Predicts chess tournament outcomes by simulating millions of possible futures. Given a tournament schedule and player ratings, it estimates each player's chance of winning the tournament, expected final score, and per-game win/draw/loss probabilities, updated after every round.
Project page: https://vltanh.github.io/projects/chess-monte-carlo-simulation/
Direct links to the interactive dashboards:
- Open: https://vltanh.github.io/assets/chess/candidates2026.html
- Women: https://vltanh.github.io/assets/chess/candidateswomen2026.html
A self-contained interactive HTML page (no server, no dependencies) generated by tools/viz/generate_html.py. Features:
- Win probability timeline with per-player toggle chips and round selector
- Standings table with sortable columns, inline win-% bars, and player ratings
- Title race chart showing contenders vs eliminated players (✗), determined by a 4-phase algorithm: max-reachable-points → per-game guaranteed floor → 1M uniform sampling → exhaustive DFS
- Scenario explorer: interactive SVG decision tree - inject hypothetical results, follow truth, or find winning paths for any player (weighted/uniform sampling → precomputed path → DFS fallback); breadcrumb trail with inline edit popovers
- Match predictions: per-game win/draw/loss bars for every round, with actual results highlighted in gold; collapsible past/future round panels
- Rank distribution heatmap with sortable columns and color-intensity scaling
- Expected final score timeline tracking projected points across rounds
- Hyperparameter appendix: Pareto front scatter chart, best-trial table, grouped parameter display
- Player info table with FIDE IDs and Classical/Rapid/Blitz ratings
- Dark theme, mobile-responsive, smooth animations, custom scrollbars
The commentary below covers the Open section only. See the Women's dashboard for the Women's section.
Round 14 results: Fabi beat Esipenko, Pragg–Hikaru drew, Anish beat Bluebaum, Sindarov–Wei Yi drew
- ✗ Fabi beat Esipenko: draw predicted at 50.2%; Fabi won (29.6%); model rightly had Fabi's winning chances above Esipenko's (20.1%)
- ✓ Pragg–Hikaru drew: draw predicted at 52.5%; correct prediction
- ✗ Anish beat Bluebaum: draw predicted at 52.8%; Anish won (25.0%); model rightly had Anish's winning chances above Bluebaum's (22.2%)
- ✓ Sindarov–Wei Yi drew: draw predicted at 46.7%; correct prediction; Sindarov coasted to the title with a draw
Sindarov wins the 2026 Candidates Tournament with 10.0/14, a full 1.5 points clear of Anish Giri. Sindarov earns the right to challenge the World Champion in the 2026 World Championship match.
Final standings vs pre-tournament prediction (Round 1):
| Rank | Player | Final Pts | Expected Pts (R1) | Δ | Pre-tournament win prob |
|---|---|---|---|---|---|
| 1 | Sindarov | 10.0 | 7.32 | +2.68 | 16.1% (3rd favorite) |
| 2 | Anish | 8.5 | 7.00 | +1.50 | 11.3% (5th) |
| 3 | Fabi | 7.5 | 7.60 | −0.10 | 21.6% (1st favorite) |
| 4 | Wei Yi | 7.0 | 7.07 | −0.07 | 12.6% (4th) |
| 5 | Hikaru | 6.5 | 7.41 | −0.91 | 18.8% (2nd favorite) |
| 6 | Bluebaum | 6.0 | 6.81 | −0.81 | 8.5% (6th) |
| 7 | Pragg | 6.0 | 6.40 | −0.40 | 5.7% (7th) |
| 8 | Esipenko | 4.5 | 6.39 | −1.89 | 5.5% (8th) |
- Biggest upset vs model: Sindarov, the 3rd-favorite at 16.1%, crushed expectation by +2.68 points and ran away with the title. A tournament-long outperformance rather than a single hot streak.
- Second surprise: Anish (5th-favorite, 11.3%) finished clear 2nd at +1.50 above expectation.
- Model's top two underdelivered: Fabi (favorite, 21.6%) finished 3rd near his expected points; Hikaru (2nd-favorite, 18.8%) faded to 5th at −0.91.
- Worst underperformer: Esipenko at −1.89, matching his pre-tournament weak prospect but finishing even below floor expectations.
- Model calibration: the pre-tournament favorites did not win, but the expected-points were close for 5 of 8 players (|Δ|<1.0). The two tails (Sindarov +2.68, Esipenko −1.89) reflect that rating-based priors plus velocity adjustments still underweight in-tournament form swings.
