44 65% vs 78 35%

459

Help my worm brain out. Using dirty math, we have 8 flush outs (no 9), and 3 straight outs.

So 11 outs. Using multiply x 4 rule, that's 44% equity.

Now, let's say the turn doesn't pair the board, now we have 10 outs. Even if you discounted yourself to 10 outs otf, that's still 40% equity not 35%.

What am I missing?

I haven’t done the full calculation but 35% seems reasonable. You are missing two things about the “rule of 4”:

1. In this case it’s not the major issue, but the rule of 4 is only an approximation, especially as the number of outs increases. This should be obvious by considering an extreme example. Suppose you have two spades and flop a flush. What is the probability that either the turn or the river will be a red card? There are 26 red cards; it should be obvious that the rule of 4 gives a wrong answer. In general, the more outs the less accurate the rule is.

2. The more critical issue - the rule of 4 gives an approximate probability that either the turn or river will be one of your outs. It does not give you your probability of winning the hand. Usually these are close, but not in cases where villain has significant redraw outs, such as this. I think you are underestimating the chances of a paired board. Using the rule of 4 as an approximation, there are 7 cards that pair, giving 28%. If the turn doesn’t pair , there are 3 additional pairing cards on the river, so add about 6% for a total of 34%. Since it’s an approximation, call it 1/3 probability of pairing.

Now we use the rule of 4 to calculate two cases. In 2/3 of the hands we win by catching an out, which happens about 44% of the time. In 1/3 of the hands. We have only 1 out, which we hit 4% of the time. Therefore we win
2/3 x 44% + 1/3 x 4% = 31%. That’s not far off considering we’ve used an approximation twice to get this answer.

http://twodimes.net/h/?z=14784005
pokenum -h 8h 7h - 4c 4s -- 4h 5h 9c
Holdem Hi: 990 enumerated boards containing 9c 5h 4h
cards win %win lose %lose tie %tie EV
8h 7h 344 34.75 646 65.25 0 0.00 0.347
4s 4c 646 65.25 344 34.75 0 0.00 0.653

Rule of 4 is shorthand and not precise,

The percentage of time you hit your str8 or flush is:

11/47 + 11/46 - (11/47*11/46) = 41.45%

The above doesn't take into account the time villain hits one of his 10 outs to a FH or quads (or your 1 out to beat him even when he improves)

Just because you make your hand doesn't mean you win.

Is there not a math or so forum anymore? In practice, how do you know what he has? If you do or so, there are many ways to play this hands, and it includes implied odds.

you hit your straight or flush 44% of the time. unfortunately for you, 33% of that time, he makes a boat or quads.

This

We can draw out on him, but he can also draw out on us.

Is there an easy way to calculate our true Equity then if we know our opponent has a set?

Something I can do on the fly at the table?

You can open Equilab, choose any board, give your opponent a set and add your own hand like Top Pair or Straight Draw or any hand you like and check how much equity you have. Repeat this process with different hands and boards and you will get a gist how much equity you have against a certain hand.

Once you have practiced enough then it will be something you can do on the fly at the tables.

Explain when you will know your opponent has a set?

Well, this is a fair point, we never "know" that, but there's certain lines which will strongly indicate that sets consist of the majority of villain's range. If a tight player flats pre then raises us on a T62 rainbow board, what do you think he has most of the time?

Live reads in my small player pool. But there are a 100 ways you can know, but let's not make that the point of the thread.

-someone bets, you semi bluff raise your SFD, and old man coffee 4 bet jams. Now it's a math problem, how do we discount his 33% full house / quad equity from our 44%?

I already gave you the method, but there’s no really simple one step way. 2/3 of the time he doesn’t get quads or a boat; you win 44% of those hands. 44% x 2/3 = 29.3%. 1/3 of the time he hits, and you have one out. You win 4% in this case. 1/3x4%= 1.3%. Total winning chance for the two cases is 30.6% — not too bad for an approximation you could do at the table.

Why do you feel this is important?

Might also be slow played AA or KK ..or someone trying to punish the habitual c-bettor with absolute air. So yes: Sets will be a part of their range but I wouldn't necessarily say it's the majority of it.

Because tight players flat big pairs pre and bluff raise dry flops all the time

So I can calculate my true Equity In situations where I have reverse implied odds.

Again there are many situations where I know EXACTLY what my opponent is holding. Not going to turn this thread in to a debate as to how I know that.

Why do you need to calculate it at the table? It is known.

Got shoved on in original post hand history, and assumed my SFD equity was higher than in actuality it was. Yes I knew he had a set. It would have been nice to calculate my true Equity on the fly and in the future.

And would the difference between what you calculated at the time and what it actually was made you change your decision?

Yes. And you can apply that to many other scenarios the classic one being when you have over cards with a flush draw if your over cards are live or not, or swimming your opponent just has two pair of your over card still may not be good if he hits two pair so yes this particular question pertains to many different scenarios

In which case you're overthinking incredibly marginal decisions. Then again you have x-ray vision so I don't know why I'm coaching here as you should never lose

Having 10% different equity in certain situations is a good thing to know I would not consider that marginal.

Dare I say it can make you the difference between a winning and losing player

No one calculates this on the fly. They study situations away from the table and apply at the table.

I dare say this is the dictionary definition of can't see the wood for the trees, best of luck in your future endeavours