sshe pg 159 interpretation please

[tinhat]

Hey all -

Probably a simple question - I just don't understand the statement.

The first paragraph of pg 159 in sshe says "Against two opponents you will win well over 1/3 of the time...". How is that calculated (and/or determined)? I understand it's in context of this specific hand example but don't know where the "1/3 against two opponents" comes from...

[Dead]

I'll explain it for you.

You have 9 flush outs(9 remaining clubs in the deck). You will make a flush approximately 35% of the time based on that fact. That's more than 1/3 already. But sometimes you will hit your flush and still lose to a boat, etc.

But you also have 6 overcard outs on top of it(3 aces, 3 nines) so you are likely to win this hand about 40% of the time. Your overcard outs won't be good all of the time, but they'll be good a lot of the time.

So against two opponents, you can expect to win this hand about 40% of the time. So we say that you have 40% pot equity. This means that every flop bet going in benefits you, since your FAIR SHARE of the pot is only 1/3, or 33%(since you have two opponents).

This can change on the turn however, with only one card left to come. Your equity can drop dramatically at this point.

This is why it is often beneficial to raise this flop from late position and take the free card, if offered, on the turn.

Hope this helps,
Dead

[tinhat]

[ QUOTE ]
I'll explain it for you.

You have 9 flush outs(9 remaining clubs in the deck). You will make a flush approximately 35% of the time based on that fact. That's more than 1/3 already. But sometimes you will hit your flush and still lose to a boat, etc.

[/ QUOTE ]

Check.

[ QUOTE ]
But you also have 6 overcard outs on top of it(3 aces, 3 nines) so you are likely to win this hand about 40% of the time. Your overcard outs won't be good all of the time, but they'll be good a lot of the time.


[/ QUOTE ]

Ok, here I'm not getting my mind around something - where does the "40%" come from? Is that 40% just because of the overcards? Or is it another 5% added to the 35% flush part?

And secondly, for either answer, how does one translate overcards into % win? I understand X% to make a hand but I don't understand going from that to % win. Is it something like "40% chance to make my hand which I expect as the best hand will win <= 100% of the time."? If so, how do you make a more precise estimate of the number of times you'd win?

[ QUOTE ]
So against two opponents, you can expect to win this hand about 40% of the time. So we say that you have 40% pot equity. This means that every flop bet going in benefits you, since your FAIR SHARE of the pot is only 1/3, or 33%(since you have two opponents).


[/ QUOTE ]

My main confusion about Ed's passage is the statement "against two..." - what changes if it's against, for example, 3 or 4 opponents? I'm assuming the % win is based on # of opponents - if that's correct, why is that so and how is it quantified?

Anyone?

[Aaron W.]

[ QUOTE ]
My main confusion about Ed's passage is the statement "against two..." - what changes if it's against, for example, 3 or 4 opponents? I'm assuming the % win is based on # of opponents - if that's correct, why is that so and how is it quantified?

[/ QUOTE ]

If you have many opponents, you have a higher chance of being outdrawn after you make your hand (or your outs are more likely to be tainted). This isn't quantified in any strict mathematical way (it's too complicated to be of value), so it's just an estimate. Against two opponents, you expect your hand to hold almost all of the time. Against 3 or 4, it's slightly less, depending on the board texture and the action. If I gave a blanket response of "your hand will hold 80% of the time", it would be 'close enough' for any generic estimate for a generic hand. You can decrease it if you feel that the board is draw-heavy and you're not drawing to the nuts, or increase it if you have a drawless board and drawing to a strong hand.

[TimsterToo]

I really didn't get pot equity in the beginning and still have trouble with it so please indulge me and tell me if this assumtion is right or wrong:

You have a hand.

heads up you'll win 45% of the time
against 2 you'll win 40% of the time

so pot equity wise it's smart to fold that hand heads up as you have to put in 50% of the pot to win but you should raise the same hand against two as you only have to pay 33,33% to win 40%?

I understand that there's more involved but just understanding the principal in it's simplest form would put me on track.

How do I know which percentage which hands will win against any number of opponents? /images/graemlins/confused.gif

[GrunchCan]

Here's a quick & dirty - but very close to correct - way of calculating equity with only a draw.

First - and this is the most important part - you must accurately compute the value of your hand in outs. This means you have to count up all the cards that improve your hand, and then discount those outs to account for all the times you spike your draw and still lose. For example, just becasue you have 2 overcards to the board (ie AKo to a flop of Q72) doesn't mean your hand is worth 6 outs. Typically we say that 1 overcard is worth (dy default) 1.5 outs. So if you have 2 overcards, its worth closer to 3 outs, not 6.