Overall model performance, good and bad:
Parameters were tuned on 2022 and 2024 Candidates, which may have different characteristics than 2026.
Good calls:
- Win-chance ordering within matches: when "draw" was modal but a decisive result occurred (Wei Yi–Esipenko R13, Fabi–Esipenko R14, Anish–Bluebaum R14), the actual winner was usually the side assigned higher win probability.
- Expected points close for 5/8 players: Fabi, Wei Yi, Hikaru, Bluebaum, Pragg all within ±1.0 of projection.
- Eventually caught Sindarov's rise: although slow to lift him above Fabi and Hikaru early, once Sindarov's lead opened up the model tracked it cleanly. Title probability climbed through the middle rounds and converged fast at the end (95.8% → 98.2% → 99.5% → 100%), with a reasonable narrowing of remaining scenarios round by round.
Poor calls:
- Draw model over-predicts: nearly every close-rated game defaulted to "draw most likely". Perfect 4/4 all-draw rounds (R11, R12) partly an artifact of spamming draws, not real discrimination.
- Velocity term under-reacts: pre-tournament, model blends static Elo with recent rating trajectory to estimate entering strength. Blend too conservative: Sindarov's upward trajectory left him at 3rd-favorite, not co-favorite.
- Form term under-reacts: in-tournament, model updates strength from round results. Update too slow: Sindarov's early dominance lagged in winner-probability, Esipenko's collapse (−1.89) not tracked.
Takeaway: solid at aggregate probabilities once leader is clear. Weak at draw prediction (over-applied) and at reacting to form shifts (both velocity and in-tournament form under-weighted).
Round 14
Round 13 results: Wei Yi beat Esipenko, Anish–Sindarov drew, Hikaru–Bluebaum drew, Fabi–Pragg drew
- ✓ Anish–Sindarov drew: draw predicted at 48.6%; correct prediction; the draw mathematically clinches the tournament for Sindarov
- ✓ Hikaru–Bluebaum drew: draw predicted at 52.4%; correct prediction
- ✓ Fabi–Pragg drew: draw predicted at 44.9%; correct prediction; Fabi's inability to convert as favourite persists to the final
- ✗ Wei Yi beat Esipenko: draw predicted at 54.4%; Wei Yi won; the model correctly placed Wei Yi's winning chances (26.1%) well above Esipenko's (19.5%)
- Sindarov has clinched the title at 100% — at 9.5/13, his lead is mathematically uncatchable with one round to play; Anish locked into 2nd at 8.0 max
Standings after R13 (1 round remaining):
| Player | Pts | Max | Status |
|---|---|---|---|
| Sindarov | 9.5 | 10.5 | 1st clinched (100%) |
| Anish | 7.5 | 8.5 | 2nd locked (100%) |
| Fabi | 6.5 | 7.5 | 3rd most likely (51.1%); can finish 3rd–6th |
| Wei Yi | 6.5 | 7.5 | 3rd at 25.2%; can finish 3rd–6th |
| Bluebaum | 6.0 | 7.0 | 3rd at 14.8%; can finish 3rd–7th |
| Hikaru | 6.0 | 7.0 | 3rd at 9.0%; can finish 3rd–7th |
| Pragg | 5.5 | 6.5 | Eliminated from top 3; 7th most likely (74.3%), can finish 4th–8th |
| Esipenko | 4.5 | 5.5 | 8th locked at 95.2%; can finish 7th–8th |
Round 14 predictions:
- Esipenko–Fabi: 20.1% / 50.2% / 29.6%, draw most likely; Fabi with higher winning chances
- Pragg–Hikaru: 21.0% / 52.5% / 26.5%, draw most likely; Hikaru with higher winning chances
- Bluebaum–Anish: 22.2% / 52.8% / 25.0%, draw most likely; Anish with slight win edge
- Sindarov–Wei Yi: 32.1% / 46.7% / 21.2%, draw most likely; Sindarov with higher winning chances even with the title already secured
Round 13
Round 12 results: Esipenko–Pragg drew, Bluebaum–Fabi drew, Sindarov–Hikaru drew, Wei Yi–Anish drew
- ✓ Esipenko–Pragg drew: draw predicted at 50.2%; correct prediction
- ✓ Bluebaum–Fabi drew: draw predicted at 54.1%; correct prediction
- ✓ Sindarov–Hikaru drew: draw predicted at 47.8%; correct prediction; Sindarov continues to coast toward the title
- ✓ Wei Yi–Anish drew: draw predicted at 49.1%; correct prediction; Anish needed a win but could not break through
- Perfect 4/4 round - the second consecutive all-draw round called correctly
- Win probs: Sindarov rose to 99.5% (from 98.2%); Anish slipped to 0.5% (from 1.8%); Fabi eliminated at 0.0% (from 0.01%)
Standings after R12 (2 rounds remaining):
| Player | Pts | Max | Status |
|---|---|---|---|
| Sindarov | 9.0 | 11.0 | Virtually clinched; min score of 9.0 already unreachable by all but Anish |
| Anish | 7.0 | 9.0 | Only remaining challenger (0.5%); must beat Sindarov in R13 |
| Fabi | 6.0 | 8.0 | Eliminated - max 8.0 cannot catch Sindarov's floor of 9.0 |
| Bluebaum | 5.5 | 7.5 | Eliminated |
| Wei Yi | 5.5 | 7.5 | Eliminated |
| Hikaru | 5.5 | 7.5 | Eliminated |
| Pragg | 5.0 | 7.0 | Eliminated |
| Esipenko | 4.5 | 6.5 | Eliminated |
What would it take?
