mathless_11bit_rng.py

import random

def toss_coin():
	return random.randint(0, 1)

def roll_die():
	return random.randint(1, 6)

def pick_1_from_n_cards(n):
	return random.randint(1, n)

digits = [None, None, None, None]

sequence = "".join(["H" if toss_coin() else "T" for _ in range(7)])

if sequence in ["HHHHHHH", "TTTTTTT", "HTTTTTT"]: # you could early-exit this if you hit TH or HTH etc.
	# >= 2000 (48/2048 = 3/128 chance)
	digits[0] = 2
	digits[1] = 0
	if roll_die() == 1:
		# >= 2040 (8/48 = 1/6 chance)
		digits[2] = 4
		digits[3] = pick_1_from_n_cards(8) - 1
	else:
		digits[2] = pick_1_from_n_cards(4) - 1
		digits[3] = pick_1_from_n_cards(10) - 1
else:
	# < 2000
	digits[0] = toss_coin()
	digits[1] = pick_1_from_n_cards(10) - 1
	digits[2] = pick_1_from_n_cards(10) - 1
	digits[3] = pick_1_from_n_cards(10) - 1

print("".join(map(str, digits)))