Couple of questions about percentages.

wagon596

wagon596

Legend
Bronze Level
Joined
Apr 27, 2008
Total posts
3,767
Awards
13
Chips
11
1.What are the percentages that at least one player at a ten player table be dealt a pocket pair.
2. What percent, for lets say 4 or 5 players, will pair the board on the flop.
Thanks
 
wagon596

wagon596

Legend
Bronze Level
Joined
Apr 27, 2008
Total posts
3,767
Awards
13
Chips
11
I did some research, so I'll answer my own question..lol
Dealt a pair- 0.0588 %
Pair the board- 29.0 %
 
Matt Vaughan

Matt Vaughan

King of Moody Rants
Bronze Level
Joined
Feb 20, 2008
Total posts
7,150
Awards
5
Chips
6
odds any given player is dealt a PP:

First player: First card can be any card in the deck, but second card must be the same number card, of which there are 3.

52/52 x 3/51 = 3/51 = 0.0588 = 5.88%

Which is what you said, except that you didn't quite remember how decimal to percentage changes work. If you're only talking about a few players you could multiply it by the number of players, but this is not quite correct. Assume the first player was NOT dealt a pocket pair. Now for two numeral sets there are only 3 cards of each of those number remaining in the deck, so things get tricky.

Second player: Again, the first card doesn't matter (50 cards remaining). For the second card, 11/13 times they have 3 ways to draw it, but 2/13 times they have only 2 ways to draw it.

50/50 x ((11/13 x 3/49) + (2/13 x 2/49)) = .0508 = 5.08%

Notice that it's a bit smaller. This calculation gets more complex the more players there are, and depending on what assumptions we make. I'd be curious if anyone has a simpler, more elegant way of tackling the question.
 
wagon596

wagon596

Legend
Bronze Level
Joined
Apr 27, 2008
Total posts
3,767
Awards
13
Chips
11
Odds any given player is dealt a PP:

First player: First card can be any card in the deck, but second card must be the same number card, of which there are 3.

52/52 x 3/51 = 3/51 = 0.0588 = 5.88%

Which is what you said, except that you didn't quite remember how decimal to percentage changes work. If you're only talking about a few players you could multiply it by the number of players, but this is not quite correct. Assume the first player was NOT dealt a pocket pair. Now for two numeral sets there are only 3 cards of each of those number remaining in the deck, so things get tricky.

Second player: Again, the first card doesn't matter (50 cards remaining). For the second card, 11/13 times they have 3 ways to draw it, but 2/13 times they have only 2 ways to draw it.

50/50 x ((11/13 x 3/49) + (2/13 x 2/49)) = .0508 = 5.08%

Notice that it's a bit smaller. This calculation gets more complex the more players there are, and depending on what assumptions we make. I'd be curious if anyone has a simpler, more elegant way of tackling the question.
I see what you're saying , I think,, it's one or the other if I'm thinking right. Not both like I posted. Thanks for clearing that up.
 
D

ddeely1

Rock Star
Silver Level
Joined
Jan 5, 2010
Total posts
128
Chips
0
I think you get a pocket pair 1/16 hands. I am pretty sure this is the 5.88%. 1/16 is actually 6.25% but that is the fraction I learned.
 
ovitoo

ovitoo

Legend
Bronze Level
Joined
Jul 30, 2012
Total posts
1,980
Awards
1
US
Chips
75
you had it wagon. just misplaced your decimal.
 
Matt Vaughan

Matt Vaughan

King of Moody Rants
Bronze Level
Joined
Feb 20, 2008
Total posts
7,150
Awards
5
Chips
6
I think you get a pocket pair 1/16 hands. I am pretty sure this is the 5.88%. 1/16 is actually 6.25% but that is the fraction I learned.

The number is exactly what I quoted for a single player before:

52/52 x 3/52 = 5.88% Approximations are fine, but this is where the number actually comes from mathematically.

Although I always learned it as the odds of being dealt a given pocket pair is 1/220, so with 13 different types of pocket pairs, 13/220. 1/16 is close, but I feel like it's more useful to consider it in percentages anyway. Idk about you, but I have trouble visualizing 13/220. 1/16 is a bit easier I suppose since you can think of halving something 4 times, but meh. Percentages ftw imo :)
 
Top