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How often will you see 2 or 3 players at fullring with the same suit pre? How often will you see 2 or 3 players at fullring with the same suit pre?
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12-26-2013 , 02:41 PM
#1
apkrnewb
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How often will you see 2 players at full ring with the same suited cards?
How often will you see 3 players at full ring with the same suited cards?
This would be pre flop. Thanks
Having a hard time finding this! Cheers
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-26-2013 , 04:23 PM
#2
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Quote:
Originally Posted by apkrnewb
How often will you see 2 players at full ring with the same suited cards?
How often will you see 3 players at full ring with the same suited cards?
This would be pre flop. Thanks
Having a hard time finding this! Cheers
For a 9 player table, about 2.1% for 2 or more players, and about 0.0085% for 3 or more players.

The probability of 2 or more players having a specific suited hand, like AKs, is by inclusion-exclusion:

C(9,2)*4*3/C(52,2)/C(50,2) -
2*C(9,3)*4*3*2/C(52,2)/C(50,2)/C(48,2) +
3*C(9,4)*4*3*2*1/C(52,2)/C(50,2)/C(48,2)/C(46,2)

≈ 0.0264%

If we multiply that by C(13,2) possible suited hands, we get about 2.1%. This over counts the times that we get more than 1 possible suited hand duplicated, but this will be small enough to ignore. We could also treat the different hands as independent and get essentially the same result.

The probability of 3 or more players having a specific suited hand is

C(9,3)*4*3*2/C(52,2)/C(50,2)/C(48,2) -
3*C(9,4)*4*3*2*1/C(52,2)/C(50,2)/C(48,2)/C(46,2)

≈ 0.0001095%

Multiplying this by C(13,2) gives about 0.0085%.
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-26-2013 , 07:31 PM
#3
apkrnewb
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Thanks Man!
You guys have really got me thinking in a different way.
Much Obliged
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-27-2013 , 08:30 AM
#4
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Quote:
Originally Posted by BruceZ
For a 9 player table, about 2.1% for 2 or more players.
I checked this with a sim, and it came out between 2.04% and 2.05% with 99.9% confidence. That makes sense since the calculation gave 2.057%, and we knew it was a little high. The independence calculation gave 2.037%, and that's a little low.


Code:
players = 9

deck = c(1:13,101:113,1001:1013,10001:10013)
sims = 0
count = 0
while(1) {
  cards = sample(deck, 2*players, F)
  found = FALSE
  for (i in 1:(players-1)) {
    c1 = 2*i-1
    c2 = c1+1 
    if ( abs(cards[c1]-cards[c2]) < 13 ) {
      card1 = max(cards[c1],cards[c2])%%100
      card2 = min(cards[c1],cards[c2])%%100
      hand1 = card1*100 + card2
      for (j in (i+1):players) {
        c1 = 2*j-1
        c2 = c1+1
        if ( abs(cards[c1]-cards[c2]) < 13 ) {
          card1 = max(cards[c1],cards[c2])%%100
          card2 = min(cards[c1],cards[c2])%%100
          hand2 = card1*100 + card2
          if (hand1 == hand2) {
            count = count + 1
            found = TRUE
            break
          }
        }
      }
    }
    if (found) break
  }
  sims = sims + 1
}
p = count/sims
error = 3.29*sqrt(p*(1-p)/sims)
p
p-error
p+error
sims
> p
[1] 0.020443162006527
> p-error
[1] 0.0203915607740503
> p+error
[1] 0.0204947632390036
> sims
[1] 81404677
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-27-2013 , 09:42 AM
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I thought the OP was asking about how often two players at a 9-handed game would both hold two cards of the same suit. That is, two players each hold two clubs.

I think Bruce is answering how often two players hold hands of the same rank that are suited, but of different suits. That is, one players holds AsKs and another holds AcKc.

OP seemed satisfied though so maybe I am reading it wrong.
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-27-2013 , 12:04 PM
#6
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Quote:
Originally Posted by Sherman
I thought the OP was asking about how often two players at a 9-handed game would both hold two cards of the same suit. That is, two players each hold two clubs.

I think Bruce is answering how often two players hold hands of the same rank that are suited, but of different suits. That is, one players holds AsKs and another holds AcKc.

OP seemed satisfied though so maybe I am reading it wrong.
Thanks Sherman that's exactly what i was asking.
If i have K of diamonds and 9 of diamonds and i am sitting at 9 or 10 person table, how often will someone else at the table hold 2 diamonds pre flop?
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-27-2013 , 12:06 PM
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Quote:
Originally Posted by apkrnewb
Thanks Sherman that's exactly what i was asking.
If i have K of diamonds and 9 of diamonds and i am sitting at 9 or 10 person table, how often will someone else at the table hold 2 diamonds pre flop?
That isn't even remotely what you asked no matter how you read the original post.
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-27-2013 , 12:08 PM
#8
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Awkwardly worded "same suited cards" meant "cards of the same suit" I'm assuming.
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-27-2013 , 12:09 PM
#9
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Quote:
How often will you see 2 players at full ring with the same suited cards?
Is an entirely different question from

Quote:
If i have K of diamonds and 9 of diamonds and i am sitting at 9 or 10 person table, how often will someone else at the table hold 2 diamonds pre flop?
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-27-2013 , 12:38 PM
#10
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Quote:
Originally Posted by BruceZ
Is an entirely different question from
Well if you read his question completely literally the answer would be never.
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
12-28-2013 , 02:56 AM
#11
apkrnewb
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Quote:
Originally Posted by BruceZ
That isn't even remotely what you asked no matter how you read the original post.
Sorry. Sometimes when I'm trying to get exactly to the question, i get things muddled up. Sorry about the confusion
How often will you see 2 or 3 players at fullring with the same suit pre? Quote
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