Odds of paired flop?

Pipunch

What are the odds of a paired flop?

Seems to be happening pretty frequently.

Talon

 doing a very quick calculation based upon a six handed table and ignoring all of the variables that are unknown it comes out to about 23.5%  which is about 1 in 4 or 3-1

patwalshh

In Response to Re: Odds of paired flop?:

 doing a very quick calculation based upon a six handed table and ignoring all of the variables that are unknown it comes out to about 23.5%  which is about 1 in 4 or 3-1
Posted by Talon

I think he's asking whats the odds of the board pairing, as in 993 or KKA etc. It's 17%

Talon

 That is the figure i have quoted for you. Based on ignoring the unknown variables. these variables will take the figure down but it will be different every hand based upon these unknowns.

Pipunch

If i can be bothered to go through hand history i might add it up cause it's way above 17. I've been seeing them about 4/10 flops i think.

patwalshh

In Response to Re: Odds of paired flop?:

If i can be bothered to go through hand history i might add it up cause it's way above 17. I've been seeing them about 4/10 flops i think.
Posted by Pipunch

4/10 flops when it should be 2/10 flops.. Never?!?!? If you saw 999, 10 times today maybe your onto something. But the standard deviation of 17% can be huge. 

patwalshh

In Response to Re: Odds of paired flop?:

 That is the figure i have quoted for you. Based on ignoring the unknown variables. these variables will take the figure down but it will be different every hand based upon these unknowns.
Posted by Talon

And variables being using 78 card decks lol? It's a pretty simple calculation.. 

(52/52 x 48/51 x 44/50) = 1-0.82824 = .17176 = 17.18%

Talon

ok if you want the maths of it.

  12 cards removed for the hands. leaves us a total of forty. Depending whether live or online it may go down to 39. Then we have to disregard the cards which are in the hands because they can not be known.

  so we ignore the first card out because it is irrelevant.
  the odds of the second pairing the first are 3/39
 The odds of the third card pairing either the first or second are 6/38.

  this gives us a total that comes to 23.5%.

  Admittedly the real figure in each given hand will be lower due to cards having been dealt hitting the board. But it will be different for every hand.

Glenelg

HI Guys,
This thread caught my eye last night & it'd been doing my head in ever since! lol  I'm NOT a maths expert but as I'm trying hard to improve my poker I'm desperately trying to learn pot odds/probability etc.  Anyhoo, when i read the first post from Pip I thought it would be around 20% and googled to see if I could find the answer.  It took a while but I came across a % quoted as 16.1% (5:1).  Unfortunately it didn't give the maths in how this was arrived at.  As I'm not a maths expert I had difficulty understanding Pat's answer and Talon's answer made sense.  However, could I offer my logical slant on how to arrive at the answer? Someone else will have to do the maths tho! There may be errors in this logic but I LOVE a challenge!

There are 78 PP's possible in 52 cards. (Each set of cards (4) has 6 possible pp potential x 13 = 78)
Therefore I'm thinking that after the hole cards are dealt there are 40 cards left with the potential of having 60 pp. This is where my maths let me down tho.  There is a possibility of between 0 and 6 PP's being dealt in the hole cards?. So I'm guessing this is the "variable" Talon mentioned?  So this changes the potential to between 54-60 chances? The flop will be 3 x cards with the possibility of any 2 being a pair.

I'm not sure where to go from here tho........HELP!

Pad
p.s. Am I over-thinking this?

EDIT: I think this sounds similar to Talons explaination? However, the 3/39 & 6/38 I don't understand?

GaryQQQ

Patwalshh is correct.

The simplest way to look at it mathematicly is to work out the chances that the the flop won't be paired;

The second card must not match the first, which is any 48 out of the 51 remaining cards, then the third card must not match either the first or the second, which is any 44 of the 50 remaining cards.

(48/51)x(44/50)=0.828

So there's an 82.8% chance the flop won't be paired, therefore a 17.2% chance it will be paired. Thats the same as 1 in every 5.8 flops being paired.

There are no variables. With each new flop there is exactly a 17.2% chance it will be paired. It makes no difference how many players are dealt in; the flop is always 3 random cards from 52.

Over small samples you can easily see big variations, ie over 100 hands either 27 paired flops, or only 7 paired flops would be nothing to get excited about. As the samples get bigger the proportion should get much closer to 17.2%. Over 1,000 hands it'll probably be within 1% (16.2% to 18.2%). Over say 100,000 hands it'll probably be within 0.1% (17.1% to 17.3%).

