Two Plus Two Older Archives  

Go Back   Two Plus Two Older Archives > General Gambling > Probability

Reply
 
Thread Tools Display Modes
  #1  
Old 08-12-2003, 05:17 PM
ccwhoelse? ccwhoelse? is offline
Senior Member
 
Join Date: Jul 2003
Location: u rook rike charlie brown
Posts: 371
Default searched but did not find, possible hands

how many possible starting hand combinations are there, thanks?
Reply With Quote
  #2  
Old 08-12-2003, 06:17 PM
NoChance NoChance is offline
Senior Member
 
Join Date: Jul 2003
Location: MN
Posts: 363
Default Re: searched but did not find, possible hands

I think there are 169 possible hands. This chart is an interesting read.

169 hands
Reply With Quote
  #3  
Old 08-12-2003, 06:19 PM
ccwhoelse? ccwhoelse? is offline
Senior Member
 
Join Date: Jul 2003
Location: u rook rike charlie brown
Posts: 371
Default *N/M* thanks

Reply With Quote
  #4  
Old 08-13-2003, 04:30 AM
FastCards FastCards is offline
Junior Member
 
Join Date: Oct 2002
Location: Scotland
Posts: 26
Default Possible hands in detail + the chances of getting \"no cards\"

169 different starting hands.

There are (52*51)/(2*1) ways of selecting 2 cards from 52, so there are 1326 distinct starting hands.

Breakdown:
Pairs: 13 different, 6 combinations each
Suited non-pair: 78 different, 4 combos each
Unsuited pair: 78 different, 12 combos each

(13*6)+(78*4)+(78*12) = 1326.

Only slightly related to this (but hopefully of some interest), a friend said last night that he had played 250 hands in the Pokerstars WCOOP 500 Hold'em and "never saw a pair bigger than TT [img]/images/graemlins/frown.gif[/img]". He wanted to know the probability of this happening. *

24 of the 1326 hands are AA,KK,QQ or JJ so the chances of getting one of these hands is (24/1326) = 1.8%. So, the chances of not getting one of these hands in 250 deals is

(1-(24/1326) to the power 250 = 1.04%

A step further; the chance of not getting AA,KK,QQ or JJ in n hands would seem to be (1-(24/1326) to the power n. This gives the chance of not getting one of these hands as:

1 hand: 98.2%
10 hands: 83.3%
25 hands: 63.3%
50 hands: 40.1%
100 hands: 16.1%
150 hands: 6.5%
200 hands: 2.6%
250 hands: 1.0%
300 hands: 0.4%

If you include AKs and AKo, then you have a probability of 40/1326 for each hand

1 hand: 97.0%
10 hands: 73.6%
25 hands: 46.5%
50 hands: 21.6%
100 hands: 4.7%
150 hands: 1.0%
200 hands: 0.2%


* As it happens, I had AA 3 times, KK at least twice and saw QQ and JJ each at least once but unfortunately 128th out of 548 runners paid 0. [img]/images/graemlins/wink.gif[/img] Perhaps someone with more time/skill than me could produce a formula to work out the chance of getting AA/KK/QQ or JJ x times in y deals???
Reply With Quote
  #5  
Old 08-13-2003, 07:04 AM
BruceZ BruceZ is offline
Senior Member
 
Join Date: Sep 2002
Posts: 1,636
Default Re: Possible hands in detail + the chances of getting \"no cards\"

Perhaps someone with more time/skill than me could produce a formula to work out the chance of getting AA/KK/QQ or JJ x times in y deals???

By the binomial distribution, the probability of exactly x in y deals is:

C(y,x)*(24/1326)^x*(1 - 24/1326)^(y-x)

For at least x in y deals, use binomdist in Excel to compute the probability of at most x-1, and subtract this from 1.
Reply With Quote
  #6  
Old 08-13-2003, 08:48 AM
FastCards FastCards is offline
Junior Member
 
Join Date: Oct 2002
Location: Scotland
Posts: 26
Default Re: Possible hands in detail + the chances of getting \"no cards\"

Thanks Bruce. You are a credit to this forum.
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 03:39 AM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, vBulletin Solutions Inc.