- Sindarov (99.5%): already at 9.0 with 2 to play. Even losing both remaining games keeps him at 9.0, which only Anish can match (at best). A single draw in R13 (vs Anish) seals the title outright, as Anish could reach at most 8.5. The only path where Sindarov does not win first place: Anish beats him in R13, Anish beats Bluebaum in R14, AND Sindarov loses to Wei Yi in R14, producing a 9.0–9.0 tie decided by FIDE tiebreak.
- Anish (0.5%): 2 points behind with 2 to play. Must win both remaining games (vs Sindarov in R13, vs Bluebaum in R14) AND Sindarov must lose to Wei Yi in R14. That produces a 9.0–9.0 tie and a FIDE rapid/blitz tiebreak. A draw in R13 mathematically eliminates Anish.
Round 13 predictions:
- Wei Yi–Esipenko: 26.1% / 54.4% / 19.5%, draw most likely; Wei Yi with higher winning chances
- Anish–Sindarov: 22.3% / 48.6% / 29.0%, draw most likely; Sindarov with higher winning chances; Anish must win to stay alive
- Hikaru–Bluebaum: 28.0% / 52.4% / 19.6%, draw most likely; Hikaru with higher winning chances
- Fabi–Pragg: 38.9% / 44.9% / 16.2%, draw most likely; Fabi with higher winning chances
Round 12
Round 11 results: Anish–Esipenko drew, Hikaru–Wei Yi drew, Fabi–Sindarov drew, Pragg–Bluebaum drew
- ✓ Anish–Esipenko drew: draw predicted at 50.8%; correct prediction
- ✓ Hikaru–Wei Yi drew: draw predicted at 48.2%; correct prediction
- ✓ Fabi–Sindarov drew: draw predicted at 41.5%; correct prediction
- ✓ Pragg–Bluebaum drew: draw predicted at 51.8%; correct prediction
- Perfect 4/4 round - all four draws called correctly
- Win probs: Sindarov rose to 98.2% (from 95.8%); Anish slipped to 1.8% (from 3.9%); Fabi at 0.01% (from 0.3%) - a rounding error away from elimination
Round 12 predictions:
- Esipenko–Pragg: 25.7% / 50.2% / 24.1%, draw most likely; essentially even; a dead rubber for both eliminated players
- Bluebaum–Fabi: 22.1% / 54.1% / 23.8%, draw most likely; Fabi must win to keep any hope alive
- Sindarov–Hikaru: 31.3% / 47.8% / 20.9%, draw most likely; Sindarov with higher winning chances; a win clinches the tournament outright
- Wei Yi–Anish: 24.1% / 49.1% / 26.9%, draw most likely; Anish with higher winning chances; must win to have any chance in R13
Round 11
Round 10 results: Esipenko–Bluebaum drew, Sindarov beat Pragg, Wei Yi–Fabi drew, Anish–Hikaru drew
- ✓ Esipenko–Bluebaum drew: draw predicted at 47.5%; correct prediction
- ✓ Wei Yi–Fabi drew: draw predicted at 47.1%; correct prediction
- ✓ Anish–Hikaru drew: draw predicted at 48.6%; correct prediction
- ✗ Sindarov beat Pragg: draw predicted at 45.5%; Sindarov won; the model correctly placed Sindarov's winning chances (36.9%) well above Pragg's (17.6%)
- Win probs: Sindarov surged to 95.8% (from 87.4%) after extending his lead; Anish slipped to 3.9% (from 9.9%) after the draw; Fabi collapsed to 0.3% (from 1.7%) - effectively out of contention
Round 11 predictions:
- Anish–Esipenko: 30.1% / 50.8% / 19.1%, draw most likely; Anish with higher winning chances
- Hikaru–Wei Yi: 28.5% / 48.2% / 23.3%, draw most likely; Hikaru with higher winning chances
- Fabi–Sindarov: 30.6% / 41.5% / 28.0%, draw most likely; essentially even; Fabi needs a win to have any hope of catching Sindarov
- Pragg–Bluebaum: 24.1% / 51.8% / 24.0%, draw most likely; essentially even
Round 10
Round 9 results: Hikaru–Esipenko drew, Anish beat Fabi, Pragg–Wei Yi drew, Bluebaum–Sindarov drew
- ✓ Hikaru–Esipenko drew: draw predicted at 45.5%; correct prediction
- ✓ Pragg–Wei Yi drew: draw predicted at 43.9%; correct prediction; Pragg had a winning position but blundered to a draw despite being the lower-probability side (25.3% vs Wei Yi's 30.9%)
