Can Magnus Carlsen Win the 2025 World Rapid Championship?

A Monte Carlo Simulation of the Final Four Rounds

Python
R
Chess
Monte Carlo
Simulation
Author

Kieran Mace

Published

December 28, 2025

Introduction

The 2025 World Rapid Chess Championship in New York is reaching its climax. After 9 grueling rounds of rapid chess, Magnus Carlsen sits on 7.0 points, chasing the leaders as the tournament enters its final stretch. With four rounds remaining (Rounds 10-13), the championship remains wide open.

In a 13-round Swiss tournament with over 200 players, predicting the winner is far more complex than a direct knockout. Players are paired based on their current score, meaning Magnus’s path to victory depends not just on his own results, but on how the entire field performs.

This analysis uses Monte Carlo simulation to answer the key question:

What are Magnus Carlsen’s chances of winning the World Rapid Championship, and how does his Round 10 result affect those odds?

The Challenge of Swiss System Tournaments

Unlike a round-robin or knockout format, Swiss system tournaments pair players with similar scores each round. This creates fascinating dynamics:

  • Leaders face each other: The top scorers are paired against each other, making it harder to maintain a lead
  • Half-point leads matter: In rapid chess with high draw rates, every half point is precious
  • Tiebreaks add complexity: Points alone may not determine the winner

For our simulation, we’ll focus on the primary criterion: final point total. Tiebreaks (Buchholz, Sonneborn-Berger, etc.) add another layer but require tracking every player’s full history.

Data Sources

We scrape live data from Chess-Results, the official tournament management system:

Code 
import pandas as pd
import numpy as np
from simulation import (
    load_crosstable_after_rd9,
    load_round_pairings,
    outcome_probs,
    simulate_with_round10_outcome
)

# Load current standings
standings = load_crosstable_after_rd9()

# Load Round 10 pairings
rd10_pairings = load_round_pairings()

# Find Magnus's pairing
magnus_pairing = rd10_pairings[
    (rd10_pairings["white"] == "Carlsen Magnus") |
    (rd10_pairings["black"] == "Carlsen Magnus")
]

Current Standings (After Round 9)

Code 
standings_r <- py$standings %>%
  head(15) %>%
  select(rank, name, rtg, pts) %>%
  rename(
    Rank = rank,
    Player = name,
    Rating = rtg,
    Points = pts
  )

kable(standings_r, caption = "Top 15 players after Round 9")
Top 15 players after Round 9
Rank Player Rating Points
1 Carlsen Magnus 2824 10.5
2 Artemiev Vladislav 2727 9.5
3 Erigaisi Arjun 2714 9.5
4 Niemann Hans Moke 2612 9.5
5 Dominguez Perez Leinier 2703 9.5
6 Vachier-Lagrave Maxime 2730 9.0
7 Sindarov Javokhir 2704 9.0
8 So Wesley 2702 9.0
9 Giri Anish 2685 9.0
10 Esipenko Andrey 2649 9.0
11 Sevian Samuel 2658 9.0
12 Dubov Daniil 2686 9.0
13 Mamedyarov Shakhriyar 2707 9.0
14 Shimanov Aleksandr 2554 8.5
15 Erdogmus Yagiz Kaan 2446 8.5

Round 10 Pairings (Published)

Code 
# Get top board pairings
pairings_r <- py$rd10_pairings %>%
  head(10) %>%
  select(board, white, white_rtg, white_pts, black, black_rtg, black_pts) %>%
  rename(
    Board = board,
    White = white,
    `W.Rtg` = white_rtg,
    `W.Pts` = white_pts,
    Black = black,
    `B.Rtg` = black_rtg,
    `B.Pts` = black_pts
  )

kable(pairings_r, caption = "Top 10 boards for Round 10")
Top 10 boards for Round 10
Board White W.Rtg W.Pts Black B.Rtg B.Pts
1 Carlsen Magnus 2824 7.0 Sarana Alexey 2641 7.0
2 Niemann Hans Moke 2612 7.5 Artemiev Vladislav 2727 7.5
3 Abdusattorov Nodirbek 2717 7.0 Erdogmus Yagiz Kaan 2446 7.0
4 Vachier-Lagrave Maxime 2730 6.5 Gukesh D 2692 6.5
5 Erigaisi Arjun 2714 6.5 Sevian Samuel 2658 6.5
6 Maghsoodloo Parham 2669 6.5 Mamedyarov Shakhriyar 2707 6.5
7 Shimanov Aleksandr 2554 6.5 Sindarov Javokhir 2704 6.5
8 Dominguez Perez Leinier 2703 6.5 Mamedov Rauf 2610 6.5
9 Henriquez Villagra Cristobal 2586 6.5 So Wesley 2702 6.5
10 Nepomniachtchi Ian 2762 6.0 Lazavik Denis 2576 6.5
Code 
# Magnus's Round 10 opponent
magnus_row = magnus_pairing.iloc[0]
if magnus_row["white"] == "Carlsen Magnus":
    magnus_color = "White"
    opponent_name = magnus_row["black"]
    opponent_rtg = magnus_row["black_rtg"]
else:
    magnus_color = "Black"
    opponent_name = magnus_row["white"]
    opponent_rtg = magnus_row["white_rtg"]

