Does 2/4 rule fail miserably in certain scenarios?

[Daithi]

I was messing around with an equity calculator and came across this example. I must be doing something wrong.

vs

Board:

Let's count outs. The 85 needs sixes. We count 3 outs (excluding spades for all outs). 3 jacks and 3 eights.

Thats 9 outs. 9x4=36. Not including backdoor flush which is usually additional 4%. So we are looking here around 35-40%.

Yet when you plug the numbers into calculator you get 25.96%

 

[TenJack]

Because you hand would be 789T, a jack would also complete your straight. Also, 6s doesn't make your hand, nor the Js. The rule calculates YOUR outs, it doesn't take into account your opponents holding. any spade and you are drawing dead.

 

[57noona]

TenJack said it best it doesn't take into account of your opponents outs.

 

[Daithi]

Because you hand would be 789T, a jack would also complete your straight. Also, 6s doesn't make your hand, nor the Js. The rule calculates YOUR outs, it doesn't take into account your opponents holding. any spade and you are drawing dead.

Would you agree that my hand has 9 outs?

 

[Daithi]

TenJack said it best it doesn't take into account of your opponents outs.

Hi. How many outs does the 85 hands has?

 

[kalinichxxl]

:rock:

 

[braveslice]

Would you agree that my hand has 9 outs?

8 of spade is not out. It seems runner runners are cancelling each other out (about) so 8 outs.

 

[Daithi]

8 of spade is not out. It seems runner runners are cancelling each other out (about) so 8 outs.

Nice one, well spotted. 8 outs. So according the 2/4 rule we own 32% equity, which still 6% off.

We know villain's holding, so we know that the straight makes best hand only if the flush doesn't get in. If one street only the data is fairy accurate. But because there are 2 streets in which our best hand can be rendered into a losing hand skews the result with the 2/4 rule. Experiment: add a blank card on the turn and use the rule by 2.

Unfortunatelly, this happens a fair bit with this way of calculating your odds. Another instance I picked up on is when you have a flush draw on the Flop against a set. Your odds are much lower (almost 10%) than the result. That is of course the 2 street draw that can bring him a house.

I think you only have to worry with regards to allins on the flop and when you know that he is drawing to a stronger hand than you.

 

[VisionNutz]

Because you hand would be 789T, a jack would also complete your straight. Also, 6s doesn't make your hand, nor the Js. The rule calculates YOUR outs, it doesn't take into account your opponents holding. any spade and you are drawing dead.

This post +1

Also should be noted that when you turn the non spade Jack this gives the opponent a redraw to a higher K high straight :bebored:

so you end up with some runner runner diamond options but keep in mind all the cards that MISS gives Q high the victory in this hand.

This is a fold tbh pre flop this hand make you go broke so quick buddy!


EDIT *** I had to do a refresher but here's something I would like to share with you and for you to keep in mind ***

You only want to count your GOOD OUTS and remove any bad outs for the equation to get a more accurate valuation of your equity in the hand.

There are also ANTI OUTS - which in your hand here is Jack of spades and 6 of spades this give you a straight but your opponent Flushes.

There are also "Marginal outs" this is the Jack, its a marginal out in my opinion because the oppenent can now re draw to the King high straight (although you wouldn't really know what villain is holding unless your can get a range)

So I count

Jd Jh Jc

6d 6h 6c

for six outs - J being marginal

remember though on the turn you can peel off a diamond and go runner runner diamonds for the flush.

Assuming the action was ALL IN on the flop then yeah... you can count 6 outs!

 

[Daithi]

This post +1

Also should be noted that when you turn the non spade Jack this gives the opponent a redraw to a higher K high straight :bebored:

so you end up with some runner runner diamond options but keep in mind all the cards that MISS gives Q high the victory in this hand.

This is a fold tbh pre flop this hand make you go broke so quick buddy!

Sure. But the hand itself is not the crux of the issue, the hand is only from a simulator. The issue is reliability of the 2/4 system. Plug any scenario into your favourite hand calculator where Hero has a 9 card flush draw on the flop and Villain has a Set. You will see that the 2/4 system will give you wrong data.

Edit: This was posted before I saw your follow up edit.

 

[VisionNutz]

Sure. But the hand itself is not the crux of the issue, the hand is only from a simulator. The issue is reliability of the 2/4 system. Plug any scenario into your favourite hand calculator where Hero has a 9 card flush draw on the flop and Villain has a Set. You will see that the 2/4 system will give you wrong data.

Edit: This was posted before I saw your follow up edit.

No man there is no wrong data lol! Yes the 2/4 has a margin of error but still reliable enough for Live & Online references and only a margin of error meaning a few points off.

 

[Daithi]

You only want to count your GOOD OUTS and remove any bad outs for the equation to get a more accurate valuation of your equity in the hand.

