Lottery ticket calculator

import random
from math import comb

# 6 from 49 lottery
BALLS = 49
PICK = 6
TOTAL = comb(BALLS, PICK)  # 13,983,816

def combo_to_index(combo):
    idx = 0
    for i, val in enumerate(combo):
        idx += comb(val, i + 1)
    return idx

# Bitfield: ceil(TOTAL / 8) bytes ~ about 1.75 MB total
bitfield = bytearray((TOTAL + 7) // 8)
MB = len(bitfield) / (1024 * 1024)

print(f"Total possible tickets: {TOTAL:,}")
print(f"Bitfield size: {len(bitfield):,} bytes ({MB:.2f} MB)")
print(f"Simulating random purchases until 99% coverage...")
print(f"{'Tickets Bought':>15} | {'Unique Found':>14} | {'Coverage':>10}")
print("-" * 47)

unique_found = 0
tickets_bought = 0
target_unique = int(0.99 * TOTAL)

while unique_found < target_unique:
    # sample 0-indexed so combinatorial ranking works cleanly
    ticket = tuple(sorted(random.sample(range(BALLS), PICK)))
    tickets_bought += 1

    idx = combo_to_index(ticket)
    byte_pos = idx >> 3    # idx // 8
    bit_pos  = idx & 7     # idx % 8
    mask = 1 << bit_pos

    if not (bitfield[byte_pos] & mask):
        bitfield[byte_pos] |= mask
        unique_found += 1

    if tickets_bought % 1000000 == 0: # only printout every million tickets sold
        coverage = unique_found / TOTAL
        print(f"{tickets_bought:>15,} | {unique_found:>14,} | {coverage:>9.4%}")

# Final result
coverage = unique_found / TOTAL
print("-" * 47)
print(f"{tickets_bought:>15,} | {unique_found:>14,} | {coverage:>9.4%}  <- 99% reached!")
print(f"\nTickets bought vs total combos: {tickets_bought / TOTAL:.2f}x")
input()