## Spectacular Seven

### May 4, 2010

There’s nothing hard about this program as long as you keep straight what you are doing at each step:

```(define (seven n)   (let ((wins (make-vector 8 0))         (scores (make-vector 8 0)))     (let loop ((k n) (p 0) (winner 0) (challenger 1)                (queue '(2 3 4 5 6 7)))       (cond ((zero? k) ; simulation ends               (map (lambda (x) (exact->inexact (/ x n 1/100)))                    (vector->list wins)))             ((<= 7 (vector-ref scores winner)) ; game ends               (vector-set! wins winner                 (+ (vector-ref wins winner) 1))               (set! scores (make-vector 8 0))               (loop (- k 1) 0 0 1 '(2 3 4 5 6 7)))             ((< (rand) 1/2) ; current winner wins point               (vector-set! scores winner                 (+ (vector-ref scores winner)                    (if (<= 7 p) 2 1)))               (loop k (+ p 1) winner (car queue)                     (append (cdr queue) (list challenger))))             (else ; current challenger wins point               (vector-set! scores challenger                 (+ (vector-ref scores challenger)                    (if (<= 7 p) 2 1)))               (loop k (+ p 1) challenger (car queue)                     (append (cdr queue) (list winner))))))))```

The `wins` vector tracks which team won; at the end of the simulation, the sum of the wins over all teams should equal `n`. The `scores` vector tracks the scores of each team in a single game, and is reset at the beginning of each game; `p` keeps track of the point count in each game, to determine if a particular point has a value of 1 or 2. Here are the winning percentages we get after a million simulated games:

```> (seven 1000000) (16.3057 16.2836 13.8705 12.4255 10.2218 10.2573 8.877 11.7586)```

The first two teams have similar winning percentages; since it is fifty/fifty that either wins the first point, that makes sense. Winning percentages decrease for each succeeding team until the last, who can win the game if they win the four points they play, with 1 on the first point and 2 on each of the next three points. In real jai alai games, handicappers put the best teams in the fourth, fifth and sixth post positions to make games more exciting.

We used rand from the Standard Prelude. You can run the program at http://programmingpraxis.codepad.org/6bcXRB4Z.

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### 5 Responses to “Spectacular Seven”

1. […] Praxis – Spectacular Seven By Remco Niemeijer In today’s Programming Praxis exercise our task is to run a simulation of a ballgame to see if the scoring […]

2. Remco Niemeijer said

```import Control.Applicative
import Data.List
import System.Random

match :: Int -> [(a, Int)] -> Int -> [(a, Int)]
match ps ~(x:y:r) w = (p,s + if ps > 7 then 2 else 1) : r ++ [c]
where ((p,s), c) = if w == 0 then (x,y) else (y,x)

game :: IO Int
game = f 0 (zip [1..8] [0,0..]) . randomRs (0,1) <\$> newStdGen
where f ps a ~(x:xs) = maybe (f (ps+1) (match ps a x) xs) fst \$
find ((>= 7) . snd) a

simulate :: Int -> IO [Float]
simulate n = (\ws -> map (\x -> 100 * (l x - 1) / l ws) . group .
sort \$ ws ++ [1..8]) <\$> replicateM n game
where l = fromIntegral . length
```
3. Gambiteer said
```;; for some reason a circular buffer seems most natural

(define (seven-2 n)
(let ((teams (list 0 1 2 3 4 5 6 7))
(scores (make-vector 8 0))
(wins   (make-vector 8 0)))

(define last-pair
(lambda (x)
(if (pair? (cdr x))
(last-pair (cdr x))
x)))

(define (team-score team)
(vector-ref scores team))

(define (increment-wins! team)
(vector-set! wins team (fx+ (vector-ref wins team) 1)))

(define (increment-score! team score)
(vector-set! scores team (fx+ (vector-ref scores team) score)))

(define (reset-all-scores teams)
(do ((i 0 (fx+ i 1))
(teams teams (cdr teams)))
((fx= i 8) teams)
(vector-set! scores (car teams) 0)
(set-car! teams i)))

(define (swap-teams! teams)
(let ((temp (car teams)))
(set-car! (cdr teams) temp)))

(set-cdr! (last-pair teams) teams)

(let loop ((k n)
(teams teams)
(points 0))
(cond ((fxzero? k) ; simulation ends
wins)
((fx<= 7 (team-score (car teams)))  ;; previous point winner wins game.
(increment-wins! (car teams))
(loop (fx- k 1) (reset-all-scores teams) 0))
((fxzero? (random-integer 2)) ; current winner wins point
(increment-score! (car teams) (if (fx<= 7 points) 2 1))
(swap-teams! teams)
(loop k (cdr teams) (fx+ points 1)))
(else ; current challenger wins point
(increment-score! (cadr teams) (if (fx<= 7 points) 2 1))
(loop k (cdr teams) (fx+ points 1)))))))
```
4. Mike said

