19-21

from functools import lru_cache

def moves(a):
    return a + 1, a + 4, a * 5


@lru_cache(None)
def game(x):
    if x >= 68:
        return 'WIN'
    if any(game(e) == 'WIN' for e in moves(x)):
        return 'P1'
    if all(game(e) == 'P1' for e in moves(x)):
        return 'V1'
    if any(game(e) == 'V1' for e in moves(x)):
        return 'P2'
    if all(game(e) in ['P1', 'P2'] for e in moves(x)):
        return 'V2'


def p19(x):
    return any(game(e) == 'P1' for e in moves(x))

print([s for s in range(1, 68) if p19(s)])
print([s for s in range(1, 68) if game(s) == 'P2'])
print([s for s in range(1, 68) if game(s) == 'V2'])