A Pure Math Situation

gaming_mouse · #1 12-02-2005, 04:35 PM

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

Preflop: Hero is MP with A[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
UTG calls, Hero raises, 1 fold, Button 3-bets, 2 folds, UTG calls, Hero caps, Button calls, UTG calls.

Flop: (13.40 SB) 7[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/club.gif[/img] (3 players)
UTG checks, Hero bets, Button raises, UTG folds, Hero calls.

Turn: (8.70 BB) J[img]/images/graemlins/heart.gif[/img] (2 players)
Hero checks, Button bets

gaming_mouse · #2 12-02-2005, 04:37 PM

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 · #3 12-02-2005, 04:52 PM

[ 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 · #4 12-02-2005, 05:03 PM

[ 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.

sk_man · #5 12-02-2005, 07:51 PM

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 · #6 12-02-2005, 07:59 PM

[ 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)

sk_man · #7 12-02-2005, 10:48 PM

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

SackUp · #8 12-02-2005, 05:18 PM

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.

gaming_mouse · #9 12-02-2005, 05:53 PM

[ 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.

SackUp · #10 12-02-2005, 07:11 PM

[ 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.

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