Two Plus Two Publishing LLC Two Plus Two Publishing LLC
 

Go Back   Two Plus Two Poker Forums > >

Notices

Probability Discussions of probability theory

Reply
 
Thread Tools Display Modes
Old 09-30-2011, 08:12 PM   #26
EvilSteve
 
EvilSteve's Avatar
 
Join Date: Mar 2006
Location: 2p2 afterlife
Posts: 13,199
Re: Number of possible flops in Holdem

Quote:
Originally Posted by phaddad View Post
DarkMagus,
I am very interested in your post. I would like to be able to get to the bare number of flops. For example, Ad 7s 2h would be the same as 7s 2h Ad. But it would also be the same as 7d Ah 2s. How many distinct flop possibilities are there?
Not sure what you're asking. His 1755 number counts those three as the same flop, A72 rainbow. And actually the first two are the exact same cards, just listed in a different order. If you want to count each specific three card combination separately, that's 52c3 = 22,100. And if for some unknown reason you care about the order the cards come down, that's 52*51*50 = 132,600 ordered three card sequences.
EvilSteve is offline   Reply With Quote
Old 02-02-2015, 04:42 PM   #27
DGAF
Pooh-Bah
 
DGAF's Avatar
 
Join Date: Jan 2009
Location: West Coast
Posts: 5,021
Re: Number of possible flops in Holdem

Quote:
Originally Posted by TheCesspit View Post
Well, that's merely 50 Choose 3:

50*49*48 / 3*2*1 = 19,600

Total possibly flops are 52 Choose 3 = 22,100
Then what is the median flop (if you have no hole cards)? Looking to do a little over/under gambling and kind of burnt out on red/black. Thx.
DGAF is offline   Reply With Quote
Old 05-05-2017, 07:01 AM   #28
CaptnCanary
newbie
 
Join Date: Jan 2007
Location: England
Posts: 17
Re: Number of possible flops in Holdem

Quote:
Originally Posted by N.Brosseau View Post
Basically, what I'm asking is, in keeping things in the perspective of what I was asking previously about pair, 2 pairs and so on showing up within the common cards (at flop, turn, river) should I take into consideration the cards that I have in evaluating the probability of these event or not when making a general evaluation.

So wouldn't the total number of possible flop be 22,100 instead of 19,600 if I'm just checking the common cards in general and not in relation with the specific pocket hand I have ?

The reason why I'm asking this is because I've been collecting data on the common cards that are popping up (my sample is at 2000 hands right now) and I'm seeing discrepancies of about 2% to 3% on the number of time a pair is showing in the common cards.

To give you a specific example, it was previous established that at least two card of the same value would show up in the common card by the river 49.29% of the time but I'm getting a value of about 46.45%.

The previously established value was based on the idea that we were considering 52 possible cards on the board, but should I only be considering 50 and take each time into consideration the hand that I have and the number of player present to determine the odds of a pair or more cards of the same value, in general, showing up on the board ?
I know this is very very old but I just wanted to say that if you were observing flops in holdem games, the stats may be biased by the hands that most players see a flop with. Players will usually see a flop with pocket pairs and will always fold many unpaired hands. So the flops you see will have a slightly reduced probability to show up with a pair on the board. This may account for a slight difference from theoretical and observed flop textures.
CaptnCanary is offline   Reply With Quote
Old 05-05-2017, 01:52 PM   #29
whosnext
Pooh-Bah
 
whosnext's Avatar
 
Join Date: Mar 2009
Location: California
Posts: 3,709
Re: Number of possible flops in Holdem

Quote:
Originally Posted by CaptnCanary View Post
I know this is very very old but I just wanted to say that if you were observing flops in holdem games, the stats may be biased by the hands that most players see a flop with. Players will usually see a flop with pocket pairs and will always fold many unpaired hands. So the flops you see will have a slightly reduced probability to show up with a pair on the board. This may account for a slight difference from theoretical and observed flop textures.
This same issue came up in a fairly recent thread. Pairs are tricky in poker. If I have a pocket pair, that increases the chances that another player has a pocket pair, not decreases. If you think about it for a little bit, the reason becomes obvious.

Same logic applies to flops as well. So if I have a pocket pair, the chance that a pair appears on the flop actually is increased compared to if I do not have a pocket pair.

It is not hard to work through the actual tallies via combinatorics:

Number of flops having at least a pair given that I hold a pocket pair = 12*C(4,3)+12*C(4,2)C(46,1)+1*C(2,2)*C(48,1)
= 3,408

Number of flops having at least a pair given that I do not hold a pocket pair = 2*C(3,3)+11*C(4,3)+2*C(3,2)C(47,1)+11*C(4,2)C(46,1 )
= 3,364

Of course, to derive the respective probs the common denominator is C(50,3) = 19,600
whosnext is offline   Reply With Quote

Reply
      

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


Forum Jump


All times are GMT -4. The time now is 01:53 PM.


Powered by vBulletin®
Copyright ©2000 - 2017, Jelsoft Enterprises Ltd.
Copyright © 2008-2010, Two Plus Two Interactive
 
 
Poker Players - Streaming Live Online