Odds of pairing AK by the river 62.55%

Toad · Aug 7, 2008

Chuck T is right.

Irexes · Aug 7, 2008

Cheers Chuck,

James, read the posts above.

(the table uses the same logic, one King or one Ace)

jdeliverer · Aug 7, 2008

ChuckTs said:
You're not paying attention to what the other posters are saying, namely

You're doing exactly what Rex said, and are wrong for our the OP's example.

Using your coin analogy you explained what you're doing wrong perfectly:

And you're carrying that over to the poker example. We don't 'stop flipping', or stop calculating the probabilities if we hit an ace or king. We run all five cards. OP's not asking the probability of hitting exactly a single ace or king (no more, no less), he's asking the probability of hitting a pair or better.

I am paying attention to what they're saying. I am not calculating the probability of hitting exactly a single ace or king; rather, the others are double-counting the probability of hitting more than one.

And for this argument, you should 'stop calculating the probabilites if we hit an ace or king' because you've already counted it. And if you already counted it, it doesn't matter whether it pairs or not. I don't think there's any more I can say to convince you though, just try to look at it again.

Irexes · Aug 7, 2008

jamesdadeliverer said:
I am paying attention to what they're saying. I am not calculating the probability of hitting exactly a single ace or king; rather, the others are double-counting the probability of hitting more than one.

And for this argument, you should 'stop calculating the probabilites if we hit an ace or king' because you've already counted it. And if you already counted it, it doesn't matter whether it pairs or not. I don't think there's any more I can say to convince you though, just try to look at it again.

At least we agree you are answering the wrong question and the answer to the OP is nearer 60%.

jdeliverer · Aug 7, 2008

Irexes said:
At least we agree you are answering the wrong question and the answer to the OP is nearer 60%.

NO!! We don't agree at all.

If you look at my original post, you can see that I calculated the probability of NEVER pairing anything. Then I subtracted that from 1, leaving us with the probability that ANYTHING paired, one pair or two pair or trips, a FH or even quads. I am taking into account all cases.

If you go by the original answer, you are counting the first pair you get, in addition to the second pair, and anything else. Thus you are counting two pair or trips twice and a full house or quads three times.

Irexes · Aug 7, 2008

Ooo hang on you are saying you are measuring the same thing.

In which case your methodology is very flawed.

glworden · Aug 7, 2008

TO FURTHER CONFUSE THE ISSUE

James, there is no animosity at all. I appreciate the discussion, even if I'm still not getting my head around it totally. It's an odd thing, isn't it, that we have all these poker players who can't agree on what is seemingly basic and common statistic. I am the OP; my logic makes sense to me and many posters are backing me up. But heck - maybe we're all wrong!

To add further to the confusion, here's an online calculator which came up with a COMPLETELY different answer. I think I entered the info correctly. We're drawing from 50 cards, drawing 5 cards with 6 outs, and only require one hit to fulfill the parameters. Now this thing is saying our probability of hitting is 38.4%.

Can you explain that one?

ChuckTs · Aug 7, 2008

Don't bother worrying about that calculator, it's probably only meant for postflop draws and adding the 5th card screwed something up. Just ignore that one.

Irexes · Aug 7, 2008

Ok, I'm going to do an about turn here I think.

There is a 54.5% chance of not drawing an A or a K. And so therefore a 45.5% chance of drawing at least one.

The logic of your other posts makes sense too. So unless someone comes along with further evidence to the contrary, apologies James.

Zach, where are you??

Irexes · Aug 7, 2008

I'm blaming this on not having eaten for two days due to stomach bug fwiw.

jdeliverer · Aug 7, 2008

glworden, I have no idea what the software is doing here, but I'll try to figure it out. anything under 40% is ridiculously low, as AK has a higher chance than that of beating pocket 2's. I'm assuming AK doesn't have a 10% chance of hitting a straight or flush

Irexes · Aug 7, 2008

We posted at the same time, see my previous post, I've been converted.

jdeliverer · Aug 7, 2008

Ok I figured it out.

That calculator is doing what Irex thought I was doing. It calculates getting exactly one out.

Replacing the Required box with 2 we get 0.0938 and with 3 we get 0.009.

0.3844+0.0938+0.009 = 0.4872
Which is our answer

glworden · Aug 7, 2008

Isn't this fun?

