big draws w/o fold equity

[JKratzer]

here's a situation that comes up occasionally when i play and i'm curious if some math will show that i'm doing the wrong thing. i'm going to try to keep it simple.

5/10 nl, $1000 stacks. i raise T[img]/images/graemlins/heart.gif[/img]9[img]/images/graemlins/heart.gif[/img] to $35, everyone folds to bb who raises to $110, i call.

flop($225) J[img]/images/graemlins/heart.gif[/img]8[img]/images/graemlins/heart.gif[/img]2[img]/images/graemlins/club.gif[/img]
bb bets $200.

now, my read on him is he's a got an overpair always, for the sake of simplicity let's say he has A[img]/images/graemlins/heart.gif[/img]A[img]/images/graemlins/diamond.gif[/img].

i can raise and he will push and we will get all-in and i'm actually a slight favorite with my big draw. this is what i always do. however what i've been wondering is, would it be more correct to just call the flop and re-evaluate based on the turn card?

assume bb pushes any turn (we will have about a pot-sized bet on the turn). is peeling a card better if that means we have to fold some turns but get all-in with much better equity other times?

also note i'm giving him the ace of hearts which will help his redraws when i do hit my flush outs, if weighting all combos of AA/KK doesn't make the calculations too much more difficult that might answer the question more accurately.

[jay_shark]

Usually it is much better to raise all in if you know he will call as an underdog . There are exceptions when you may opt to just smooth call on the flop if you're getting really tempting odds to just see the turn card . For instance , if he only bets 1/6th of the pot on the flop and you have 15 outs , then there is nothing wrong with just calling . On the other hand , if he bets the whole pot then it's recommended that you just push all in .

[JKratzer]

ok i'll give it a shot. i don't do these kinds of calcs ever so i'm sure it will contain mistakes, i'd appreciate anyone pointing out where i mess up.

option 1: all-in on the flop. according to twodimes.net i have .526 equity on the flop vs red aces. that's $1052 equity or +$52.

option 2: just call the flop. that puts the turn at $625 with $690 left.

8 cards make my straight/flush w/ bb drawing dead. +$1000 ev.

6 more hearts to make my hand but give him redraws to a better flush. .886 ev so +$772

6 cards that give me a pair. .432 or -$136 (but still a call because of the overlay in the pot).

25 blanks that i can't call a turn push. -$310.

8/45(1000)+6/45(772)+6/45(-136)+25/45(-310)=+90.3

so that would seem to support just calling the flop.

[ImsaKidd]

The problem is sometimes he has JJ and you call AI on the 2h turn or 9c turn and you get pwned [img]/images/graemlins/frown.gif[/img]

In an ideal world where you can see his cards is a lot different from the real world.

If you know he has a big pair here always, isnt preflop spew? You hit basically the best draw flop and youre not making much EV. Yes you probably stack him on T9x or 99x or whatever, but seems vv marginal to me.

[ig06]

In this specific example (with the assumption you state that bb pushes any turn) I think it is better to call the flop and re-evaluate. I make the assumption that you also call the turn if you hit a T or 9 (which is clearly correct against the AA you give in the example). Here is my calculation. I neglected to consider rake but it makes no difference here.
Case 1: Push.
You invest 890 into the pot.
Final pot size is 2005.
Your equity: 52.626% (pokerstove), i.e. 1055.1513

1055.1513-890 = 165.1513
So getting it all-in has EV +165.1513

Case 2: Call 200.
On turn: Pot 625, stacks 690. Pot equity needed to call on the turn push : 34.41%

Any 7 or Q and he is drawing dead. Any of the other 6 hearts (excluding 7,8,9,T,J,Q,A) and he will be drawing to 5 outs with 44 cards left in the deck.

So 8/45 times you get 100% equity on the turn.
6/45 times you get (39/44)*100% equity on the turn =88.636363…%

A T or 9 gives you any 7,9,T,Q or any of the 6 unaccounted for hearts as outs, which means you have 18 outs (two 9s, two Ts, four 7s, four Qs, six hearts.) so enough to call.

So 6/45 times you get (18/44)*100% equity on the turn =40.90909…%

25/45 times you have to fold the turn.

So your EV is (25/45)*(-200) + (20/45)*(-890) + [(8/45)+(6/45)*(39/44)+(6/45)*(18/44)]*2005

= -111.1111-395.5555+702.7626 =196.096

i.e. 25/45 times you lose 200 and fold the turn (first term).
20/45 times you invest 890 into the pot (second term).
8 of those 45 times you get 100% equity in the pot, 6/45 you get 39/44 equity and 6/45 you get 18/44 equity (the bracketed terms).
So calling and calling the turn push if you improve has an EV of +196.096 which is better than pushing the turn.

However, do you think you ever have this scenario? I mean this assumes that villain always pays you off when your draw gets there and that his range is limited to exclude sets, bigger flush draws, hands that fold the flop, etc. I don't think it needs much of the latter (i.e. fold equity) to make pushing better (especially if he sometimes folds when you call flop and hit your draw). Also, I think people like pushing big draws to balance with sets, etc.

[ig06]

[ QUOTE ]
option 1: all-in on the flop. according to twodimes.net i have .526 equity on the flop vs red aces. that's $1052 equity or +$52.

[/ QUOTE ]

I prefer to count your equity from the flop. In other words the money that went in pre-flop is the pot's. So the EV of folding the flop = 0. Thats why my my answer is different to yours (apart from you rounding the EV which doesn't really matter :-)). So, agreed in this example but don't you think pushing is still better in almost any real scenario?

[JKratzer]

[ QUOTE ]
but don't you think pushing is still better in almost any real scenario?

[/ QUOTE ]

yes

[ig06]

Ok,btw if some of my comments above sound like teaching a granny to suck eggs (I haven't play higher than 400NL and my game has more leaks than I care to mention) its unintended! I was genuinely curious if you ever a good enough read to come close to this scenario.

[JKratzer]

well in the example i gave my read would have to be really good, even a little bit of fold equity (from AK or maybe QQ sometimes) would make a push win. however, some other factors could swing it closer to a call. if we were deeper, if he bet less on the flop, stuff like that. all of that being said, if the decision is really close it doesn't matter which way i go and would choose whatever fits best with my style/metagame/etc. this was meant mainly as math exercise for myself and thought it might be somewhat interesting for others.