There are also ANTI OUTS - which in your hand here is Jack of spades and 6 of spades this give you a straight but your opponent Flushes.

There are also "Marginal outs" this is the Jack, its a marginal out in my opinion because the oppenent can now re draw to the King high straight (although you wouldn't really know what villain is holding unless your can get a range)

So I count

Jd Jh Jc

6d 6h 6c

for six outs - J being marginal

remember though on the turn you can peel off a diamond and go runner runner diamonds for the flush.

Assuming the action was ALL IN on the flop then yeah... you can count 6 outs!

What about 8h and 8c? Similarly like Jacks they contribute toward villains straight draw but they still make you the best hand if he doesn't hit runner runner.

 

[Daithi]

No man there is no wrong data lol! Yes the 2/4 has a margin of error but still reliable enough for Live & Online references and only a margin of error meaning a few points off.

I don't know is the difference between 32% and 26% only a marginal error. That is huge!

Hero:
Villain:
Board:

 

[VisionNutz]

What about 8h and 8c? Similarly like Jacks they contribute toward villains straight draw but they still make you the best hand if he doesn't hit runner runner.

As stated in the previous post the "8" is not what you're drawing to its a marginal out since you dont really know what your opponent has. You're drawing to an open ended straight bro. That means 8 outs with two anti outs (the jack of spades and 6 of spades) at least that is how I understand it.. sure the turn can bring on some sweaty cards but we are currently under the assumption that its all in on the flop.


Now as for you're other topic/inquiry about the set vs flush -

I have just plugged in numbers about your set vs flush draw scenarios and you are correct that the sim shows 75% vs 25% but I am trying to figure out why because the truth is math doesnt lie lol


so bare with me a moment - I think - and again Im not like an expert but lets learn this together

 

[Daithi]

Sure

 

[VisionNutz]

Sure

Okay bro so with our new scenario that you've provided here

Q ♦ Q ♥ Villain

6 ♠ vs 9 ♠ Hero

the flop comes 2 ♠ 3 ♠ Q ♣



Currently on this flop villain has 75% to win the hand

Hero have about 25%

But we need to take into consideration the rest of the hand (turn and river). This is where we calculate probabilites and after doing some research this post says it the best


https://www.cardschat.com/forum/learning-poker-57/equity-calculation-set-vs-flush-draw-380719/


Scroll down to the username "Vinnie" and read his post (4th post)

 

[Amanda A]

On the general reliability of the 2, 4 rule, I heard that if you are all in and will definitely see 2 cards and your outs are over 8, you need to do a modification. You multiply outs by 4 then subtract (outs-8)So if you have 15 outs 2 cards to come is 60 – (15-8) =53 percent chance of winning. This is more accurate that just multiplying by 4 and getting 60, you don't have 60% chance of winning, 53% is more accurate.

 

[Gildog89]

I think the concept that's missing here is that the odds of hitting your out is not the same thing as hand equity. The 2/4 rule gives you odds of hitting one of your outs. Hand equity is odds of winning the hand. You can hit your out and still lose the hand. The 2/4 rule is just for odds of hitting your out. The equity calculator factors in the time you hit your out, but still lose the hand.

 

[VisionNutz]

I think the concept that's missing here is that the odds of hitting your out is not the same thing as hand equity. The 2/4 rule gives you odds of hitting one of your outs. Hand equity is odds of winning the hand. You can hit your out and still lose the hand. The 2/4 rule is just for odds of hitting your out. The equity calculator factors in the time you hit your out, but still lose the hand.

Yes great information!! Thank you as well as I am still learning these concepts too! Of course in game its much harder to calculate the accuracy of equity in a hand and more useful to get an estimate on pot odds to Equity ratios

here is a good site to read up on too

http://www.pokerology.com/lessons/drawing-odds/

:icon_stud

 

[Daithi]

Okay bro so with our new scenario that you've provided here

Q ♦ Q ♥ Villain

6 ♠ vs 9 ♠ Hero

the flop comes 2 ♠ 3 ♠ Q ♣



Currently on this flop villain has 75% to win the hand

Hero have about 25%

But we need to take into consideration the rest of the hand (turn and river). This is where we calculate probabilites and after doing some research this post says it the best


https://www.cardschat.com/forum/learning-poker-57/equity-calculation-set-vs-flush-draw-380719/


Scroll down to the username "Vinnie" and read his post (4th post)

Very good sleuthing indeed. But that provides theory on how to get the real number, which is something we don't really need hehe. We need to get accurate results from the 2/4 rule if possible. I think my initial insinuation was correct that runner runners to the nuts seriously mess up 2/4 rule.