I'm just amazed that this seemingly simple question is so hard to grasp. I think James is winning converts by the force of his conviction; he really sounds like he knows what he's talking about.

I'm not trying to convince anybody. I'm just trying to figure out how to approach it and why I'm wrong.

How many of you (us) thought you knew the answer to this? How many thought 62%? How many still think that?

Gary

Irexes · Aug 7, 2008

Do the maths for not hitting gl as per James' first post, using Excel or similar.

It's pretty convincing

glworden · Aug 7, 2008

Irexes said:
Do the maths for not hitting gl as per James' first post, using Excel or similar.

It's pretty convincing

OK, here's a thought. We're trying to hit a pair or better? You could use Jame's method of never pairing a card, yet still end up with a straight or flush. How do you figure those chances in?

Irexes · Aug 7, 2008

That's a different question and you can use pokerstove or similar to compare the equity of hands like that.

glworden · Aug 7, 2008

Irexes said:
That's a different question and you can use pokerstove or similar to compare the equity of hands like that.

Does poker stove give yo an answer to the basic question: pairing an A or K by the river?

Irexes · Aug 7, 2008

Nope the maths in James' OP does that.

Toad · Aug 7, 2008

James,

Tell me if I'm on the right track here. When you say we can't simply add the probabilities I had to take a simpler example:

We are going to flip a coin 4 times and want to find out the probability that heads will come up at least once.

.5+.5+.5+.5=2

(obvioulsly not possible since prob has to be between 0 and 1)

By your math we take the odds that it won't happen, mutiply and subtract from one.

1-(.5*.5*.5*.5)= .875 or 87.5% that we will hit heads at least once.

Right?

My brain hurts...

Dwilius · Aug 7, 2008

This is a long thread, I haven't read it all so maybe its already answered but, 62.5% is wrong because its from adding 6/50 + 6/49...instead of 6/50 + (44/50*6/49)...

jdeliverer · Aug 7, 2008

D'wilius - exactly right

Toad - Yup (except you did something wrong since 1-(.5*.5*.5*.5) = 0.9375.

It's the same as 0.5 (chances we get heads 1st time) + 0.5 (chances we will get heads 2nd time)*0.5(chance we have not gotten heads yet) + 0.5(chances we get heads 3rd time)*0.25(chance we have not gotten heads yet + 0.5(chances we get heads 4th time)*0.125(chance we have not gotten heads yet) = 0.5 + 0.5*0.5 + 0.5*0.25 + 0.5*0.125 = 0.9375.

Note that for all calculations past the first flip, we disregard any situations in which we got heads in the first flip because we already counted those situations.

Toad · Aug 7, 2008

yeah I did .5^3 instead of .5^4

So I'm going to have to flip-flop and agree with James on this one...

...not a flip-flop of presidential proportions, but a flip-flop nonetheless.

boogeyman316 · Aug 7, 2008

Wow!
I always used to things the OP way. So does this effect the way we calculate outs?

dj11 · Aug 7, 2008

I was the original post who quoted CardPlayer mag in one of those little blurbs that fill space saying that AK will pair by the river 60% of the time.

Its a number I generally use, but won't go broke over too often.

Edit add, several minutes later...

I found my original post of this in this thread;

https://www.cardschat.com/forum/gen...ourite-hold-em-article-79328/?highlight=blurb

My post was;

blah blah blah,

Most interesting snipet from the issue currently in my reading room is a Poker Odds blurb which states;

'The chances of either an Ace or a King appearing on the board by the river are 60 percent.'

This does not say that those are the odds of pairing AK by the river. It is entirely possible tho that I extrapolated in another post (hopefully burried extra deep) that those odds were valid for pairing.

Odds of pairing AK by the river 62.55%

Toad

Rock Star

Irexes

Legend

jdeliverer

Legend

Irexes

Legend

jdeliverer

Legend

Irexes

Legend

glworden

Visionary

Attachments

ChuckTs

Legend

Irexes

Legend

Irexes

Legend

jdeliverer

Legend

Irexes

Legend

jdeliverer

Legend

glworden

Visionary

Irexes

Legend

glworden

Visionary

Irexes

Legend

glworden

Visionary

Irexes

Legend

Toad

Rock Star

Dwilius

CardsChat Regular

jdeliverer

Legend

Toad

Rock Star

boogeyman316

Rising Star

dj11

Legend

About CardsChat

Our Community

Our Site