Some questions regarding pot-equity etc.

[Big kicker]

Here is something I don´t understand about pot-equity and other things. If somebody could explain it for me I would be very glad.

Let´s say we are on the flop with a nut flush draw in a limit hold´em game so we have about 35% or a 1 to 2 chance of making our flush and winning by the river. Our chance of winning by the turn is about 20% or 1 to 4. We are HU and the other player bets 1$ and the pot is now 3$ (I assume he is not bluffing) so the pot odds give us 25 % or 1 against 3. If we use the river-chance (RC) we should call and if we use the turn-chance (TC) we should fold. What is the correct play?

From my point of view the correct play is to use the TC and fold because the RC implies that we continue to the river and we don´t know what is going to happen on the turn.

For example: if the other player bets 2$ on the turn and we call to see the river (I assume that if we make our flush on the river the other player will check and fold to at bet from us) we will have invested 3$ (1$ to see the turn and 2$ to see the river) to win 5$ (the 3$ pot and the other players 2$ bet on the turn). This equals implied pot odds of 1 to 1,67 which makes the RC-call a wrong decision.

If the other player would call a bet on the river or if he would check the turn the RC would be correct – but unless we have a really good read on him we don´t know what is going to happen. And in a no limit game it gets even worse as he could go all-in on the turn.

So far it has been quite simple but all this give me another problem. Lets say we are in the BB (1$) and UTG raises to 2$, everybody folds to us. Here the litteratur recommends a call with almost any hand because we are getting 1 to 3 pot odds and most of the time we have at least 25 % of winning by the river. But isn´t this the same situation as before and therefore a wrong call? The 25% is only if we stay to the end of the hand and we don´t know what is going to happen on the flop , turn and river! Shouldn´t it be the chance that our hand is the best 25% of the times on the flop that we should base our decision on?
(I can understand using the 25% if we had to go all-in to call, because then we know for sure we will see the river).

Another problem is the pot-equity descripted in “Small stakes hold´em – winning big with expert play” on page 35-38. It says that if we have 35% pot-equity of making our hand by the river we can bet out if we think at least 2 opponents will call, but again we don´t really know if we are staying in the hand to the river. If the 2 (or more) opponents begins to raise and reraise on the turn maybe we would have fold.

I hope it make sense [img]/images/graemlins/smile.gif[/img]

[AaronBrown]

You have to figure these things backwards. Start with the river. If you hit your flush, you'll obviously bet. If you don't you'll fold (since you're sure he's not bluffing, and we'll ignore unlikely scenarios like you getting three of a kind).

On the turn, you'll obviously bet if you have your flush. If you don't, there will be $7 in the pot. You'll have to put in $2 to see the river card. 9 times out of 46 it will make your flush and (assuming he'll call) you'll win $9. 37 times out of 46 you'll lose your $2. 9x$9 = $81, 37x$2 = $74, so it's positive EV to call. Your EV is ($81 - $74)/46 = $0.15.

Now on the flop, you have to pay $1 to see the turn card. If it makes your flush, it wins you $8 ($4 in the pot now, plus $2 on each of the turn and river). If it doesn't make your flush, it gets you $0.15. (9/47)*$8 + (38/47)*$0.15 = $1.65 so it's worth $1 to call.

This analysis would change if he would fold or raise you if three matching suits appear on the board.

[AaronBrown]

You are correct about the last two analyses. However, with most hands it's worth $1 to see the flop with $3 already in the pot. You could hit two pair or three of a kind with anything, and maybe a chance at a straight or a flush. Another advantage is you know a lot about the raiser's hand (unless she's very loose or unpredictable, in which case you want to be in anyway because you might have the best hand), she knows almost nothing about yours (since you'll play anything). That's worth money.

A lot of this depends on your ability relative to the other player. If you can put her on two high cards, then you can bluff with any three low cards on the flop. You might be able to win a lot with two pair. On the other hand, if she is likely to outplay you, you might want to stay away from this hand, even with the favorable odds.

[Big kicker]

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You have to figure these things backwards.

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Thanks allot for the answers. I have not used the backwards-approach before.

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On the turn, you'll obviously bet if you have your flush. If you don't, there will be $7 in the pot.

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Isn´t it 6$ (4$ from the flop + 2$ bet from the other player)?

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This analysis would change if he would fold or raise you if three matching suits appear on the board.

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Yes. That is why I would, most of the time, only look one step ahead when calculating odds (from the startinghand to the flop, from the flop to turn etc.) when sitting at the table. Of course you can sometimes make rough estimates of what is going to happen but if there is more than one opponent or it is a no limit game it gets to complicated.

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Another advantage is you know a lot about the raiser's hand (unless she's very loose or unpredictable, in which case you want to be in anyway because you might have the best hand), she knows almost nothing about yours (since you'll play anything)

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Yeah I can see your point.

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You are correct about the last two analyses

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Ok. The problem is that I just have a hard time believing that Sklansky, Miller and Malmuth would be wrong about the "pot-equity".