How much score is expected for in 2048 for given highest tile on board, and probability of 4 popping up instead of 2

score_2048.py

import sys
import random
# import argparse

def score_2048(highest_tile, probability_of_four = 0.2, verbose=False):
	if verbose:
		print "Input: ", highest_tile

	if highest_tile == 4:
		if random.random() <= probability_of_four:
			if verbose:
				print "  Four"
			return 0
		else:
		 return 4
	else:
		# If we need highest tile, we must have summed its two constituents
		result = highest_tile  + score_2048(highest_tile / 2) + score_2048(highest_tile / 2)
		if verbose:
			print "result: ", result
		return result


if __name__ == "__main__":
	if len(sys.argv) != 4:
		print "Usage: python score_2048.py <highest_tile_on_board> <probability_of_four> <verbose>"
		sys.exit(0)

	result = 0
	# do 100 times and take average
	for i in range(100):
		result = result + score_2048(int(sys.argv[1]), float(sys.argv[2]), verbose=bool(int(sys.argv[3])))

	print "Result: ", result / 100.0
	print bool(int(sys.argv[3]))