- ✓ Bluebaum–Sindarov drew: draw predicted at 46.3%; correct prediction; Sindarov had a winning position but blundered to a draw
- ✗ Anish beat Fabi: draw predicted at 40.5% with Fabi win at 38.5%; Anish won despite having lower winning chances (21.0% vs 38.5%); wrong direction
- Win probs: Sindarov holds at 87.4% (from 85.8%); Anish surged to 9.9% (from 4.0%) after the upset win; Fabi collapsed to 1.7% (from 8.3%)
Round 10 predictions:
- Esipenko–Bluebaum: 23.6% / 47.5% / 28.9%, draw most likely; Bluebaum with higher winning chances
- Sindarov–Pragg: 36.9% / 45.5% / 17.6%, draw most likely; Sindarov with higher winning chances
- Wei Yi–Fabi: 25.7% / 47.1% / 27.1%, draw most likely; essentially even; Fabi needs a win to keep any hope alive
- Anish–Hikaru: 27.0% / 48.6% / 24.3%, draw most likely; Anish with higher winning chances
Round 9
Round 8 results: Esipenko–Sindarov drew, Wei Yi–Bluebaum drew, Anish beat Pragg, Hikaru beat Fabi
- ✓ Wei Yi–Bluebaum drew: draw predicted at 47.4%; correct prediction
- ✗ Esipenko–Sindarov drew: Sindarov win predicted at 41.2% over draw at 40.8%; Sindarov drew; a leader with Black and a near-insurmountable lead has every incentive to play for safety, which the model's standing-based draw multiplier only partially captures
- ✗ Anish beat Pragg: draw predicted at 51.2%; Anish won; the model correctly placed Anish's winning chances (28.6%) above Pragg's (20.2%)
- ✗ Hikaru beat Fabi: draw predicted at 47.4%; Hikaru won; the model gave Hikaru an extremely marginal win edge (26.33% vs 26.27%); effectively no directional signal
- Win probs: Sindarov climbed to 85.8% (from 80.6%); Fabi dropped sharply to 8.3% (from 15.9%) after the loss; Anish rose to 4.0% (from 1.5%) after the win
Round 9 predictions:
- Hikaru–Esipenko: 34.9% / 45.5% / 19.6%, draw most likely; Hikaru with higher winning chances
- Fabi–Anish: 38.5% / 40.5% / 21.0%, draw most likely; Fabi with higher winning chances; key duel for second place
- Pragg–Wei Yi: 25.3% / 43.9% / 30.9%, draw most likely; Wei Yi with higher winning chances
- Bluebaum–Sindarov: 21.0% / 46.3% / 32.7%, draw most likely; Sindarov with higher winning chances
Round 8
Round 7 results: Wei Yi beat Esipenko, Sindarov–Anish drew, Bluebaum–Hikaru drew, Pragg–Fabi drew
- ✓ Sindarov–Anish drew: draw predicted at 43.4%; correct prediction
- ✓ Bluebaum–Hikaru drew: draw predicted at 49.4%; correct prediction
- ✓ Pragg–Fabi drew: draw predicted at 44.4%; correct prediction
- ✗ Wei Yi beat Esipenko: draw predicted at 46.2%; Wei Yi won; the model correctly placed Wei Yi's winning chances (30.1%) above Esipenko's (23.7%)
- Sindarov barely moved: 80.6% (from 78.8%); drawing cost almost nothing with the lead this large; Fabi slipped to 15.9% (from 16.8%)
Round 8 predictions:
- Esipenko–Sindarov: 18.0% / 40.8% / 41.2%, Sindarov win the top prediction; Esipenko at 2/7 was an extreme underdog
- Wei Yi–Bluebaum: 28.5% / 47.4% / 24.1%, draw most likely; Wei Yi with higher winning chances
- Anish–Pragg: 28.6% / 51.2% / 20.2%, draw most likely; Anish with higher winning chances
- Hikaru–Fabi: 26.3% / 47.4% / 26.3%, draw most likely; perfectly balanced; Fabi needs a win to stay alive
Round 7
Round 6 results: Fabi–Esipenko drew, Hikaru–Pragg drew, Anish–Bluebaum drew, Sindarov beat Wei Yi
- ✓ Hikaru–Pragg drew: draw predicted at 48.1%; correct prediction
- ✓ Anish–Bluebaum drew: draw predicted at 48.7%; correct prediction
- ✗ Fabi–Esipenko drew: Fabi win predicted at 43.6% with draw at 40.5%; the game ended in a draw; Fabi's inability to convert against lower-rated players is the central story
- ✗ Sindarov beat Wei Yi: draw predicted at 47.3%; Sindarov won; the model correctly placed Sindarov's winning chances (29.7%) above Wei Yi's (23.1%)
