# How a local partner decodes a plan change. Three types of foreign team, as the partner sees them:
#   committed   - changes plan in 5 % of months, whatever happens;
#   adaptive    - changes plan when the market state shifts (95 %), almost never otherwise (2 %);
#   opportunist - changes plan in 35 % of months, whenever it privately pays, ignoring the state.
# The state shifts in 30 % of months, so the adaptive team also changes plan in about 30 % of months.
# The partner starts with prior 0.45 / 0.45 / 0.10 and watches 12 months.
PRIOR = {"committed": 0.45, "adaptive": 0.45, "opportunist": 0.10}

def p_change(team, shift):
    if team == "committed":
        return 0.05
    if team == "adaptive":
        return 0.95 if shift else 0.02
    return 0.35

def posterior(months, sees_state):
    """months: list of (shift, change). If the state is not verifiable, the partner averages over it."""
    post = dict(PRIOR)
    for shift, change in months:
        for t in post:
            if sees_state:
                p = p_change(t, shift)
            else:
                p = 0.3 * p_change(t, True) + 0.7 * p_change(t, False)
            post[t] *= p if change else 1 - p
    z = sum(post.values())
    return {t: v / z for t, v in post.items()}

year = [(True, True)] * 4 + [(False, False)] * 8          # 4 shifts, 4 changes, all in shift months
odd = [(True, True)] * 3 + [(True, False)] + [(False, True)] + [(False, False)] * 7
cases = (("A  4 changes, reason not verifiable", year, False),
         ("B  4 changes, each with the agreed state indicator", year, True),
         ("C  as B, but one change came without the indicator", odd, True))
for label, months, sees in cases:
    post = posterior(months, sees)
    print(label)
    print("   " + "   ".join(f"{t} {PRIOR[t]:.2f} -> {post[t]:.2f}" for t in PRIOR))
# A  4 changes, reason not verifiable
#    committed 0.45 -> 0.01   adaptive 0.45 -> 0.81   opportunist 0.10 -> 0.18
# B  4 changes, each with the agreed state indicator
#    committed 0.45 -> 0.00   adaptive 0.45 -> 1.00   opportunist 0.10 -> 0.00
# C  as B, but one change came without the indicator
#    committed 0.45 -> 0.00   adaptive 0.45 -> 0.87   opportunist 0.10 -> 0.12