Consecutive Cashes in the World Series of Poker

Probability Puzzles in R

Peter Chi

Assistant Professor of Statistics Villanova University

World Series of Poker

  • ~ 6000 entrants in recent years
  • Prize money awarded to top 10% - cashing

 

Poker Professional Ronnie Bardah:

  • Cashed in 2010, 2011, 2012, 2013, 2014
Probability Puzzles in R

Simplifying assumptions

  • 6000 players every year
  • Same players each year
  • All player have identical ability
Probability Puzzles in R

The intersection function

players <- c(1:20)

cash_year1 <- sample(players, 4)
cash_year1

20  4 11 14

cash_year2 <- sample(players, 4)
cash_year2

18  7 19  4

intersect(cash_year1, cash_year2)

4
Probability Puzzles in R

Storing cashes as a matrix

players <- c(1:20)

cashes <- replicate(3, sample(players, 4))
cashes

      [,1] [,2] [,3]
 [1,]    4    5    1
 [2,]   11   19    6
 [3,]   18   16    9
 [4,]   12   14   17
Probability Puzzles in R

The Reduce function

cashes <- replicate(3, sample(players, 4))
cashes

      [,1] [,2] [,3]
 [1,]    4    5    1
 [2,]   11   19    6
 [3,]   18   16    9
 [4,]   12   14   17

in_all_three <- Reduce(intersect, list(
    cashes[, 1], cashes[, 2], cashes[, 3]))

in_all_three

integer(0)

length(in_all_three)

0
Probability Puzzles in R

Let's simulate the<br> World Series of Poker!

Probability Puzzles in R

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