- Win probs: Sindarov surged to 78.8% (from 62.2%) while Fabi dropped to 16.8% (from 28.1%); Fabi's draw combined with Sindarov's win collapsed the race
Round 7 predictions:
- Esipenko–Wei Yi: 23.7% / 46.2% / 30.1%, draw most likely; Wei Yi with higher winning chances
- Sindarov–Anish: 34.5% / 43.4% / 22.1%, draw most likely; Sindarov with higher winning chances
- Bluebaum–Hikaru: 24.0% / 49.4% / 26.6%, draw most likely; Hikaru with slight win edge
- Pragg–Fabi: 23.1% / 44.4% / 32.6%, draw most likely; Fabi with higher winning chances; needs points to stay in contention
Round 6
Round 5 results: Pragg–Esipenko drew, Fabi beat Bluebaum, Sindarov beat Hikaru, Anish–Wei Yi drew
- ✓ Pragg–Esipenko drew: draw predicted at 44.8%; correct prediction
- ✓ Anish–Wei Yi drew: draw predicted at 48.5%; correct prediction
- ✗ Fabi beat Bluebaum: draw predicted at 46.3%; Fabi won; the model correctly placed Fabi's winning chances (35.4%) above Bluebaum's (18.3%)
- ✗ Sindarov beat Hikaru: draw predicted at 49.4%; Sindarov won despite Hikaru having the marginal win edge (25.6% vs 25.0%); wrong direction by the narrowest margin
- Win probs: Sindarov extended his lead to 62.2% (from 51.1%), Fabi recovered slightly to 28.1% (from 24.9%); Sindarov's 4.5/5 gave him commanding odds
Round 6 predictions:
- Fabi–Esipenko: 43.6% / 40.5% / 15.8%, Fabi win the top prediction; model expected him to capitalize on the rating gap and close on Sindarov
- Hikaru–Pragg: 31.8% / 48.1% / 20.1%, draw most likely; Hikaru with higher winning chances
- Anish–Bluebaum: 28.9% / 48.7% / 22.4%, draw most likely; Anish with higher winning chances
- Wei Yi–Sindarov: 23.1% / 47.3% / 29.7%, draw most likely; Sindarov with higher winning chances
Round 5
Round 4 results: Anish beat Esipenko, Wei Yi–Hikaru drew, Sindarov beat Fabi, Bluebaum–Pragg drew
- ✓ Wei Yi–Hikaru drew: draw predicted at 49.3%; correct prediction
- ✓ Bluebaum–Pragg drew: draw predicted at 51.9%; correct prediction
- ✗ Sindarov beat Fabi: draw predicted at 50.8%; Sindarov won; the model barely placed Sindarov's winning chances (25.2%) above Fabi's (24.0%); the tournament's turning point as Sindarov opened a 1-point lead
- ✗ Anish beat Esipenko: draw predicted at 49.2%; Anish won; the model correctly placed Anish's winning chances (26.5%) above Esipenko's (24.3%)
- Win probs swung sharply: Sindarov surged to 51.1% (from 32.0%) while Fabi collapsed to 24.9% (from 44.1%); Sindarov now a clear favourite at 3.5/4
Round 5 predictions:
- Pragg–Esipenko: 30.5% / 44.8% / 24.7%, draw most likely; Pragg with higher winning chances
- Fabi–Bluebaum: 35.4% / 46.3% / 18.3%, draw most likely; Fabi with higher winning chances; key bounce-back opportunity after R4 loss
- Hikaru–Sindarov: 25.6% / 49.4% / 25.0%, draw most likely; near three-way split
- Anish–Wei Yi: 27.9% / 48.5% / 23.5%, draw most likely; Anish with higher winning chances after R4 win
Round 4
Round 3 results: Bluebaum–Esipenko drew, Sindarov beat Pragg, Fabi beat Wei Yi, Hikaru–Anish drew
- ✓ Bluebaum–Esipenko drew: draw predicted at 49.2%; correct prediction
- ✓ Hikaru–Anish drew: draw predicted at 47.9%; correct prediction
- ✗ Fabi beat Wei Yi: draw predicted at 48.8%; Fabi won; the model correctly placed Fabi's winning chances (31.6%) above Wei Yi's (19.6%)
- ✗ Sindarov beat Pragg: draw predicted at 49.8%; Sindarov won; the model correctly placed Sindarov's winning chances (28.1%) above Pragg's (22.1%)
- Win probs surged for both winners: Fabi jumped to 44.1% (from 33.3%), Sindarov climbed to 32.0% (from 23.0%); Fabi led despite equal standing, and the model weighed opponent quality
Round 4 predictions:
- Esipenko–Anish: 24.3% / 49.2% / 26.5%, draw most likely; Anish with slight win edge
