7)+(38/44*-2) and so on. It still is a calldown, but I'm getting about +0.82 in my calculations.

[/ QUOTE ]

I don't understand what you are doing. In my calculation, the 5.3 is half of what you will win if you call down and split the pot. It includes the two additional bets your opponent puts in.

[SackUp]

[ QUOTE ]
[ QUOTE ]
Where is the option for peel the turn and fold the river UI?

I think a lot of players will raise AK on the flop and continue through on the turn, but then check behind on the river.

I don't think a TAG is betting AK on the river UI too often, so we can safely fold for that bet.

[/ QUOTE ]

This is interesting. However, think of it from his POV. After peeling the turn, we have an AK sticker on our forehead. If he has AK too, folding our AK is a pretty nice proposition, especially since a raise is unlikely and he could safely fold to one.

[/ QUOTE ]

I agree, though this is assuming a lot of things.

1) that he knows we are also a TAG.
2) He is a smart TAG and can pick up on this.
3) He is willing to bluff 3 streets in a row.

I'm not saying this is not possible, but I don't see this too often in the 2/4 games I'm playing. Heck I don't see this in many upper limit games either.

So I don't think many TAGs are making this move too often. And even if they did sometimes, I think the times they don't far outway the times they do.

Otherwise if we are just calling down anyhow, then the river should be a b/f line so we have the chance to fold his AK or AQ.

[BWebb]

[ QUOTE ]
[ QUOTE ]
In your math, isn't it incorrect to include bets you put in on later streets? Calling down from the turn you against AK it is (9/24)*(4.3) since you are making the decision on the turn. Same with QQ, (6/24)((6/44*8.7)+(38/44*-2) and so on. It still is a calldown, but I'm getting about +0.82 in my calculations.

[/ QUOTE ]

I don't understand what you are doing. In my calculation, the 5.3 is half of what you will win if you call down and split the pot. It includes the two additional bets your opponent puts in.

[/ QUOTE ]

I'm a moron, I misread and got that there was 7.7 in the pot pre-bet.

[Nick C]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
In your math, isn't it incorrect to include bets you put in on later streets? Calling down from the turn you against AK it is (9/24)*(4.3) since you are making the decision on the turn. Same with QQ, (6/24)((6/44*8.7)+(38/44*-2) and so on. It still is a calldown, but I'm getting about +0.82 in my calculations.

[/ QUOTE ]

I don't understand what you are doing. In my calculation, the 5.3 is half of what you will win if you call down and split the pot. It includes the two additional bets your opponent puts in.

[/ QUOTE ]

I'm a moron, I misread and got that there was 7.7 in the pot pre-bet.

[/ QUOTE ]

When we're locked into a split on the turn, our share of the pot is 4.35 BBs (minus rake). We have no share of any turn or river bets our opponent makes, but we have to match those bets to claim our half of the 8.7 BB pot that existed when the turn betting began.

[gaming_mouse]

[ QUOTE ]

Otherwise if we are just calling down anyhow, then the river should be a b/f line so we have the chance to fold his AK or AQ.

[/ QUOTE ]

This is a really good point, especially against this player, who will almost never bluff raise the river. The choice should have been between fold, or c/call followed by bet/fold on the river.

I still don't like c/call and fold UI. Even ignoring the chance that we fold a chopping hand on the river (and it is nonzero, though you make a good case for its being unlikely), we are not getting the odds we need because our hand will be good less than 50% of the time even when we hit.

[sk_man]

My numbers came out a little diffent than yours. I tried it both with and without TT, because I'm not sure if I would eliminate them.

AK - 9
AA - 3
KK - 3
QQ - 6
JJ - 3
TT - 6

Drawing Dead: JJ and AA, 6 combos, EV -2
6 outs: TT and QQ, 12 combos, EV -.2681
6 outs (without TT): QQ, 6 combos, EV -.2681
3 outs: KK, 3 combos, EV -1.1341
Tied: AK, 9 combos, EV 4.35

Then we just average each situation weighted by the number of combos, and that should give us our EV for the hand.

Including the TTs, I came out with .6843, and without them, it was .92245. Still a call down, but if we start to discount AK, then it becomes very close.

To get the EV, I was taking the odds that the hero will win the hand, multiplying it by the size of the pot (at the end of the hand) and subtracting the amount we have to call to see the showdown.

EV = O*(P + 4) - 2

This might be a little off, because there's a good chance villian would check through TT and maybe QQ on the river. So, in that case the EV would be:

EV = O*(P + 2) - 1

I don't really care about the exact numbers. I just want to know, if I'm doing this right.

[gaming_mouse]

[ QUOTE ]


EV = O*(P + 4) - 2

This might be a little off, because there's a good chance villian would check through TT and maybe QQ on the river. So, in that case the EV would be:

EV = O*(P + 2) - 1

I don't really care about the exact numbers. I just want to know, if I'm doing this right.

[/ QUOTE ]

I don't want to think about what you did, cause it seems confusing. But I dont think I made a mistake. Much easier way to conceptualize EV:

EV = (chance you win)*(amount you profit) + (chance you lose)*(amount you lose)

[ QUOTE ]
Where is the option for peel the turn and fold the river UI?

[/ QUOTE ]

[gaming_mouse]

[ QUOTE ]
[ QUOTE ]
Where is the option for peel the turn and fold the river UI?

[/ QUOTE ]

[/ QUOTE ]

Read the post I made 3 above yours. I think this line is clearly wrong.

[sk_man]

If you mean what I think you mean by "amount you profit" and "amount you lose," then they're the same equatuon.

[BWebb]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
In your math, isn't it incorrect to include bets you put in on later streets? Calling down from the turn you against AK it is (9/24)*(4.3) since you are making the decision on the turn. Same with QQ, (6/24)((6/44*8.7)+(38/44*-2) and so on. It still is a calldown, but I'm getting about +0.82 in my calculations.

[/ QUOTE ]

I don't understand what you are doing. In my calculation, the 5.3 is half of what you will win if you call down and split the pot. It includes the two additional bets your opponent puts in.

[/ QUOTE ]

I'm a moron, I misread and got that there was 7.7 in the pot pre-bet.

[/ QUOTE ]

When we're locked into a split on the turn, our share of the pot is 4.35 BBs (minus rake). We have no share of any turn or river bets our opponent makes, but we have to match those bets to claim our half of the 8.7 BB pot that existed when the turn betting began.

[/ QUOTE ]

I was right and wrong. The calculation was slightly off for AK but mine was off for the rest. I shouldn't try to do the math problems at work /images/graemlins/grin.gif

Would this be a viable question following this discussion?

How many bets will you gain from this play?