Compute coefficients for FA Cup probability trees. See https://www.rmorrison.net/mnemozzyne/2023/01/24/optimising-the-fa-cup/

fa-cup.py

"""
Compute coefficients for FA Cup probability trees.
See https://www.rmorrison.net/mnemozzyne/2023/01/24/optimising-the-fa-cup/
"""

from typing import List
from dataclasses import dataclass


@dataclass
class Fixture:
    hosts: str
    visitors: str
    history: str


@dataclass
class Round:
    fixtures: List[Fixture]

    def __str__(self):
        all_journeys = "".join([f.history for f in self.fixtures])
        coefficients = [f"{all_journeys.count(c)}{c}" for c in "hax"]
        return "(" + " + ".join([c for c in coefficients]) + f") / {len(self.fixtures)}"


rounds = [Round(fixtures=[Fixture(hosts="h", visitors="a", history="h")])]
for r in range(0, 5):
    new_round = Round(fixtures=[])
    prev_round = rounds[r]
    for f in prev_round.fixtures:
        new_round.fixtures.append(Fixture(f.hosts, "x", f.history + f.hosts))
        new_round.fixtures.append(Fixture("x", f.hosts, f.history + "x"))
        new_round.fixtures.append(Fixture(f.visitors, "x", f.history + f.visitors))
        new_round.fixtures.append(Fixture("x", f.visitors, f.history + "x"))
    rounds.append(new_round)
    print(new_round)