Back to the Card Table
Card Table · evaluation
Can an LLM find the best partition?
The bonus question in Project 3 asked for every highest-scoring way to group a hand. The exact solver answers it by checking every partition. Here a language model gets the same seeded hands, returns a grouping as JSON, and is scored against the solver and two simple baselines, with uncertainty on every number.
Without a key the page still runs the solver and the baselines. With your own key, each call goes straight from your browser to the provider and is recorded in the AI audit log, where you can review and export it.
Same inputs for every player
The hands
Hand 1 is dealt from seed 2019, hand 2 from 2020, and so on, by the same dealer as the Card Table. The exact solver, the greedy baseline and the LLM all see the same hands. 30 or more hands are recommended: in a simulation, the nominal 95% interval for a mean gap held the true value 82% of the time with 10 hands and 91% with 30. Changing the hands clears results on screen; every call stays in the AI audit log.
Optional · bring your own key
Run the LLM
Checking for a key…
30 hands · seed 2019 · 10 cards each
Scoreboard
| Player | Hands | Valid grouping | Optimal | Mean gap to best (points) |
|---|---|---|---|---|
| Exact solvercomp10001go_best_partitions: every partition checked. The reference. | 30 | 100% by construction | 100% by construction | 0 by construction |
| Greedy baselineTake the best legal group left, repeat. | 30 | 100% by construction | 73% (56% to 86%) | 5.6 (1.8 to 10.6) |
| All singletonsPlay every card alone. The floor. | 30 | 100% by construction | 0% (0% to 11%) | 99.2 (81.4 to 116.1) |
| LLM claude-haiku-4-5Claude Haiku 4.5, when you run it | Not run yet. | |||
Exact solver
comp10001go_best_partitions: every partition checked. The reference.
- Hands
- 30
- Valid grouping
- 100% by construction
- Optimal
- 100% by construction
- Mean gap to best (points)
- 0 by construction
Greedy baseline
Take the best legal group left, repeat.
- Hands
- 30
- Valid grouping
- 100% by construction
- Optimal
- 73% (56% to 86%)
- Mean gap to best (points)
- 5.6 (1.8 to 10.6)
All singletons
Play every card alone. The floor.
- Hands
- 30
- Valid grouping
- 100% by construction
- Optimal
- 0% (0% to 11%)
- Mean gap to best (points)
- 99.2 (81.4 to 116.1)
LLM claude-haiku-4-5
Claude Haiku 4.5, when you run it
Not run yet.
“By construction”: the solver checks every partition and both baselines only ever play legal groups, so those cells are certain, not estimated. Rates: Wilson 95% intervals. Gaps: percentile bootstrap intervals, nominal 95%, 10,000 resamples, seed 10001; on gaps shaped like these (mostly 0, a few large) they held the true mean 91% of the time at 30 hands in a simulation, so read them as somewhat too narrow. An answer that is not a valid grouping is scored as the hand played as singletons, so failures count against the gap instead of disappearing. See how this is evaluated.
