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I have a pocket pair at a 9 handed table I have a pocket pair at a 9 handed table

07-30-2018 , 11:56 AM
let's say I have pocket Deuces at a 9 handed table, how often will one of the other 8 players have a deuce?
I have a pocket pair at a 9 handed table Quote
07-30-2018 , 12:09 PM
Quote:
Originally Posted by apkrnewb
let's say I have pocket Deuces at a 9 handed table, how often will one of the other 8 players have a deuce?
Do you mean how often will 1) only one other player have exactly one duece, 2) at least one other player have exactly one deuce (meaning two other people could have exactly one), or 3) anyone has at least one (which captures instances in which only one person has one, or two people have one, or another person also has a pair)? Those all have different answers.
I have a pocket pair at a 9 handed table Quote
07-30-2018 , 02:34 PM
Quote:
let's say I have pocket Deuces at a 9 handed table, how often will one of the other 8 players have a deuce?
Probability 101: When confused about a probability think of the opposite (because all probabilities must add up to 1)
I.e.:
"Probability that someone else has a deuce (or two)" + "Probability that no one else has a deuce" = 1

In other words:

"Probability that someone else has a deuce (or two)" = 1 - "Probability that no one else has a deuce"

Now we can easily figure this one out:
"Probability that no one else has a deuce"

There's 8 other players holding 16 cards and 50 unknown cards of which 48 are non-deuces.
So the probability is:
48/50 for the first of those 16 cards to not be a deuce
its then
47/49 for the second of those 16 cards to not be a deuce
etc.

48/50 * 47/49 * ... * 33/35
= 0.46 (roughly)

So the probability that someone is holding a deuce (or two) is
1 - 0.46 = 0.54
I have a pocket pair at a 9 handed table Quote
07-30-2018 , 06:08 PM
Using combos,

P(at least 1 person has 1 or more deuces)= 1-C(48,16)/C(50,16) =1 - 45.8% = 54.2%
I have a pocket pair at a 9 handed table Quote
07-30-2018 , 09:35 PM
Thanks for the great explanation! I'm getting better still not sure though. Are you saying around half the time i have pocket 22 one of the other 8 players is gonna have at least one of the two remaining deuces. Seems like that would be way to much!
I have a pocket pair at a 9 handed table Quote
07-31-2018 , 10:59 AM
Quote:
Originally Posted by apkrnewb
Thanks for the great explanation! I'm getting better still not sure though. Are you saying around half the time i have pocket 22 one of the other 8 players is gonna have at least one of the two remaining deuces. Seems like that would be way to much!
It is what it is.

Probability intuition is a tricky thing. You rarely meet someone who has the same birthdayas you (day/mo), yet in a room of 23 people there is 50% chance two people will have the same birthday
I have a pocket pair at a 9 handed table Quote
07-31-2018 , 01:32 PM
Quote:
Probability intuition is a tricky thing.
Good thing, too! It's how poker players make their money (i.e. by fish grossly misjudging probabilities)
I have a pocket pair at a 9 handed table Quote
07-31-2018 , 07:34 PM
Quote:
Originally Posted by antialias
Good thing, too! It's how poker players make their money (i.e. by fish grossly misjudging probabilities)
Assuming fish even think about probabilities.
I have a pocket pair at a 9 handed table Quote
08-01-2018 , 12:10 PM
Yikes! Thank you very much a Antialias and as always Statmanhal WOW
I have a pocket pair at a 9 handed table Quote

      
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