monte carlo tile drawer

simmer.py

import random
import sys


def to_freqs(tiles):
    """ Convert tiles to freq dictionary. """
    f = {}
    for t in tiles:
        if t not in f:
            f[t] = 1
        else:
            f[t] += 1
    return f


def tiles_in_rack(tiles, rack):
    """

    Check if tiles are in rack.

    >>> tiles_in_rack('ABC', 'ABC')
    True

    >>> tiles_in_rack('ABC', 'AB')
    False

    >>> tiles_in_rack('BOOT', 'BOOOTTOB')
    True

    >>> tiles_in_rack('BOOTBB', 'BOOOTTOB')
    False

    >>> tiles_in_rack('A', 'BCDEFG')
    False

    """
    rfreq = to_freqs(rack)
    for t in tiles:
        if t not in rfreq or rfreq[t] == 0:
            return False
        rfreq[t] -= 1
    return True


def simmer(pool, desired_rack, num_drawing):
    iterations = 0
    successes = 0
    while True:
        plist = list(pool)
        random.shuffle(plist)
        if tiles_in_rack(desired_rack, plist[:num_drawing]):
            successes += 1

        iterations += 1
        if iterations % 10000 == 0:
            print('Success rate: {}, iterations: {}'.format(
                successes/iterations, iterations))


if __name__ == '__main__':
    pool = sys.argv[1]
    desired_rack = sys.argv[2]
    num_drawing = int(sys.argv[3])
    simmer(pool, desired_rack, num_drawing)

This can be used like:

python simmer.py <pool> <tiles> <number-being-drawn>

For example,

python simmer.py DEEEIINOQR? DEQ? 6

This gives you the probability of drawing at least DEQ? on a 6-tile draw from the pool DEEEIINOQR? by using the Monte Carlo method. An analytical solution is a bit more complicated.