In python:

jai_alai_match() accepts a list of ratings to indicate the relative strengths of the players. The probablility of a player winning a point is the ratio of the players rating to the sum of both players ratings (see the threshold calculation below). The default is that each player is equally likely to win a point.

```from random import random

ID  = 0
RTG = 1
PTS = 2

def jai_alai_match(rating=*8):
queue = [[n,rating[n],0] for n in range(8)]
pts = 0
player1 = queue.pop(0)
while player1[PTS] < 7:
player2 = queue.pop(0)

threshold = player1[RTG]/float(player1[RTG] + player2[RTG])
if random() > threshold:
player1,player2 = player2,player1

player1[PTS] += (1 if pts<8 else 2)
queue.append(player2)

pts += 1

return [player1] + queue

def simulate(reps=10000,ratings=None):
hist = *8
for n in range(reps):
result = jai_alai_match(ratings) if ratings else jai_alai_match()
winner = result
hist[winner[ID]] += 1

for h in hist:
print "{0:5.2}".format(h*100.0/reps),
print

#test
simulate()
simulate(ratings=[ 100, 100, 100, 100, 100, 100, 100, 160 ])
```
5. slabounty said

A Ruby implementation. There’s quite a few improvements to make, but I’m getting tired of looking at it ;-). This is quite a few more lines than the other implementations, but maybe someone will find it useful.

I haven’t posted here before, but it looks like a great site.

```require 'getoptlong'

class Team
attr_accessor :score
attr_accessor :games_won

def initialize(team_number)
@score = 0
@games_won = 0
@team_number = team_number
end

def <=> (t)
if @team_number < t.team_number
return -1
elsif @team_number == t.team_number
return 0
else
return 1
end
end
end

class Queue < Array
alias :enqueue :<<
alias :dequeue :shift
end

def sim_game(teams)

# Sort the teams so they're in the initial starting order and
# reset their scores to 0.
teams.sort!
teams.each { |t| t.score = 0 }

winner = teams.dequeue
total_points = 0

while winner.score < 7 do
challenger = teams.dequeue
if rand <= 0.5 then
winner.score += (total_points <= 7) ? 1 : 2
teams.enqueue challenger
else
challenger.score += (total_points <= 7) ? 1 : 2
teams.enqueue winner
winner = challenger
end
total_points += 1
end

# Increment the winners game count.
winner.games_won += 1

# Put the winner back on the queue. Doesn't matter that it's at the end, as we'll resort later.
teams.enqueue winner
end

if __FILE__ == \$PROGRAM_NAME

# Set up the command line options
opts = GetoptLong.new(
["--num_games", "-n", GetoptLong::REQUIRED_ARGUMENT],
["--verbose", "-v", GetoptLong::NO_ARGUMENT]
)

# Set the default values for the options
num_games = 100
\$verbose = false

# Parse the command line options. If we find one we don't recognize
# an exception will be thrown and we'll rescue with a message.
begin
opts.each do | opt, arg|
case opt
when "--num_games"
num_games = arg.to_i
when "--verbose"
\$verbose = true
end
end
rescue
puts "Illegal command line option."
exit
end

# Create the teams and initialize them.
num_teams = 8
teams = Queue.new
1.upto(num_teams) do |t|
teams.enqueue(Team.new(t))
end

# Run the simulation.
1.upto(num_games) do
sim_game(teams)
end

# Resort the teams and print out the winning percentages.
teams.sort!
teams.each do |t|
puts "Team #{t.team_number} winning percentage is #{(t.games_won.to_f / num_games.to_f) * 100.0}"
end

end

```