Quote from: Bayes on December 16, 2014, 10:04:10 AM
Thanks, Teo.

I wrote a similar program a while ago to generate these kinds of stats. There's a classic problem in probability called the "Coupon Collector's Problem":

Given N coupons, how many draws do you have to make before you've drawn each coupon at least once?

Obviously, in a roulette context, the coupons are spins, but you could apply it to streets, double-streets etc, just replace 37 with 12, 6 or whatever.

The program can find the average number of trials in cases where not all coupons are collected, and also the probability that at least X coupons will be collected within Y trials. e.g. The "law of the third" says that roughly 24 unique numbers will hit in 37 trials, but what is the probability that at least 24 numbers will hit in 37 trials?

The program input is:

output:

Or, what is the probability that in 20 spins, at least 8 streets will have shown up?

Input:   

Output:

This program was purely for my own use, so it only runs on a Linux command line, but if anyone's interested, here's the code (it would be quite easy to re-write in the language of your choice):

Code Select Expand

'-----------------------------------------------------------
' Given n coupons, how many coupons do you expect you need
' to draw with replacement before having drawn each coupon
' at least once?
' http://en.wikipedia.org/wiki/Coupon_collector%27s_problem
' The program finds the average number of trials in cases
' where not all coupons are collected, also the maximum
' and minimum number of trials, and the probability that
' at least m coupons will be collected within v trials.
'-----------------------------------------------------------
'xfce4-terminal -H --geometry 90x30 -e @
OPTION BASE 1

'can take a long time for large N.
CONST RUNS = 100000

SPLIT ARGUMENT$ BY " " TO arg$ SIZE dim
IF dim < 4 THEN
   PRINT "Usage: coupons <m> <n> <v>"
   PRINT "m: Number of coupons to be collected (m <= n)"
   PRINT "n: Number of coupons in the set."
   PRINT "v: Number of trials within which the probability"
   PRINT "is P that all coupons are collected."
   END
ENDIF

M = VAL(arg$[2])
N = VAL(arg$[3])
V = VAL(arg$[4])

GLOBAL coupons TYPE NUMBER ARRAY N
DECLARE t[RUNS]

trials = 0
sum = 0
class = 0
max_trials = 0
min_trials = 99999

FOR i = 1 TO RUNS
   REPEAT
      x = RANDOM(N) + 1
      INCR trials
      INCR coupons[x]
      drawn = 0
     
      FOR j = 1 TO N
         IF coupons[j] > 0 THEN INCR drawn
      NEXT j
     
      IF drawn = M OR drawn = N THEN
         t[i] = trials
         INCR sum, trials
         
         IF trials <= V THEN INCR class
         
         FOR k = 1 TO N
            coupons[k] = 0
         NEXT k
         
         ' get max & min
         IF trials > max_trials THEN
            max_trials = trials
         END IF
         IF trials < min_trials THEN
            min_trials = trials
         END IF
         
         trials = 0
      END IF
   UNTIL drawn = M OR drawn = N
NEXT i

p# = class/RUNS

PRINT
PRINT "Average number of trials needed to collect "
PRINT M, " coupons from a set of ", N, " coupons = ", sum/RUNS + 1
PRINT
PRINT "Maximum number of trials needed was ", max_trials
PRINT "Minimum number of trials needed was ", min_trials
PRINT
IF V NE 0 THEN
   PRINT "Probability of collecting at least "
   PRINT M, " coupons in ", V, " trials = ", 100 * p#, " %\n"
END IF


And I've attached the binary, in case there are any Linux users here.
[attachurl=1]

Teo, I wasn't trying to hijack your thread or steal your thunder, so feel free to delete if you like! (I just thought it seemed like an on-topic contribution).

Would you be willing to share your Labby 1.5 source code? I wanted to make some modifications such as a reverse Labouchere  function.