- Wei Yi–Hikaru: 25.8% / 49.3% / 24.9%, draw most likely; essentially even
- Sindarov–Fabi: 25.2% / 50.8% / 24.0%, draw most likely; essentially even; the key clash between the top two
- Bluebaum–Pragg: 27.2% / 51.9% / 20.9%, draw most likely; Bluebaum with higher winning chances
Round 3
Round 2 results: ALL FOUR games drew: Esipenko–Hikaru, Anish–Fabi, Wei Yi–Pragg, Sindarov–Bluebaum
- ✓ Esipenko–Hikaru drew: draw predicted at 48.8%; correct prediction
- ✓ Anish–Fabi drew: draw predicted at 51.6%; correct prediction
- ✓ Wei Yi–Pragg drew: draw predicted at 50.9%; correct prediction
- ✓ Sindarov–Bluebaum drew: draw predicted at 49.0%; correct prediction
- Win probs barely shifted after four draws: Fabi held at 33.3% (from 32.4%), Sindarov slipped to 23.0% (from 23.5%), Pragg ticked up to 10.6% (from 9.7%)
Round 3 predictions:
- Bluebaum–Esipenko: 30.5% / 49.2% / 20.3%, draw most likely; Bluebaum with higher winning chances; Esipenko's R1 loss widened the rating gap
- Pragg–Sindarov: 22.1% / 49.8% / 28.1%, draw most likely; Sindarov with higher winning chances as his R1 win carries forward
- Fabi–Wei Yi: 31.6% / 48.8% / 19.6%, draw most likely; Fabi with higher winning chances as the pre-tournament front-runner
- Hikaru–Anish: 31.6% / 47.9% / 20.5%, draw most likely; Hikaru with higher winning chances as White despite R1 loss
Round 2
Round 1 results: Fabi beat Hikaru, Sindarov beat Esipenko, Pragg beat Anish, Bluebaum–Wei Yi drew
- ✗ Fabi beat Hikaru: draw predicted at 51.9%; Fabi won; the model correctly placed Fabi's winning chances (26.5%) above Hikaru's (21.5%)
- ✗ Sindarov beat Esipenko: draw predicted at 50.5%; Sindarov won; the model correctly placed Sindarov's winning chances (31.8%) above Esipenko's (17.7%)
- ✓ Bluebaum–Wei Yi drew: draw predicted at 51.5%; correct prediction
- ✗ Pragg beat Anish: draw predicted at 51.6%; Pragg won despite Anish having higher winning chances (26.5% vs 21.9%); wrong direction
- All three R1 winners jumped sharply: Fabi 21.5% → 32.4%, Sindarov 16.1% → 23.5%, Pragg 5.7% → 9.7%; strong priors still amplified single-game results immediately
Round 2 predictions:
- Esipenko–Hikaru: 21.7% / 48.8% / 29.5%, draw most likely; Hikaru with higher winning chances
- Anish–Fabi: 22.0% / 51.6% / 26.4%, draw most likely; Fabi with higher winning chances
- Wei Yi–Pragg: 30.1% / 50.9% / 19.0%, draw most likely; Wei Yi with higher winning chances
- Sindarov–Bluebaum: 31.2% / 49.0% / 19.8%, draw most likely; Sindarov with higher winning chances
Round 1
Pre-tournament predictions
- Fabi was the favourite at 21.5%: consistent profile across all three time controls gave a stable overall estimate
- Hikaru at 18.7% despite the highest classical Elo (2810): flat classical trend and weaker rapid/blitz velocity
- Sindarov at 16.1% with only 2745 Elo: strongly rising classical trend [2721→2745, +24 pts] and improving rapid history; the model rewarded recent momentum
- Bluebaum at 8.5% for a 2695-rated player: positive classical trend with no drag from weak secondary time controls
- Pragg at only 5.7% despite his FIDE ranking: classical rating falling [2768→2741, −27 pts]; the model tracked the trend, not the name
Round 1 predictions:
- Fabi–Hikaru: 26.5% / 51.9% / 21.5%, draw most likely; Fabi with higher winning chances
- Pragg–Anish: 21.9% / 51.6% / 26.5%, draw most likely; Anish with higher winning chances
- Bluebaum–Wei Yi: 24.0% / 51.5% / 24.5%, draw most likely; essentially even
- Sindarov–Esipenko: 31.8% / 50.5% / 17.7%, draw most likely; Sindarov with higher winning chances
src/
chess_montecarlo.cpp Main C++ simulation engine (parametric draw model)