Now, once you have computed the value of your hand in discounted outs, multiply that number by 4 if you are on the flop, or 2 if you are on the turn. The resulting number is your pot equity in percent. For instance, in the AK example where our hand is worth 3 outs, on the flop we have about 12% equity in the pot.

Anybody can do this calculation sitting at the table. In fact, you must be able to do this in order to be a successful player.

There is error built in to this calculation. You must realize this. But the error is actually very small. You can use Poker Tracker, 2 dimes or some other hot-cold simulation software to verify this. If your decision is so close that this error matters, you should be taking other factors in to account anyway.

[TimsterToo]

Thanks GrunchCan I love easy ways to calculate things.

This will certainly be very valuable advice once I get my head around this pot equity vs pot odds thing. (can't be that hard can it? just don't seem to get it!! /images/graemlins/confused.gif /images/graemlins/confused.gif)

So that would mean that pot equity is not changed by the number of players in a hand? Which would make my assumptions wrong.

In your example would it mean that with using your calculation you should only place a bet if your sure that the total of bets will end up around 15BB disregarding the number of people left in the pot? How does that make it different from calculating pot odds? (although 3 outs would give me 7 to 1 pot odds on the flop so I can bet earlier, so should I or shouldn't I)

I'm going to reread that stuff again, thought I had it and I çompletely lost the plot now, I'm on theoretical poker tilt. /images/graemlins/crazy.gif The more I type and think about it the more I'm going astray. I'll probably reread this post in a couple of weeks and bow my head in shame for being so ignorant. There is this very simple "click" that my brain is blatantly refusing to make.

HELP!

[MrWookie47]

I really like that back-of-the-envelope equity estimation. I'll be using that a lot.

The reason why Grunch's estimate doesn't factor in the number of opponents is that he is assuming that if you hit your draw, you will win.

To better illustrate what happens as the number of opponents increases, it may be more enlightening to calculate your equity if you currently have the best hand. If you have the best hand, then your pot equity is a function of the total number of outs all of your opponents have against you (naturally, not counting the same card twice). You can use Grunch's estimation system again, but this time, your equity is equal to 1-4*(opponents' flop outs) or 1-2*(opponents' turn outs). As you would expect, the more opponents you have, the more outs they can have against you, so your equity decreases.

It's important to keep in mind, however, that even if your equity percentage is smaller, it is still possible to have a larger edge, i.e., your equity is greater than one divided by the number of people in the pot. For example, if you have 45s and flop a flush draw, your equity is about 35%. Heads up, this is far from great compared to 50% (1/(2 players)). If there are 10 people in the pot, however, even if you're marginally more likely to be up against a higher flush draw or lose to a full house, you will have a tremendous equity edge relative to 1/(10 players) = 10%.

[GrunchCan]

[ QUOTE ]
he is assuming that if you hit your draw, you will win.

[/ QUOTE ]

No, that's what discounting the outs is about. It's really important that you discount your outs correctly before computing equity. In fact, I'd say it's one of the most important skills in LHE.

If you have 2 overcards and discount them to 3 outs total, you are assuming that if you hit one of your overcards, you'll win the pot 50% of the time. Do you see why?

[GrunchCan]

[ QUOTE ]
So that would mean that pot equity is not changed by the number of players in a hand?

[/ QUOTE ]

Sorta kinda. First of all, your pot equity edge is what tells you weather you can bet & raise for value - not your pot equity. First count the number of opponents to see what everyone's "fair share" is. If you have 2 opponents, everybosy's fair share is 33% equity. Then compare the fair share to your actual equity. If you have 40% equity, then you hae about 7% more equity than is your fair share. You have a pot equity edge of 7%.

When you have an equity edge, you can bet or raise for value. If you don't have an equity edge, you might be able to call (pot odds tell you this), but you can't raise for value.

[MrWookie47]

Once I posted that, I just about went back added a disclaimer about how discounting outs accounts for the times you hit and don't win, but then I got lazy and distracted. I understand you perfectly, but I didn't phrase myself very well.

[crownjules]

So let me run a quick demo, sort of to try and work this through. I for one have yet to fully grasp the concepts of pot equity and equity edge and how they inter-relate with pot odds.

Lets say you're in CO with AKs. 3 limpers, you raise, both blinds and all limpers call. 6 players for 12 SBs. Flop comes 48J, two of your suit. Your fair share equity is about 17%. Counting outs we get 13.5 (9 for the NFD, 1.5 for the back door broadway, 3 for overs). 13.5 x 4 = 54% pot equity, meaning our equity edge is 37% (or friggin' HUGE). Obviously, we're betting or raising when the action comes to us.

