Western States 100 Lottery Simulator

Probability of Entry

     entrants tickets expected_winners       prob
1        1981    1981         64.98780 0.03280555
2         890    1780         57.54135 0.06465320
3         390    1560         48.80195 0.12513321
4         189    1512         44.29210 0.23434974
5          79    1264         32.71075 0.41406013
6          33    1056         21.66605 0.65654697
sums     3562    9153        270.00000 1.52754879

Western States 100 Lottery Simulator

# Goal: Compute Probability of Winning Western States Lottery

# See http://www.wser.org/lottery/ for lottery details
# We group runners into "entry pools" determined by the number of consecutive western states entries.

# Number of lotterys
simulations = 20000
# entry pools by year
year = 1:6
# Number of winners
slots = 270
# Number of winners by entry pool
entrants = c(1981, 890, 390, 189, 79,33)
# Number of tickets awarded to each entrant in entry pool
tickets_per_entrant = 2^(year - 1)

# Simulate a lottery. Returns the number of winners in each pool.
ws_lottery = function() {

  # track winners by pool
  winners = rep(0,length(year))

  while(sum(winners) < slots) {
    # number of tickets belonging to each pool
    tickets = (entrants - winners) * tickets_per_entrant
    winner = sample(year, 1, prob=tickets/sum(tickets)) 
    winners[winner] = winners[winner]+1
  }

  return(winners)
}

# Simulate 1000 drawings.
lottery_results = t(sapply(1:simulations, 
  function(x) { ws_lottery() })
)

# Sum the columns of lottery results
column_sums = apply(lottery_results, 2, sum)

# Divide by number of simulations for the expected number of winners in each pool
expected_winners = column_sums / simulations

# Probability of a member of a pool being chosen
prob = expected_winners / entrants

tbl=cbind(entrants
     ,tickets = entrants*tickets_per_entrant
     ,expected_winners
     ,prob
     )

rownames(tbl) <- year
tbl = rbind(tbl, sums=colSums(tbl))

print(tbl)