On Equity

[Absolution]

Something that has me confused about equity is that it's often used in isolation, on a single round of early betting, without regard for later streets where it gets more expensive and you may be folded out. How can you say that you're 'making money' with each round of betting that goes in (when you have an equity edge) without thinking about your action on later streets and if you will even still be around to collect?

[eviljeff]

I think of equity as the % time you will win the pot. so say you know your two opponents hole cards after the turn and you will win the pot 34% of the time. it is correct (according strictly to EV) to put an unlimited number of matched bets in the pot now even though it will be correct to fold 66% of the time on the river for a single bet.

[kiddj]

Limit play example: 4 players to the flop, no PF raise (4SB), you are on the button with A /images/graemlins/heart.gif4 /images/graemlins/heart.gif
Flop = 2 /images/graemlins/heart.gif9 /images/graemlins/heart.gifJ /images/graemlins/spade.gif
1st to act bets, 2 calls, action is on you
the probability of you making your flush by the river is ~35%
you are putting 25% of the money in the pot: you raise for value (equity tells you when you can bet/raise for value)
All call (12SB)
Turn is 6 /images/graemlins/club.gif
1st to act bets, 2 calls, action is on you (9BB)
the probability of you making your flush by the river is ~20%
you are putting 25% of the money in the pot: you call based on pot odds

Now, let's say there were 6 people still in on the turn.
the probability of you making your flush by the river is still ~20%
you are putting 17% of the money in the pot: you can raise for value here as well

The general idea is that you should win by hitting your draw a certain portion of the time and that % is greater than the portion of the pot you are contributing (it is also the consensus that the times you hit your draw and lose will be approximately offset by the times you win without hitting)

Did this come close to answering your question?

[Absolution]

I understand all that and that's a good example of how most use it. I'm just wondering, what about an example where the pot was small and a certain percentage of the time the betting on the turn no longer made it profitable for you to call to see the river. So, you raised on the flop saying you're making x% of all flop bets, but you failed to consider that you might not be around for the river to collect every time. Maybe this example just doesn't come up much.

I'm probably making it more complicated than it needs to be. I'm going to sit down tonight and work through some scenarios.

[The Nutz85]

well done i was thinking that it was like this but not sure great example thanks

[AaronBrown]

I agree with you in principle. Still, it's a good poker principle that the best hand early generally wins money. If you calculate your expectation assuming everyone checks the rest of the hand to showdown, that's a handy number to know.

If you have a made hand, this number better be positive, or you should fold. Even if it is positive, you have to think whether you would call a big bet on later rounds, which basically comes down to whether there are straight or flush possibilities and how often your opponents bluff. If you would call, you have to subtract the expected loss from your opponent drawing his hand and making a big bet. If you would fold, you have to subtract the expected loss from folding.

If you have a drawing hand, you can stay in with a negative value if you think you can make it up when you make your hand. This gives you some idea of how much extra you have to entice into the pot when you make your hand.

[SumZero]

[ QUOTE ]
I understand all that and that's a good example of how most use it. I'm just wondering, what about an example where the pot was small and a certain percentage of the time the betting on the turn no longer made it profitable for you to call to see the river. So, you raised on the flop saying you're making x% of all flop bets, but you failed to consider that you might not be around for the river to collect every time. Maybe this example just doesn't come up much.

[/ QUOTE ]

Yes, you need to consider that. Let's say the game is actually no-limit hold'em and let's say that we are facing the same post flop decision as was described above (where there was a min raise and 2 calls and action is on us with the nut 4-flush draw). Let's further say that we know due to tells, patterns, etc. that the raiser is going to move all-in (for many times the pot) on the turn on any non-heart and is going to check/fold any heart (it would be a weird player read, but go with it). Now the question becomes how often will we make our flush on the turn not by the river. Now it is worth a call (pot-odds are 7:1 and we're about 4:1) but not a raise on the flop.

[Dan Mezick]

[ QUOTE ]
Turn is 6
1st to act bets, 2 calls, action is on you (9BB)
the probability of you making your flush by the river is ~20%
you are putting 25% of the money in the pot: you call based on pot odds

[/ QUOTE ]

The pot is offering 3:1 on your bet ("you are putting 25% of the money") if you hit the flush it will win because it's the nut flush draw...but the odds of hitting your flush are 20% as stated (4:1 against) ..... how is this a good bet based on only these facts?

I realize the implied odds may help somewhat but that applies more to NL where you can make a big bet and get called big by a single player.

Could you clarify your analysis about the +EV for the bet for this specific turn-bet example? Thanks in advance.

[Absolution]

No, he's saying that he does NOT have an equity edge any more on the turn so he just calls instead of raising since he still has implied odds. You shouldn't raise the turn.

Anyway, that was kind of my point. You have to be careful when you think about one street by itself and it has always bugged me when people just talk equity, mostly on the flop. I think it can be an oversimplification and I think it's best to work through some examples of common situations (some where the betting on the turn might get out of hand for example, even in limit). From this discussion, it seems that most of the time it's safe to use it as a simplification, but I also think it's good to know the special cases where it may not work out (esp. if the edge is small).

[TaintedRogue]

[ QUOTE ]
I understand all that and that's a good example of how most use it. I'm just wondering, what about an example where the pot was small and a certain percentage of the time the betting on the turn no longer made it profitable for you to call to see the river. So, you raised on the flop saying you're making x% of all flop bets, but you failed to consider that you might not be around for the river to collect every time. Maybe this example just doesn't come up much.

I'm probably making it more complicated than it needs to be. I'm going to sit down tonight and work through some scenarios.

[/ QUOTE ]

No, you're not making it more complicated and that is exactly why I don't go by "pot equity" but rather odds of making my hand, which I believe will bet best, versus pot odds for calling with a draw on the flop and then the turn.

If you look at 65s "equity" versus AKs "equity" on twodimes.net versus 4 other players, when 65 and AK are suited in two different suits, you will find 65 has close to same equity as AK and in some instances, based upon what the other 4 players have, more equity. However, 65 is going to have to retire after the flop quite often, only to find runner runner in his suit, or 66, 55 or 65.

[TaintedRogue]

[ QUOTE ]

If you have a made hand, this number better be positive, or you should fold. Even if it is positive, you have to think whether you would call a big bet on later rounds, which basically comes down to whether there are straight or flush possibilities and how often your opponents bluff. If you would call, you have to subtract the expected loss from your opponent drawing his hand and making a big bet. If you would fold, you have to subtract the expected loss from folding.

If you have a drawing hand, you can stay in with a negative value if you think you can make it up when you make your hand. This gives you some idea of how much extra you have to entice into the pot when you make your hand.

[/ QUOTE ]

Two very excellent points.