# Equity and rule of 4 and 2

• Gold
Joined: 21.12.2012
Hi quick question.

I understand the rule of 4 and 2 quickly gives us the equity of our hand post-flop. What I don't understand is how it's getting screwed so much in equilab / poker ranger.

For example

Hand : A T

Flop : K 9 7

Villian's Range = Random(all cards)

Somehow we get a equity of 69%!! How is this possible? I thought it would be the following

3aces = 3 outs
3 tens = 3 outs
backdoor straight draw = 1 out

At max 16 outs, That's only 32% for turn and 64% for river.

Secondly if say 4 is the turn card

We still have 56% equity! now we should have 32%? We only have 1 more card to draw. Is it all implied odds? How can we include implied odds in our quick calculations? Is it all from memory?

Thanks for any help in advance!
• 13 replies
• Bronze
Joined: 01.06.2010
Hey zerker

The 4 and 2 rule is just a guideline. For the first point you made the 69% is pretty close considering that it calculates your equity from flop to river so in this case we use the *4 calculation in this one.

As said that 4 and 2 rule is just a guideline. This is an excellent example of how it might not always be accurate

Is it all implied odds?
any chance you could rephrase this question?

The implied odds don't come from memory. We use our estimate of our opponents range when considering how much implied odds we are getting.

In this example let's say we expect our opponent to have a lot of Kx hands and we hit our A we can still expect him to put a somewhat decent amount of money into the pot, that money increases our implied odds.

Hope I communicated that idea well. If not feel free to ask more questions
• Gold
Joined: 21.12.2012
Thanks legend you answered my question for the most part. I understand that equity could be around 69% from flop to river, but how can it stay around 56% on the turn? I dont understand the jump from 32%->56% on Turn -> river, Also i believe the 69% is the equity from flop -> turn in this case, but i may be wrong.
• Bronze
Joined: 27.12.2011
I think you are forgetting to take into account hands your opponent has that you already beat (Qx or Jx for example). The rule of 4 and 2 is used to calculate the chances of hit one of your outs not your equity.
• Gold
Joined: 21.12.2012
Originally posted by tdust89
I think you are forgetting to take into account hands your opponent has that you already beat (Qx or Jx for example). The rule of 4 and 2 is used to calculate the chances of hit one of your outs not your equity.
Oh wow didn't think of it that way, I guess having Tx Qx gives me a high card. It's so rare that I win with a high card I forgot that it adds equity lol.

Still a 32% -> 56% jump in equity because of a Qx seems kinda high? Just for having a high card Q?
• Bronze
Joined: 27.12.2011
Originally posted by sc2zerker

Still a 32% -> 56% jump in equity because of a Qx seems kinda high? Just for having a high card Q?

Your equity went from 69% on the flop to 56% on the turn, it didn't go up. And it isn't just queen high he could have, he could be playing any two cards.

There are a total of 1326 possible preflop hand combinatons. If he has K,9,7,4, any pocket pair, AQ, or AJ he is beating you so lets figure out how many combinations of those hands there are:

pocket pairs: 60 (taking into account the fact that there are only 3 A,K,T,9,7 and 4s left)
two pair(K9, 74 etc): 108
one pair(Kx 9X etc): 408

in total there are 576 hand that you are behind on the turn. That means that with Ace high you are ahead against 56.6% of all hands you opponent could be holding.

EDIT: If someone could check my math that would be great
• Gold
Joined: 21.12.2012
Oh ok, that makes a lot of sense thank you!

It's an interesting way of thinking, Which maybe makes me believe i'm approaching the game completely wrong. I'm thinking on post-flop, Does he have a top pair, does he have mid pair, does he have a flush draw? Maybe I should be thinking "how far ahead am i? Is it worth betting?"
• Bronze
Joined: 27.12.2011
You also have to take into account that your opponent like isn't playing with any two cards. He's very unlikely to playing cards such as 6-2 off suit.

As an example suppose your opponent is only playing broadway cards and pocket pairs. If you plug that range into equilab you'll find that you only have 41% equity on the turn.
• Gold
Joined: 21.12.2012
Yes, Im currently doing some equity training in poker ranger(it's like equilab on steriods). I set my range to the SHC and my opponent range to the SHC and a wide range including around 15% more hands.(it has 2 range values for villian while training)
• Bronze
Joined: 01.06.2010
• Gold
Joined: 21.12.2012

It is profitable when equity % > calling % ?

Correct?
• Bronze
Joined: 17.01.2011
well, yes and no. that is pretty much only relevant when going allin or on the river, when you can call and are guaranteed to see a showdown for no further cost.
else you can get pushed off your hand and not "realize your equity", or while you have odds to call that street, the call expectation might actually be negative due to the possibility of future bets... this is an interesting read.

so in practice what does that mean? playability matters, and think about what might happen in future streets. this also gives some insight as to why position is so important.

example: K3o is a "better" hand than QJs, so why don't we play K3o more often?
because it has really bad playability. it's hard to play K high, when you miss the flop you will be pretty much hopeless (almost non-existant drawing potential), bottom pair is hardly much help, and even when you hit top pair it might be hard to know where you stand.
so it's tough to actually get to showdown and realize your equity.
• Bronze
Joined: 24.04.2011
Originally posted by sc2zerker
Hi quick question.

I understand the rule of 4 and 2 quickly gives us the equity of our hand post-flop. What I don't understand is how it's getting screwed so much in equilab / poker ranger.

For example

Hand : A T

Flop : K 9 7

Villian's Range = Random(all cards)

Somehow we get a equity of 69%!! How is this possible? I thought it would be the following

3aces = 3 outs
3 tens = 3 outs
backdoor straight draw = 1 out

At max 16 outs, That's only 32% for turn and 64% for river.

Secondly if say 4 is the turn card

We still have 56% equity! now we should have 32%? We only have 1 more card to draw. Is it all implied odds? How can we include implied odds in our quick calculations? Is it all from memory?

Thanks for any help in advance!

yeah and if villain's range is any 2 then you might aswell be up against T2. and then your outs are all the cards beside 2.... Your outs are the cards that make you have the best cards.
• Bronze
Joined: 12.10.2011
Your outs are the cards that make you have the best cards.
This is not entirely true, as you only need outs if you don't have the best hand. So in your example of AT vs T2 on that flop, AT doesn't really have outs, since it doesn't need to improve to be the best hand. Instead, T2 has 3 outs to improve to the best hand, namely the 3 remaining 2s in the deck.