star2.py

from dataclasses import dataclass
from functools import cache
import numpy as np

@dataclass(eq=True, frozen=True)
class State:
    position1: int
    position2: int
    score1: int
    score2: int
    player_turn: int

dicesum_odds = (
    (3,1),
    (4,3),
    (5,6),
    (6,7),
    (7,6),
    (8,3),
    (9,1)
)

def new_position(position, dice_sum):
    return (position + dice_sum -1) % 10 +1

@cache
def count_wins(s: State):
    if s.score1 >= 21:
        return np.array((1,0), dtype=np.int64)
    if s.score2 >= 21:
        return np.array((0,1), dtype=np.int64)

    wins = np.array((0,0), dtype=np.int64)
    for dice_sum, odds in dicesum_odds:
        if s.player_turn == 1:
            pos = new_position(s.position1, dice_sum)
            new_s = State(pos, s.position2, s.score1 + pos, s.score2, 0)
        else:
            pos = new_position(s.position2, dice_sum)
            new_s = State(s.position1, pos, s.score1, s.score2 + pos, 1)
        wins += count_wins(new_s) * odds

    return wins

position1 = 7
position2 = 8
print(max(count_wins(State(position1, position2, 0, 0, 1))))