A question about equity
 

I have been thinking lately about the situation in which I open-raise preflop, flop a quality draw and get led into on the flop heads up. I typically autoraise the flop in this spot, but I never really know what to do when checked to on the turn at which time the pot contains 4.25 big bets.

<font color="blue"> Before I go on, do you guys usually bet or check behind here if your draw has showdown value?

What if your draw has no showdown value?</font>

Lets assume that I have a J high four-flush and get checked to on the turn after my autoraise on the flop. Lets also assume for simplicity sake that the board is big and I value my pair outs at zero so I will fold on the river unless I make the flush. So I have 9 outs (only the flush cards).

Check my methodology here:

I have 9/46 or about 20% equity. My opponent has 37/46 or about 80% equity (assuming that he will autobet any river and I will fold if I don't make my flush). Now when deciding whether to bet the turn, I must evaluate the 3 possible results of my turn bet.

1) He folds and I win 4.25 big bets.

2) He calls and I lose .6 big bets <font color="blue"> which is the difference in our respective equities multiplied by the amount that I put in on the turn. (80%-20%)*(1BB) = .6 BB LOSS. </font>

3) He checkraises and I lose 1.2 big bets. (80%-20%)*(2BB) = 1.2 BB LOSS.


So now I just estimate the percentage of time I think he will take each of actions 1), 2) and 3) and multiply them by the resulting gain or loss of each and add the terms up to find the EV of a turn bet.


EV OF A TURN BET =
(% HE FOLDS)*(4.25) + (% HE CALLS)*(-.6) + (% HE CRs)*(-1.2)


<font color="blue">Is this methodology correct?</font>


Thanks,
Cartman

Re: A question about equity
 

methodology looked correct. When my draw has showdown value, I am almost always calling a river bet if I check behind on the turn, as villain will bet often enough when behind (clearly strong reads change this).

If you are deciding between checking behind the turn and calling the river, or betting the turn and checking behind the river UI, it is always better to bet the turn. without improving your hand, you are more likely to be ahead on the turn than the river. By betting the turn, and encouraging your opponent to check to you on the river, you put your 1 bet in with the highest equity, and have the opportunity to bet the river again if you improve.

Reads change this, clearly don't bet against someone who will only bet or call a bet with a reasonable made hand. Some lags might be capable of folding the turn, but pounce on the weakness shown after your turn check with a river bluff.

Re: A question about equity
 

I usually bet the turn and check behind unimproved on the river when my draw has showdown value. My real dilemma is when I don't have showdown value and folding equity is dominant factor. What do you do in this situation?

Thanks,
Cartman

Re: A question about equity
 

All you can do is make the best estimate you can. There are no standard rules. You have to evaluate the chances your opponent will fold based on whatever information you have. This isn't to say these decisions aren't important, just that poker tracker won't help you maintain a stellar recodr in these situations. estimating folding euities, showdown value, and choosing a correct line HU is one of the most difficult parts of the game for me, and, I would suspect, many players.

Re: A question about equity
 

Am I correct that the "cost" of betting the turn when he doesn't fold is the difference in our respective equities multiplied by the amount that I put in on the turn?

In this case (80%-20%)*(1BB) = .6 BB LOSS when he calls and (80%-20%)*(2BB) = 1.2 BB LOSS when he checkraises and I call.

Thanks,
Cartman

Re: A question about equity
 

[ QUOTE ]
Is this methodology correct?

[/ QUOTE ]

no, you want to evaluate your ev including the river action.

ev(turn bet) =

(%folds)*4.25 + (%calls)*.8*-1 + (%calls)*.2*(6.25) + (%raises)*.8*-2 + (%raises)*.2*(8.25) =

= 4.25*f + (-.8 + 1.25)*c + (-1.6 + 1.65)*r

= 4.25f + .45c + .05r

you should check over this, im half asleep.

Re: A question about equity
 

[ QUOTE ]
In this case (80%-20%)*(1BB) = .6 BB LOSS when he calls and (80%-20%)*(2BB) = 1.2 BB LOSS when he checkraises and I call.

[/ QUOTE ]

youre correct, that is your equity on the turn bets in those situations.

Re: A question about equity
 

I think the avarage opponent calls the turn bet too often to make this a profitable play. LAGs and, in a lesser degree, TAGs often c/r and the typical passive player calls down. But let's say u bet the turn. What % of the time do u follow up with a riverbet (with ur low SD value hands in particular)? Do u look at ur opponents folded to riverbet %?

Re: A question about equity
 

Hey Cartman,

In your J-hi example, I think it is a clear check-behind on the turn.

Given that the board is big, and we figure to be behind a made hand, our flop raise started out for fold equity but now is for a free card. We have 0 showdown value, and it is nearly impossible for our opponent to have a better hand that will fold to the turn bet - he will either have some sort of draw (cards bigger than ours - straight or flush, though rarely a smaller flush) or a made hand, given that he called the flop. To gain sufficient fold equity vs the draws we would have to bet the turn and river, and the pot is far too small to risk 2BB in a multi-street bluff like this.

So, we check the turn. Villain will bet into us on the river with made hands, allowing us to raise. Draws may bluff at the river, but fold to the raise. [when we hit]
When we miss we just fold. Mission accomplished. We got our money in when our equity was high, gave ourselves a chance to put in multiple bets when improving, and almost always folded the worst hand.