First of all I used the improved version of 2/4. That is when you multiple by 4x any amount of outs greater than 8, you subtract the final result by the difference. For example 12 outs by 4 equals 48.
48-4= 44% (Actual 44.96%)

On the by 2 rule you add +1 to the result. 12 outs x 2 = 24
24+1=25 (actual 25.5 Turn, 26 River)

Now if we know that he can draw to the nuts let's try to remove 2 outs. With the set instead of 8 outs we use 6. 6x4=24
24+1=25 pretty sweet result

Let's see the previous example with the draw. (Although I also like your suggestion with removing the marginals). Say we go with all outs. We use 8 outs. We remove 2.
6x4=24
24+1=25
Although for backdoor flush I would normally account extra 4%, so with that we'd have 29% which 3% over and it is a lot.

I guess these are only 2 spots I found it off. The one with the draw is a folder anyway. Unless it was a weirdly large pot and a short stack pushed us. How often does that happen?

And the other one is the flush draw vs set. Where we have to remember to take away 2 outs. Needs to be tested though hehe.

EDIT: Amanda beat me to it. Didn't see the previous posts before posting. But sure no harm

 

[VisionNutz]

Very good sleuthing indeed. But that provides theory on how to get the real number, which is something we don't really need hehe. We need to get accurate results from the 2/4 rule if possible. I think my initial insinuation was correct that runner runners to the nuts seriously mess up 2/4 rule.

First of all I used the improved version of 2/4. That is when you multiple by 4x any amount of outs greater than 8, you subtract the final result by the difference. For example 12 outs by 4 equals 48.
48-4= 44% (Actual 44.96%)

On the by 2 rule you add +1 to the result. 12 outs x 2 = 24
24+1=25 (actual 25.5 Turn, 26 River)

Now if we know that he can draw to the nuts let's try to remove 2 outs. With the set instead of 8 outs we use 6. 6x4=24
24+1=25 pretty sweet result

Let's see the previous example with the draw. (Although I also like your suggestion with removing the marginals). Say we go with all outs. We use 8 outs. We remove 2.
6x4=24
24+1=25
Although for backdoor flush I would normally account extra 4%, so with that we'd have 29% which 3% over and it is a lot.

I guess these are only 2 spots I found it off. The one with the draw is a folder anyway. Unless it was a weirdly large pot and a short stack pushed us. How often does that happen?

And the other one is the flush draw vs set. Where we have to remember to take away 2 outs. Needs to be tested though hehe.

EDIT: Amanda beat me to it. Didn't see the previous posts before posting. But sure no harm

Excellent results I think Gildog & Amanda says it really well also!

Thank you!

 

[Daithi]

I think the concept that's missing here is that the odds of hitting your out is not the same thing as hand equity. The 2/4 rule gives you odds of hitting one of your outs. Hand equity is odds of winning the hand. You can hit your out and still lose the hand. The 2/4 rule is just for odds of hitting your out. The equity calculator factors in the time you hit your out, but still lose the hand.

Yes, fair point. Yet the results from the 2/4 rule are used to compare to the pot equity though...

 

[Daithi]

Excellent results I think Gildog & Amanda says it really well also!

Thank you!

I'm testing more hands like flush/straight draw vs flush. I find that you must remove 3 cards (plus the improved version of 2/4 of course) to get a very good result. In my set example above we have a backdoor straight draw.

8 outs for flush. Remove 3 this time. We get 20%. We add another 4% for backdoor straight and we get 24% (where actual is 25.5%). The same result like we did with removing only 2 outs. I've erroneously added +1 in above post, which shouldn't be there, you add +1 only by 2 (one street), but we did by 4.

 

[Daithi]

Works like a charm for the other situation too!

vs

Board:

We will include the marginal outs too because as it is now they will produce a winning hand, we don't know if he's gonna hit overpair over our 8.

So we use 3x Jacks, 3x Sixes, 2x Eights. Total 8 outs. Take away 3.
5 outs multiply by 4 is 20%. Plus our backdoor flush 4%. Gives a result of 24%. Pretty close! Perhaps we can actually add 5% for backdoors.

Another example:
vs

Board

Outs: 2x Queens, 2x Jacks, 3x Kings, 3x Eights, 10 outs.
We remove 3 outs. 7x4 is 28%. Plus our 4% backdoor flush. 32% (actual 32.42%).

Hows that?

 

[Daithi]

You can use it to workout your equity against perceived range and then you just average them out based on combos.

Or is there any other, better and easier way?

EDIT: This is a response to MettaGame's post, that seems to be gone now.

Mettagame:
You cant compare your equity vs an unknown hand.The 2/4 rule is basically good for using for known clean outs or perceived clean outs to gauge rough equity quickly.It's not going to give you an accurate outcome in very high variance situations.