Lets say that two of the limpers have bet/called when the action comes to you, you raise. Two fold, the rest call. 4 players and a pot of 14 BBs. Turn is another J not of your suit. Now we have no straight draw and we have to consider that spiking an A or K will not win this pot. We'll discount our overs to 1 out each, and the NFD still at 9 for a total of 11 outs. Fair share equity is 25%. 11 x 2 = 22%, so we have lost quite a bit of our equity in this pot and no longer have an edge. We would check if given the opportunity and pot odds (45/11 = 4:1 odds) would allow us to call even a 3-bet cold if it came to that.

How'd I do?

[GrunchCan]

[ QUOTE ]
So let me run a quick demo, sort of to try and work this through. I for one have yet to fully grasp the concepts of pot equity and equity edge and how they inter-relate with pot odds.

Lets say you're in CO with AKs. 3 limpers, you raise, both blinds and all limpers call. 6 players for 12 SBs. Flop comes 48J, two of your suit. Your fair share equity is about 17%. Counting outs we get 13.5 (9 for the NFD, 1.5 for the back door broadway, 3 for overs). 13.5 x 4 = 54% pot equity, meaning our equity edge is 37% (or friggin' HUGE). Obviously, we're betting or raising when the action comes to us.

Lets say that two of the limpers have bet/called when the action comes to you, you raise. Two fold, the rest call. 4 players and a pot of 14 BBs. Turn is another J not of your suit. Now we have no straight draw and we have to consider that spiking an A or K will not win this pot. We'll discount our overs to 1 out each, and the NFD still at 9 for a total of 11 outs. Fair share equity is 25%. 11 x 2 = 22%, so we have lost quite a bit of our equity in this pot and no longer have an edge. We would check if given the opportunity and pot odds (45/11 = 4:1 odds) would allow us to call even a 3-bet cold if it came to that.

How'd I do?

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Gold star.

The only thing that is questionable is the flop raise of the EP bettor. This is a very complex scenario. If everybody folded for the 2 except your early opponent whe put the first bet in, your raise wasn't for value anymore becasue you didn't have an equity edge when the smoke cleared. Do you see this?

I'm not saying the raise was wrong. I'm saying the scenario wasn't cut-and-dried. See Entity's playalong post for a similar example. It comes down to deciding if you raise, how many opponenets will come along.

Overall though, great job.

[jba]

[ QUOTE ]
[ QUOTE ]
So that would mean that pot equity is not changed by the number of players in a hand?

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Sorta kinda.

[/ QUOTE ]

I believe the cleanliness of your outs is affected by the number of players in a hand. If you have AK on a Q72 board, there is a better chance that you'll win with top pair A or K against 1 player than 7. Against 1 you might have 4-5 clean outs whereas against 7 maybe 2-3 (i'm sorta making these numbers up, assuming you have 66-75% vs 33-50% chance of top pair holding up in these cases). The fact that you have less outs affects your pot equity.

is this accurate thinking? I think this formula is the science part, determining the cleanliness of your outs seems like an art (it probably really is mostly a science, but with so many factors it sure seems like an art to a novice).

[joeski19]

I have a questions about discounting outs.

[ QUOTE ]
Counting outs we get 13.5 (9 for the NFD, 1.5 for the back door broadway, 3 for overs).

[/ QUOTE ]

3 outs for the A 3 for the K = 6 discounted to 3 outs for overs right?

If that's true then why when discounting the BDSD you have 4 Q and 4 T, but only give 1.5 ? Wouldn't you at least give it 4 out's?

[MrWookie47]

On a back door draw, you have to hit a Q and then a T, or a T and then a Q. The chance of this happening is (8/47)*(4/46) = 1.5%. This is about the same as chasing a 0.5 out draw, not a 1.5 out draw.

[Wetdog]

Great job, Grunch & crownjules. This one gets toggled to my favorites.

[TimsterToo]

[ QUOTE ]
So let me run a quick demo, sort of to try and work this through. I for one have yet to fully grasp the concepts of pot equity and equity edge and how they inter-relate with pot odds.

Lets say you're in CO with AKs. 3 limpers, you raise, both blinds and all limpers call. 6 players for 12 SBs. Flop comes 48J, two of your suit. Your fair share equity is about 17%. Counting outs we get 13.5 (9 for the NFD, 1.5 for the back door broadway, 3 for overs). 13.5 x 4 = 54% pot equity, meaning our equity edge is 37% (or friggin' HUGE). Obviously, we're betting or raising when the action comes to us.