chess_montecarlo_alt.cpp Experimental variant using an ordered-logit outcome model
json.hpp, pcg_random.hpp, pcg_extras.hpp Third-party headers (fetched by install.sh)
bin/ Compiled binary (chess_montecarlo)
configs/ Hyperparameter files (tuned presets and defaults)
data/
players.jsonc Player registry (name, alias, FIDE ID)
<tournament>.jsonc Tournament definition (schedule, players, tiebreak mode)
raw/ Cached FIDE rating histories and Lichess PGN downloads
db/ Optuna SQLite databases from hyperparameter tuning
results/ Raw simulation data, one JSON per round, the source of truth
<tournament>/ round1.json ... round{N}.json (output of generate_rounds.py)
imgs/ Rendered images used by the README and project page
tools/
data/
build_tournament.py Build tournament JSONC from a Lichess broadcast + FIDE ratings
tuning/
tune.py Optuna multi-objective hyperparameter search
evaluate.py Score a fixed hyperparameter set against tournament data
pareto_front.py Plot Optuna Pareto front and print best trials
utils.py Shared scoring utilities
viz/
generate_rounds.py Run the C++ engine for each round, save JSON outputs → results/
visualize_timeline.py Render per-round dashboard PNGs from round JSONs → imgs/
generate_html.py Bundle template.html + viz.css + viz.js into a self-contained dashboard
template.html HTML shell for the interactive dashboard (CSS/JS injected at build)
viz.css Styles for the interactive dashboard
viz.js Chart.js logic, scenario explorer, table interactions
install.sh Setup: fetches json.hpp + PCG headers, compiles C++, installs Python deps
example.sh Full end-to-end workflow example
Each player starts with a projected rating based on their FIDE Classical, Rapid, and Blitz histories. Before each simulated game, the model computes win/draw/loss probabilities from the two players' ratings, adjusted for who has the white pieces, how aggressively each player tends to play, and how desperate they are based on the standings. After each round, ratings are updated to reflect actual (or simulated) results. This process repeats millions of times; the fraction of simulations each player wins is their estimated win probability.
- Dynamic Bayesian ratings: per-player White/Black strength estimates updated every round via MAP inference
- Velocity projection: recent rating trends across Classical/Rapid/Blitz are extrapolated forward - rising players get credit, declining players get penalized
- Parametric draw model: draw probability depends on time control (classical games draw far more than rapid/blitz) and is scaled by player style and tournament situation
- Style multiplier: aggressive pairings (many decisive games historically) shrink the draw band; solid pairings inflate it
- Standings multiplier: players behind in the standings play more aggressively; comfortable leaders play more conservatively
- FIDE tiebreak modes:
fide2026(Rapid → Blitz → Armageddon),fide2024(Rapid → Blitz → sudden-death Blitz), orshared(split probability evenly) - Parallel simulation: uses all CPU cores via
std::thread
g++ -O3 -march=native -std=c++17 -pthread src/chess_montecarlo.cpp -o bin/chess_montecarloRequires a C++17 compiler. Third-party headers (fetched into src/ by install.sh):
json.hppfor JSON parsingpcg_random.hppfor fast, high-quality random number generation
Or use the install script, which fetches the headers, builds the binary, and sets up Python dependencies:
bash install.sh./bin/chess_montecarlo configs/best_hparams_22_24.jsonc data/candidates2026.jsonc 8 > round8.jsonArguments: [hyperparameters.jsonc] [tournament.jsonc] [simulate_from_round]. The third argument (default 1) controls which round to start simulating from - earlier rounds use actual results. Output is JSON to stdout.