magnus_rtg = standings[standings["name"] == "Carlsen Magnus"]["rtg"].values[0]
magnus_pts = standings[standings["name"] == "Carlsen Magnus"]["pts"].values[0]
Magnus Carlsen’s Round 10 Matchup

Magnus Carlsen (2824) plays White against Sarana Alexey (2641).

Magnus is currently on 10.5 points after 9 rounds.

The Probability Model

For each game, we use an Elo-style probability model with an adjustable draw rate. The model:

  1. Calculates expected score using the standard Elo formula
  2. Adjusts draw probability based on rating difference (closer ratings → more draws)
  3. Splits the remaining probability between wins for each player
Code 
# Example probabilities for Magnus vs his Round 10 opponent
if magnus_color == "White":
    p_win, p_draw, p_loss = outcome_probs(magnus_rtg, opponent_rtg, draw_base=0.37)
else:
    p_loss, p_draw, p_win = outcome_probs(opponent_rtg, magnus_rtg, draw_base=0.37)

prob_display = pd.DataFrame({
    "Outcome": ["Magnus Wins", "Draw", "Magnus Loses"],
    "Probability": [f"{p_win:.1%}", f"{p_draw:.1%}", f"{p_loss:.1%}"]
})
Code 
kable(py$prob_display, caption = "Round 10 outcome probabilities for Magnus")
Round 10 outcome probabilities for Magnus
Outcome Probability
Magnus Wins 40.9%
Draw 44.8%
Magnus Loses 14.3%

The draw_base parameter is set to 0.37, reflecting the higher draw rates typical in rapid chess at the elite level.

Monte Carlo Simulation

We simulate the remaining 4 rounds (10-13) across 20,000 possible futures:

  • Round 10: Uses the published pairings from Chess-Results
  • Rounds 11-13: Uses an approximate Swiss pairing algorithm (score groups + rating sort)
Code 
# Run simulation with Round 10 outcome tracking
results = simulate_with_round10_outcome(
    n_sims=20000,
    seed=42,
    focus_top_n=80,
    draw_base=0.37,
    focus_player="Carlsen Magnus"
)

# Overall championship probability
overall_prob = results["focus_is_co_winner"].mean()

# Conditional probabilities by Round 10 outcome
cond_probs = results.groupby("focus_rd10_outcome").agg({
    "focus_is_co_winner": ["mean", "count"]
}).reset_index()
cond_probs.columns = ["Round 10 Result", "Championship Prob", "N Simulations"]
cond_probs = cond_probs.sort_values("Championship Prob", ascending=False)

Results

Overall Championship Probability

Code 
overall <- py$overall_prob

Based on 20,000 simulated tournament continuations, Magnus Carlsen has a 80.4% chance of finishing first (or tied for first) on points.

How Round 10 Affects Magnus’s Chances

Code 
cond_data <- py$cond_probs %>%
  mutate(
    `Round 10 Result` = factor(`Round 10 Result`, levels = c("Win", "Draw", "Loss"))
  )

ggplot(cond_data, aes(x = `Round 10 Result`, y = `Championship Prob`, fill = `Round 10 Result`)) +
  geom_col(width = 0.6) +
  geom_text(aes(label = sprintf("%.1f%%", `Championship Prob` * 100)),
            vjust = -0.5, size = 5, fontface = "bold") +
  scale_y_continuous(labels = percent, limits = c(0, max(cond_data$`Championship Prob`) * 1.15)) +
  scale_fill_manual(values = c("Win" = "#2E7D32", "Draw" = "#FFA000", "Loss" = "#C62828")) +
  labs(
    title = "Magnus's Championship Probability by Round 10 Result",
    subtitle = sprintf("Playing %s against %s", py$magnus_color, py$opponent_name),
    x = "Round 10 Result",
    y = "Probability of Finishing First on Points",
    caption = "Based on 20,000 Monte Carlo simulations"
  ) +
  theme(legend.position = "none")
Figure 1: Magnus’s championship probability conditional on his Round 10 result. A win dramatically improves his odds.
Code 
kable(
  cond_data %>%
    mutate(
      `Championship Prob` = sprintf("%.1f%%", `Championship Prob` * 100),
      `N Simulations` = format(`N Simulations`, big.mark = ",")
    ),
  caption = "Championship probability by Round 10 outcome"
)
Championship probability by Round 10 outcome
Round 10 Result Championship Prob N Simulations
2 Win 91.2% 7,999
0 Draw 77.9% 9,106
1 Loss 58.3% 2,895