Lets say that two of the limpers have bet/called when the action comes to you, you raise. Two fold, the rest call. 4 players and a pot of 14 BBs. Turn is another J not of your suit. Now we have no straight draw and we have to consider that spiking an A or K will not win this pot. We'll discount our overs to 1 out each, and the NFD still at 9 for a total of 11 outs. Fair share equity is 25%. 11 x 2 = 22%, so we have lost quite a bit of our equity in this pot and no longer have an edge. We would check if given the opportunity and pot odds (45/11 = 4:1 odds) would allow us to call even a 3-bet cold if it came to that.

How'd I do?

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"CLICK"

Now I've got it!

Thank you all so much for baring with me and dumbing it down a bit /images/graemlins/grin.gif

I've got something to practice with tonight!

[joeski19]

[ QUOTE ]
On a back door draw, you have to hit a Q and then a T, or a T and then a Q. The chance of this happening is (8/47)*(4/46) = 1.5%. This is about the same as chasing a 0.5 out draw, not a 1.5 out draw.

[/ QUOTE ]

Ok that makes sense. Thanks

[MD2020]

[ QUOTE ]
So let me run a quick demo, sort of to try and work this through. I for one have yet to fully grasp the concepts of pot equity and equity edge and how they inter-relate with pot odds.

Lets say you're in CO with AKs. 3 limpers, you raise, both blinds and all limpers call. 6 players for 12 SBs. Flop comes 48J, two of your suit. Your fair share equity is about 17%. Counting outs we get 13.5 (9 for the NFD, 1.5 for the back door broadway, 3 for overs). 13.5 x 4 = 54% pot equity, meaning our equity edge is 37% (or friggin' HUGE). Obviously, we're betting or raising when the action comes to us.

Lets say that two of the limpers have bet/called when the action comes to you, you raise. Two fold, the rest call. 4 players and a pot of 14 BBs. Turn is another J not of your suit. Now we have no straight draw and we have to consider that spiking an A or K will not win this pot. We'll discount our overs to 1 out each, and the NFD still at 9 for a total of 11 outs. Fair share equity is 25%. 11 x 2 = 22%, so we have lost quite a bit of our equity in this pot and no longer have an edge. We would check if given the opportunity and pot odds (45/11 = 4:1 odds) would allow us to call even a 3-bet cold if it came to that.

How'd I do?

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Thank you for this; it's quite helpful for visualizing the equity.

One thing though: Don't we lose one one our NFD outs when the board pairs on the turn? Or at the very least, it become undervauled?

[crownjules]

[ QUOTE ]
The only thing that is questionable is the flop raise of the EP bettor. This is a very complex scenario. If everybody folded for the 2 except your early opponent whe put the first bet in, your raise wasn't for value anymore becasue you didn't have an equity edge when the smoke cleared. Do you see this?

[/ QUOTE ]

I do. Had you called, you may have kept one or two more in the pot and thereby kept your equity edge on the turn. But this begs the question is preserving equity edge with strong drawing hands more important then building a pot with said hand?

[GrunchCan]

[ QUOTE ]
But this begs the question is preserving equity edge with strong drawing hands more important then building a pot with said hand?

[/ QUOTE ]

Good question. Let's play 50,000 hands and find out. /images/graemlins/smirk.gif

[crumpentunt]

Thats what I was thinking as well, I'd probably take 1 to 1.5 outs of considering the board paring when we have a FD.

[deception5]

[ QUOTE ]
Now, once you have computed the value of your hand in discounted outs, multiply that number by 4 if you are on the flop, or 2 if you are on the turn. The resulting number is your pot equity in percent. For instance, in the AK example where our hand is worth 3 outs, on the flop we have about 12% equity in the pot.

[/ QUOTE ]

I always thought is was *2+2 to determine your outs for the next card, no?

[GrunchCan]

[ QUOTE ]
[ QUOTE ]
Now, once you have computed the value of your hand in discounted outs, multiply that number by 4 if you are on the flop, or 2 if you are on the turn. The resulting number is your pot equity in percent. For instance, in the AK example where our hand is worth 3 outs, on the flop we have about 12% equity in the pot.

[/ QUOTE ]

I always thought is was *2+2 to determine your outs for the next card, no?

[/ QUOTE ]

Do you mean to determine the odds that you'll draw one of your outs? For instance, if you have 8 outs, then there is a (8*2)+2 = 18% chance that you'll hit one of them on the very next card.

If this is what you mean, then yes this is basically correct. But this isnt how you compute equity - at least, not if there's still more than 1 card to come.

Plus there's error in this computation too, and if a difference of 2% is enough to change a decision, then the decision is close enough that it probably doesn't matter much what you do.