The expected amount of time it takes to complete the art wing of the museum in Animal Crossing: New Horizons

redd.py

from datetime import date, timedelta
from fractions import Fraction as F


def tries_before_next(already_collected):
    """How many more real pieces you'll need to buy on average to get the next
    new one
    """

    chance_new = F(43 - already_collected, 43)
    chance_new = chance_new * F(4, 5) + F(1, 5)
    return 1 / chance_new

def main():
    # How many real pieces you'll need to buy to get all unique ones
    pieces_total = sum(tries_before_next(n) for n in range(43))

    # How many visits that'll take, at an average of 1.4 real pieces/visit
    visits = pieces_total / F('1.4')

    # The date that gives, assuming one visit per two weeks
    approx_date = date.today() + timedelta(days=round(visits * 14))
    print(
        f'{float(pieces_total)} pieces, {float(visits)} visits, '
        f'ETA {approx_date}'
    )


if __name__ == '__main__':
    main()