GaryQQQ

Just a thought, if 10 players are prepared to a look at the last 100 flops in their hand history we can quickly build up a 1,000 hand sample.

1267

you 2 got 17 % , but you need to take away the 1 % (when the board trips up) , so the 16.1 percent Glenelg googled is correct.  

As for the talon maths ,whats going on there .....

Glenelg

In Response to Re: Odds of paired flop?:

Patwalshh is correct. The simplest way to look at it mathematicly is to work out the chances that the the flop won't be paired;
Posted by GaryQQQ

Thanks a bundle Gary - NOT!! I'm gonna have to take the p.m. off to study this now!!!  ;-(

Glenelg

In Response to Re: Odds of paired flop?:

Just a thought, if 10 players are prepared to a look at the last 100 flops in their hand history we can quickly build up a 1,000 hand sample.
Posted by GaryQQQ

The 16.1% I found said it was from a 100,000 sample.  Trips were mentioned but I can't find it now to post the link!

donkeyplop

Wheres merenovice when you need him?

He was the maths guru!

petethepla

In Response to Odds of paired flop?:

What are the odds of a paired flop? Seems to be happening pretty frequently.
Posted by Pipunch

u are dead right, not only paired flops but straight an d flush flops alot like the lower hands pree win more often mostly on river and a lot of runner runner
i put it down to the rng which im not sure but i reckon rngs come in differant types being less random cheap  but dearest to rent would be more random and i will be contacting alderney to find out

Talon

  There are two major problems arising in this thread.
  Firstly the question what cards are held make all the difference to the possible outcomes. So the first card out could be impossible to pair up at all. This is a major unknown variable and would take some very complex mathematics to come to a sensible answer using these factors.

  Secondly people are putting up calculations based upon 52 cards. This can never be the case because the maximum number of cards in the deck can only be 48 and that is on a HU game. The flop can never be dealt from a full deck.

  The maths that i did used a six player table as its basis. But for the sake of simplicity i had to then ignore the possibility of the flop hitting any of the hands available. This meant that my answer was skewed on the high side because of this. I am aware of the error factor in my calculations and it would be too complex to try to eliminate this error totally. My answer is accurate only if no cards coming out match a players holding in any way. So in effect these are the maximum possible odds in this given situation. So as i said the true answer is lower than mine but the maths is way to complicated to be able to put on this forum

Pipunch

^ but then there'd be no maths to poker.

'I have 12 outs'

'NO. Those other 8 players could all hold your outs therefore you can't factor that in' ?

djblacke04

odds on paired flop are... 

(3/40 +3/40-- so 6/40) ..... that 3/20... assuming the table is 6 handed..

Glenelg

In Response to Re: Odds of paired flop?:

  There are two major problems arising in this thread.   Firstly, the question what cards are held make all the difference to the possible outcomes. So the first card out could be impossible to pair up at all. This is a major unknown variable and would take some very complex mathematics to come to a sensible answer using these factors.   Secondly, people are putting up calculations based upon 52 cards. This can never be the case because the maximum number of cards in the deck can only be 48 and that is on a HU game. The flop can never be dealt from a full deck.   The maths that i did used a six player table as its basis. But for the sake of simplicity i had to then ignore the possibility of the flop hitting any of the hands available. This meant that my answer was skewed on the high side because of this. I am aware of the error factor in my calculations and it would be too complex to try to eliminate this error totally. My answer is accurate only if no cards coming out match a players holding in any way. So in effect these are the maximum possible odds in this given situation. So as i said the true answer is lower than mine but THIRDLY, the maths is way to complicated to be able to put on this forum
Posted by Talon

Hi Talon, 
Firstly, Thats what I thought "There is a possibility of between 0 and 6 PP's being dealt in the hole cards?" Am I correct in saying this is a major variable?

Secondly, That's also what I thought, i.e. that the max is 60pp from a 40 deck (i.e. after the hole cards have been dealt)

Thirdly, is there an idiots version? ;-) I'd be interested to see your maths?

As I said in my post this a.m. my maths isn't great BUT I'm keen to learn poker probs. (I need all the help I can get!)

pad

Pipunch

Talon you're confusing ACTUAL maths from the variables. We never know which cards are already live in the game so we cannot assume.

Doing 'real' maths on the deck is absolutely pointless. In a poker context we have to assume that all other cards except our own are live in the deck otherwise it's a MASSIVE error.

I see what you're trying to say but it's an exercise in futility to suggest that we should perform real full deck calculations in poker when we know what our hole cards are.