Output fields:
| Field | Description |
|---|---|
winner_probs |
Tournament win probability per player |
expected_points |
Average final score per player |
rank_matrix |
Probability of finishing in each position |
game_probs |
Per-game win/draw/loss probabilities by round |
python tools/data/build_tournament.py BLA70Vds -o data/candidates2026.jsonc
python tools/data/build_tournament.py BLA70Vds --tiebreak fide2026
python tools/data/build_tournament.py BLA70Vds --as-of 2024-04 # slice FIDE history
python tools/data/build_tournament.py BLA70Vds --no-fide # skip FIDE fetchRequires pip install requests python-chess.
The two directories play distinct roles: results/ holds raw simulation data (one JSON per round, treated as the source of truth); imgs/ holds rendered visualizations derived from it. Every visualization script reads from results/ and writes into imgs/.
# 1. Simulate all rounds → results/ (one JSON file per round)
python tools/viz/generate_rounds.py configs/best_hparams_22_24.jsonc data/candidates2026.jsonc results/candidates2026/
# 2. Render per-round dashboard PNGs → imgs/candidates2026/
python tools/viz/visualize_timeline.py results/candidates2026/
# 3. Generate the self-contained interactive HTML dashboard
# (reads from results/, writes a single HTML file wherever you point --output)
python tools/viz/generate_html.py \
--tournament data/candidates2026.jsonc \
--rounds results/candidates2026/ \
--hparams configs/best_hparams_22_24.jsonc \
--db db/tuning_22_24.db \
--output candidates2026.htmlRequires pip install matplotlib pandas numpy pillow.
python tools/tuning/tune.py configs/default_hparams.jsonc data/candidates2022.jsonc data/candidates2024.jsonc \
--db db/tuning_22_24.db --trials 10000Uses Optuna to minimize two objectives simultaneously:
- Weighted Game Brier Score - how well individual game outcomes are predicted
- Rank RPS - how well final tournament standings are predicted
# Visualize Pareto front
python tools/tuning/pareto_front.py db/tuning_22_24.db --save imgs/pareto/tuning_22_24.png
python tools/tuning/evaluate.py configs/best_hparams_22_24.jsonc data/candidates2022.jsonc data/candidates2024.jsoncReports per-round: Game Brier, Winner Brier, Points MSE, and Rank RPS.
Hyperparameters (configs/best_hparams_22_24.jsonc): Key groups - simulation settings (runs, map_iters), MAP priors (prior_weight_known/sim), rating initialization (initial_white_adv, velocity_time_decay, lookahead_factor), cross-time-control blending (rapid_form_weight, blitz_form_weight, color_bleed), draw model (classical_nu, rapid_nu, blitz_nu), aggression (agg_prior_weight, default_aggression_w/b, standings_aggression).
Tournament (data/candidates2026.jsonc): Top-level fields - gpr (games per round), tiebreak mode, players array (FIDE ID, name, ratings, rating histories), schedule array (white/black FIDE IDs, round, optional result). Games without a result field are simulated.
| Parameter | Value | What it means |
|---|---|---|
initial_white_adv |
19.5 Elo | Small advantage for having the white pieces |
lookahead_factor |
5.00 | Rising players get strong credit for their trend |
velocity_time_decay |
0.313 | Recent form matters much more than older results |
classical_nu |
2.17 | Classical games draw very often |
rapid_nu / blitz_nu |
0.22 / 0.025 | Rapid and blitz are far more decisive |
standings_aggression |
0.109 | Tournament position has a small effect on playing style |
- Inspired by Thomas Dondorf's Reddit posts on Candidates simulations.
- Tournament schedules and live results via the Lichess broadcast API.
- Player ratings and rating histories via FIDE.
- Model design and C++/Python implementation developed with help from Google Gemini and Anthropic Claude.
- Interactive dashboard designed with Claude via the
/frontend-designskill.