Can Stopping After Two Losses Boost Your Honor of Kings Rank? A Math Model

I enjoy playing Honor of Kings in my spare time and wondered whether stopping after two consecutive losses is the optimal strategy for increasing rank.

Honor of Kings Rank Model

Assumptions

Win‑rate adjustment : The player starts with an initial win probability (based on 2023‑2024 preseason data) and it decreases after each game until it reaches a lower bound.

Star adjustment rule : Winning adds one star, losing subtracts one star (star protection is ignored).

Daily game limit : At most 10 games per day.

Consecutive‑loss stop rule : Play stops after a specified number of consecutive losses.

IID assumption : Each game outcome is independent, and win probability depends only on the number of games played.

Notation

p_i: win probability at the i‑th game.

n: actual number of games played in a day, determined by the stop rule.

ΔS: net change in stars for the day.

L: loss‑stop threshold (number of consecutive losses).

Model Construction

Win‑rate model : If the initial win probability is p_0, then p_i = max(p_min, p_0 – i·δ) where δ is the per‑game decay.

Star change model : Each win adds +1 star, each loss –1 star, so ΔS = Σ_{i=1}^{n} (win_i ? 1 : –1).

Game count model : The game stops when either the daily limit (10) is reached or L consecutive losses occur.

To illustrate, we first consider a simple scenario: at most 3 games per day and stop after two consecutive losses. The possible daily outcomes are:

Win three games in a row.

Win one then lose two consecutively.

Win two then lose one.

Lose two consecutively and stop.

For each case we compute the probability (using the decreasing win‑rate formula) and the resulting star change. The expected daily star change under this simple setting is 0.128 stars.

Simulation Results

We then simulate 1,000,000 days with up to 10 games per day, varying the loss‑stop threshold from 1 to 10. The Python code used is:

<code>import numpy as np

# parameters
initial_win_prob = 0.56
max_games = 10
sim_days = 1000000
loss_limits = range(1, 11)

def simulate_day_decreasing_winrate(loss_limit):
    games_played = 0
    stars_change = 0
    consecutive_losses = 0
    current_win_prob = initial_win_prob
    while games_played < max_games and consecutive_losses < loss_limit:
        if np.random.rand() < current_win_prob:
            stars_change += 1
            consecutive_losses = 0
        else:
            stars_change -= 1
            consecutive_losses += 1
        games_played += 1
        current_win_prob = max(0.05, current_win_prob - 0.01)
    return stars_change

average_changes_decreasing = []
for limit in loss_limits:
    results = [simulate_day_decreasing_winrate(limit) for _ in range(sim_days)]
    average_change = np.mean(results)
    average_changes_decreasing.append(average_change)

average_changes_decreasing
</code>

The simulation yields the following average daily star growth:

Stop after 1 loss: 0.214 stars

Stop after 2 losses: 0.330 stars

Stop after 3 losses: 0.328 stars

Stop after 4 losses: 0.322 stars

Stop after 5 losses: 0.302 stars

Stop after 6 losses: 0.301 stars

Stop after 7 losses: 0.300 stars

Stop after 8 losses: 0.302 stars

Stop after 9 losses: 0.301 stars

Stop after 10 losses: 0.306 stars

Thus, allowing two consecutive losses before stopping provides the highest expected star increase; longer loss tolerances give diminishing returns.

We also examined how the optimal stop threshold changes with different initial win probabilities (50 %–65 %). The results show that higher initial win rates favor larger loss thresholds, with the best average daily star growth rising from –0.036 at 50 % to over 2.1 stars at 65 %.

In summary, a moderate gaming schedule that stops after two consecutive defeats maximizes rank growth under realistic win‑rate decay, while excessive play reduces the benefit.