Distribution of Final Scores

Code 
results_r <- py$results

ggplot(results_r, aes(x = focus_pts, fill = focus_rd10_outcome)) +
  geom_histogram(binwidth = 0.5, position = "identity", alpha = 0.7, color = "white") +
  scale_fill_manual(
    values = c("Win" = "#2E7D32", "Draw" = "#FFA000", "Loss" = "#C62828"),
    name = "Round 10"
  ) +
  labs(
    title = "Distribution of Magnus's Final Score",
    subtitle = "Across 20,000 simulated tournament continuations",
    x = "Final Points (after Round 13)",
    y = "Number of Simulations",
    caption = "Starting from 7.0 points after Round 9"
  ) +
  theme(legend.position = "top")
Figure 2: Distribution of Magnus’s final score across all simulations, colored by Round 10 result.
Code 
score_summary <- results_r %>%
  group_by(focus_rd10_outcome) %>%
  summarise(
    `Mean Score` = mean(focus_pts),
    `Median Score` = median(focus_pts),
    `Min Score` = min(focus_pts),
    `Max Score` = max(focus_pts),
    .groups = "drop"
  ) %>%
  rename(`Round 10` = focus_rd10_outcome) %>%
  arrange(desc(`Mean Score`))

kable(score_summary, digits = 2, caption = "Summary statistics for Magnus's final score")
Summary statistics for Magnus’s final score
Round 10 Mean Score Median Score Min Score Max Score
Win 13.26 13.5 11.5 14.5
Draw 12.76 13.0 11.0 14.0
Loss 12.29 12.5 10.5 13.5

Winning Score Analysis

What score is needed to win this tournament?

Code 
ggplot(results_r, aes(x = max_pts)) +
  geom_histogram(binwidth = 0.5, fill = "#1565C0", color = "white", alpha = 0.8) +
  geom_vline(aes(xintercept = mean(max_pts)), color = "#FF6F00", linetype = "dashed", linewidth = 1) +
  annotate("text", x = mean(results_r$max_pts) + 0.3, y = Inf,
           label = sprintf("Mean: %.1f", mean(results_r$max_pts)),
           vjust = 2, hjust = 0, color = "#FF6F00", fontface = "bold") +
  labs(
    title = "Distribution of Tournament-Winning Score",
    subtitle = "What score does the eventual winner typically achieve?",
    x = "Winning Score (Points)",
    y = "Number of Simulations"
  )
Figure 3: Distribution of the winning score across all simulations. The tournament appears to require around 10-11 points to win.

Ties for First Place

Code 
tie_stats <- results_r %>%
  summarise(
    `Sole Winner` = mean(n_tied == 1),
    `2-Way Tie` = mean(n_tied == 2),
    `3+ Way Tie` = mean(n_tied >= 3)
  )

In Swiss tournaments, ties are common. Across our simulations:

  • 79.4% of tournaments end with a sole winner
  • 13.6% end in a 2-way tie
  • 7.0% end in a 3+ way tie

Caveats and Limitations

This simulation has several important limitations:

Simulation Limitations

  1. Approximate Swiss pairings: Rounds 11-13 use a simplified pairing algorithm that doesn’t enforce:

    • No repeat pairings
    • Strict color alternation
    • Full FIDE floating priorities

  2. No tiebreaks: We only consider final point totals, not Buchholz, Sonneborn-Berger, or other tiebreak criteria

  3. Static Elo model: Player form can vary significantly in rapid chess; we assume consistent performance

  4. Top-80 focus: We simulate only the top 80 players by points/rating to keep computation tractable

Despite these limitations, the simulation provides valuable insight into the probability landscape heading into the tournament’s final day.

Conclusion

Monte Carlo simulation reveals the high-variance nature of Swiss system tournaments. Even with a relatively small number of rounds remaining, the uncertainty compounds across games and pairings.

For Magnus Carlsen, the message is clear: Round 10 is crucial. A win would significantly boost his championship odds, while a loss would make an already challenging path considerably steeper.

The beauty of Swiss tournaments is that dramatic comebacks remain possible—but the mathematics of probability suggest Magnus needs to maximize his point total starting now.

Technical Notes

This analysis uses:

  • Python for Monte Carlo simulation and web scraping from Chess-Results
  • R/ggplot2 for data visualization
  • Quarto for reproducible polyglot data science
  • Reticulate for seamless Python-R integration

Data is scraped live from Chess-Results at render time.

Analysis current as of December 28, 2025, after Round 9 of the World Rapid Championship.