**Now, the question becomes harder when we give ourselves an A-hi FD, and we make the board less scary (say 1 broadway card). Our aces may now be outs, and possibly our kicker card too, depending on how raggy the last 2 board cards are. We would expect an aggressive opponent to 3bet the flop with top pair often, so we can diminish(but certainly not eliminate) that possibility.

Since the board is raggier it is now more likely that we have a hand that is currently best. If our opponent is prone to bluffing, checking behind the turn is nice because an unpaired hand has at best 4-5 outs(heart pairs don't win it for him) so he only needs to bluff relatively infrequently to make up for the small share of equity we forfeit letting him draw for free. If we are only ahead a small %-age of the time we would prefer to not call the river bet, but that is player dependant.

So, in this picture 2 factors are most important: 1) how often we have the best hand 2) how often our opponent will bluff a worse hand if we check behind. Important conisderations: who raised preflop? If he did, are we likely outkicked if he is calling down with A-hi? If he didn't, will he call down with A- or K-hi?

In this HU-situation at the 10/20 IMO we will have the best hand here a decent amount of the time. So, if the player is known to bluff/bet too much I will check behind and call a river bet because he would have folded worse hands had I bet the turn. Additionally we dodge turn c/r's that would prevent us from calling the river and possibly folding the best hand.

If the player is more passive(calling station/fish etc) then I will bet the turn and take the free showdown since he will call with K8 trying to pair up. When we are c/r'd here we are almost certainly beat and can fold the river UI confidently.

That ended up being real long - I hope it made sense. I'll clarify if necessary.

Surf

Re: A question about equity
 

Nice post, Surf. I detoured the original intent of my question by making the board big for the purpose of removing my pair outs. I agree this looks like a clear check when the flop is big cards. I think it is more interesting when the flop is low. I tend to take the free card unless a big card hits the turn in which case I bet the turn trying to represent a paired overcard.

Against aggressive opponents I used to almost always take the free card and then usually call a river bet when my busted draw had showdown value. But in a response to one of my posts, Nikla made the following comment:

"Free cards heads up...yuck! I hope you didn't take them;)"

and it really messed with me. Maybe he didn't mean it as a blanket statement, but it made me think that maybe I should routinely be firing again with my draws. What do you guys think?

Cartman

Re: A question about equity
 

[ QUOTE ]
That ended up being real long - I hope it made sense.

[/ QUOTE ]

that ended up being an awesome post, thank you.

Re: A question about equity
 

[ QUOTE ]
If you are deciding between checking behind the turn and calling the river, or betting the turn and checking behind the river UI, it is always better to bet the turn. without improving your hand, you are more likely to be ahead on the turn than the river. By betting the turn, and encouraging your opponent to check to you on the river, you put your 1 bet in with the highest equity, and have the opportunity to bet the river again if you improve.


[/ QUOTE ]

Grreat post! I havn't thought about that. A post of gold.

Re: A question about equity
 

Hey Cartman,

Regarding Nikla's post:

If I understand the general idea, it is that even if we have a hand such as K9-hi which isn't inspiring in of itself, it is actually a hand with a significant amount of showdown value heads-up. This assumes our opponent will peel loosely and often has a hand worse than ours. In a multiway pot gone headsup this does not apply. Additionally, many opponents who are loose preflop will only call the flop with some draw or pair or big Ace.

Giving a free card in position is bad when we are often ahead because:
-We don't give our opponent the chance to make a mistake by calling incorrectly
-We forfeit our hand's showdown value since only the best of our unpaired hands can call a river bet
-We make ourselves easier to play against - players are more likely to peel lightly on the flop if they can expect a free card with any regularity

However, other factors sway a bet to a check, as mentioned above:
-How likely our opponent is likely to bluff-raise a worse hand on the turn
-If our opponent would fold correctly on the turn but bluff incorrectly on the river
-How likely we are to have the best hand

Accurately judging how often our A-or K-hi hand is best is a difficult endeavor to say the least, but the most important. When we are often behind it is clearly wrong to bet, since we will not fold worse hands. Reading the board texture, knowing our opponent(whether by stats, category LAG/TAG etc or hopefully by reads) and recognizing the flow of the game (have we been consistently showing down winners?) all factor into this difficult analysis.

Surf

Re: A question about equity
 

i recall exactly which post Nikla made this comment and i too was under the impression that heads up Nikla would fire again on the turn with very very few exceptions. also in your post you said you are more inclined to fire again on the turn if a "big card" hits. can you define specifically what your "big cards" are. i realize A is in that catagory and i assume K as well, but what about Q?

Re: A question about equity
 

I think it is a decent assumption that the typical opponent will never ever fold a pair heads up. So the point of betting when a "big card" hits in my opinion is not because he will think "Uh oh, I had better fold my small pair because an Ace just hit and it is likely that the preflop raiser now has a pair of Aces". I think the reason it is good to bet the big card is because often he called the flop bet with one or more overcards which are no longer overcards because of the turn card.

So I guess it is not so much the sheer size of the turn card as it is the distance between the top card on the flop and the turn card.

Cartman

Re: A question about equity
 

Some passives won't bet the river with a pair (and it's likely they're ahead) when u didn't bet the turn. In this case u save a bet with ur A and K-high hands when u miss, don't u? Do u think this aspect outweights the fold equity u create by betting the turn? I think it does