cat box puzzle

cat.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

from random import randint
from functools import reduce

print("There is a row of boxes. A cat is hiding in one of the boxes.")
print("Every time you check a box, the cat (invisibly) moves to an adjacent box.")
print()
print("Find a pattern that corners the cat with the least number of checks!")
print("  (select a box with 100% probability to win)")
print()

while True:
	try:
		n_boxes = int(input("How many boxes in the row? (≥2) \x1B[1m"))
		if (n_boxes >= 2):
			print("\x1B[0m", end='')
			break
	except ValueError:
		print("\x1B[0mPlease enter an integer!")
		pass
	except KeyboardInterrupt:
		print("\x1B[0m\nBye!")
		exit(0)
	else:
		print("\x1B[0mBox count must be at least 2!")

boxprob = [1 / n_boxes for i in range(n_boxes)]
print("Box Index                 : |" + "".join(map(lambda p: "\x1B[1m%7s\x1B[0m |" % (p + 1), range(n_boxes))))

guesses = 0

while True:
	print("Probabilities             : |" + "".join(list(map( lambda p: "\x1B[1m%7.4g%%\x1B[0m|" % (p * 100), boxprob))))
	# select box to check
	while True:
		try:
			b = int(input("Check box number (1-%d): \x1B[1m" % n_boxes)) - 1
			if ((b >= 0) and (b < n_boxes)):
				print("\x1B[0m", end='')
				break
		except ValueError:
			print("\x1B[0mPlease enter an integer between 1 and %d!" % n_boxes)
		except KeyboardInterrupt:
			print("\n\x1B[0mBye!")
			exit(0)
		else:
			print("\x1B[0mBox number must be between 1 and %d!" % n_boxes)
	guesses += 1
	print("Box %d goes to 0%% probability" % (b + 1))
	boxprob[b] = 0
	# rescale probabilities
	scale = reduce((lambda x, y: x + y), boxprob)
	if (scale == 0):
		print("\nCat cornered after %d checks! Score: %.3g%%\n" % (guesses, max(n_boxes - 2, 1) * 200 / guesses))
		exit(0)
	boxprob = list(map(lambda r: r / scale, boxprob))
	print("Probabilities after choice: |" + "".join(list(map( lambda p: "\x1B[1m%7.4g%%\x1B[0m|" % (p * 100), boxprob))))
	# move cat
	print("\n→ Cat moves one box left or right\n")
	boxprobn = [0 for z in range(n_boxes)]
	for i in range(n_boxes):
		if (i == 0):
			boxprobn[i + 1] += boxprob[i]
		elif (i == (n_boxes - 1)):
			boxprobn[i - 1] += boxprob[i]
		else:
			boxprobn[i + 1] += boxprob[i] / 2
			boxprobn[i - 1] += boxprob[i] / 2
	boxprob = boxprobn