Open Side Menu Go to the Top
Register
Odds of top 4 of 5 top stacks at same table? Odds of top 4 of 5 top stacks at same table?

12-18-2017 , 03:44 AM
This came up on my table...

42 left out of 126...

Whats the chances of 4 of the 5 top stacks being at the same 9 handed table...

I know its possible, but what are the odds... This cat saying its next to impossible...
Odds of top 4 of 5 top stacks at same table? Quote
12-18-2017 , 06:24 AM
It is kinetic based on the closeness of the bubble and me being on the outside looking in.

Why would this be moved to the Global thread?
Odds of top 4 of 5 top stacks at same table? Quote
12-18-2017 , 12:39 PM
P(at least 4 of the top 5 stacks at same table) = C(9,4)*34 / C(42,5) = 1 in 198.57
Odds of top 4 of 5 top stacks at same table? Quote
12-18-2017 , 01:14 PM
A brute force approach shows that at least 4 out the 5 biggest stacks will seat at the same table about ~1.9 times out of 100, if I understood your question correctly.

There are 42 players. For each of them, you select a position between 1 and 42. I assume that positions 1-9 go to table 1, 10-18 to table 2 and the other 3 tables will be 8-handed. Here is the code in R that enumerates any possible position combo for the top 5 and counts the maximum number of top stacks at the same table:

Code:
top5<-combn(42,5)
tables<-matrix(rep(1:5,c(9,9,8,8,8))[top5],nrow=5)
howmany<-apply(tables,2,function(x) max(tabulate(x)))
setNames(tabulate(howmany)/length(howmany),1:5)
           1            2            3            4            5 
0.0487522747 0.7175161167 0.2150686284 0.0181692505 0.0004937296
Odds of top 4 of 5 top stacks at same table? Quote
12-18-2017 , 01:52 PM
Have they all come from broken tables? Did they all start at the same table? I think it makes a difference.
Odds of top 4 of 5 top stacks at same table? Quote
12-18-2017 , 02:59 PM
Assuming table seats are randomly assigned, isn't this just a repeated application of the hypergeometric distribution?

I get the prob is:

= {2*[C(9,5)*C(33,0)+C(9,4)*C(33,1)]+3*[C(8,5)*C(34,0)+C(8,4)*C(34,1)]} / C(42,5)

= 15,876 / 850,668

= 1.8662980%
Odds of top 4 of 5 top stacks at same table? Quote
12-18-2017 , 03:47 PM
I forgot some tables will be 8-handed. Worse, I forgot it doesn't matter which table the bigstacks are at!

If they have to be at a 9-handed table (a possible interpretation of OP), it's my previous answer multiplied by 2.

If they're allowed to be at an 8-handed table, it's {2*C(9,4)*34 + 3[C(8,4)+C(8,3)]} / C(42,5) = what whosnext said
Odds of top 4 of 5 top stacks at same table? Quote
12-18-2017 , 09:00 PM
You just can't assign them to tables randomly at 42 players. Tournaments don't work that way.
Odds of top 4 of 5 top stacks at same table? Quote
12-19-2017 , 05:06 AM
Quote:
Originally Posted by Didace
You just can't assign them to tables randomly at 42 players. Tournaments don't work that way.
Sure, but I think that showing that the probability of it happening randomly is 1.866% at least indicates that the odds probably aren't "next to impossible...".
Odds of top 4 of 5 top stacks at same table? Quote
12-19-2017 , 02:11 PM
Quote:
Originally Posted by heehaww
If they're allowed to be at an 8-handed table, it's {2*C(9,4)*34 + 3[C(8,4)*34+C(8,3)]} / C(42,5) = what whosnext said
Forgot to include the bolded when transcribing from my calculator.

Quote:
Originally Posted by Didace
You just can't assign them to tables randomly at 42 players. Tournaments don't work that way.
I'd be happy to provide a more realistic solution if OP provided the necessary details. Until then, I concur with Bobo Fett.
Odds of top 4 of 5 top stacks at same table? Quote
12-20-2017 , 02:03 PM
I coded up something last night that may shed light on a more realistic answer given the nature and procedures of a poker tournament.

I simulated many 126 player tournaments and checked how many of the top 5 stacks are at the same table when the tournament reaches 42 players remaining (at the moment that the 43rd player is eliminated).

I have coded random table balancing (when needed) and random table breaking (when needed). I have coded random pots between players at the same table. In the present simulation, all pots are smallish compared to the average chip stack.

In 200,000 simulated tournaments, when 42 players remain in the tournament 4 or 5 of the top 5 chip stacks are at the same table 1.27% of the tournaments.

This is due to the nature of chips being "sticky" at a table, so it is fairly difficult for multiple large chip stacks to occupy the same table early in a poker tournament. Or even midway through a poker tournament.

Comments and questions are encouraged.
Odds of top 4 of 5 top stacks at same table? Quote
12-20-2017 , 02:33 PM
Quote:
Originally Posted by whosnext
I have coded random table balancing (when needed) and random table breaking (when needed). I have coded random pots between players at the same table. In the present simulation, all pots are smallish compared to the average chip stack.
Would it matter if the tables were broke in a predetermined order?

How are you coming up with the size of the pots? Why are they "smallish"?

What is the distribution of stack sizes?
Odds of top 4 of 5 top stacks at same table? Quote

      
m