Hand by hand
Hand 1 seed 2019
ace of spades3 of diamonds3 of clubs4 of diamonds6 of hearts8 of hearts8 of diamonds9 of spadesten of heartsjack of spades- Best +67
- 4 of diamondsace of spades6 of hearts+159 of spadesten of heartsjack of spades+303 of diamonds3 of clubs+68 of hearts8 of diamonds+16
- Greedy +45
- 6 of heartsace of spades8 of hearts9 of spadesten of heartsjack of spades+513 of diamonds3 of clubs+6alone4 of diamonds8 of diamonds−12
Hand 2 seed 2020
2 of spades2 of hearts3 of spades4 of hearts7 of spades7 of hearts8 of hearts9 of diamondsten of spadesking of hearts- Best −19
- 2 of hearts3 of spades4 of hearts+97 of spades7 of hearts+14alone2 of spades8 of hearts9 of diamondsten of spadesking of hearts−42
- Greedy −19
- 7 of spades7 of hearts+142 of hearts3 of spades4 of hearts+9alone2 of spades8 of hearts9 of diamondsten of spadesking of hearts−42
Hand 3 seed 2021
2 of spades3 of clubs7 of hearts8 of hearts8 of clubs9 of hearts9 of clubsten of clubsqueen of clubsking of spades- Best −131 of 2 optima
- 7 of hearts8 of clubs9 of heartsten of clubs+34alone2 of spades3 of clubs8 of hearts9 of clubsqueen of clubsking of spades−47
- Greedy −13
- 7 of hearts8 of clubs9 of heartsten of clubs+34alone2 of spades3 of clubs8 of hearts9 of clubsqueen of clubsking of spades−47
Hand 4 seed 2022
ace of hearts2 of spades3 of hearts4 of diamonds5 of hearts7 of spades8 of diamonds8 of clubsten of heartsqueen of diamonds- Best −47
- 8 of diamonds8 of clubs+16aloneace of hearts2 of spades3 of hearts4 of diamonds5 of hearts7 of spadesten of heartsqueen of diamonds−63
- Greedy −47
- 8 of diamonds8 of clubs+16aloneace of hearts2 of spades3 of hearts4 of diamonds5 of hearts7 of spadesten of heartsqueen of diamonds−63
Hand 5 seed 2023
ace of hearts2 of spades3 of hearts3 of diamonds4 of hearts5 of hearts6 of hearts7 of spades7 of diamondsten of hearts- Best −27
- 3 of hearts3 of diamonds+67 of spades7 of diamonds+14aloneace of hearts2 of spades4 of hearts5 of hearts6 of heartsten of hearts−47
- Greedy −27
- 7 of spades7 of diamonds+143 of hearts3 of diamonds+6aloneace of hearts2 of spades4 of hearts5 of hearts6 of heartsten of hearts−47
Hand 6 seed 2024
2 of diamonds3 of diamonds3 of clubs4 of clubs6 of hearts6 of diamonds8 of heartsten of diamondsjack of spadesjack of hearts- Best +16
- 3 of diamonds3 of clubs+66 of hearts6 of diamonds+12jack of spadesjack of hearts+22alone2 of diamonds4 of clubs8 of heartsten of diamonds−24
- Greedy +16
- jack of spadesjack of hearts+226 of hearts6 of diamonds+123 of diamonds3 of clubs+6alone2 of diamonds4 of clubs8 of heartsten of diamonds−24
Hand 7 seed 2025
ace of clubs2 of diamonds4 of spades5 of diamonds5 of clubsten of diamondsqueen of spadesqueen of diamondsking of diamondsking of clubs- Best +51
- ten of diamondsace of clubsqueen of diamonds+335 of diamonds5 of clubs+10king of diamondsking of clubs+26alone2 of diamonds4 of spadesqueen of spades−18
- Greedy +25
- ten of diamondsace of clubsqueen of diamondsking of clubs+465 of diamonds5 of clubs+10alone2 of diamonds4 of spadesqueen of spadesking of diamonds−31
Hand 8 seed 2026
ace of clubs4 of hearts5 of spades5 of diamonds8 of heartsten of diamondsjack of heartsqueen of spadesking of spadesking of hearts- Best +56
- 8 of heartsace of clubsten of diamonds+27jack of heartsqueen of spadesking of hearts+365 of spades5 of diamonds+10alone4 of heartsking of spades−17
- Greedy −1
- jack of heartsace of clubsking of hearts+365 of spades5 of diamonds+10alone4 of hearts8 of heartsten of diamondsqueen of spadesking of spades−47
Hand 9 seed 2027
ace of hearts2 of spades3 of diamonds4 of spades5 of clubs6 of diamonds7 of spadesjack of diamondsqueen of spadesqueen of hearts- Best +37
- 2 of spadesace of hearts4 of spades+95 of clubs6 of diamonds7 of spades+18queen of spadesqueen of hearts+24alone3 of diamondsjack of diamonds−14
- Greedy +34
- queen of spadesqueen of hearts+245 of clubsace of hearts7 of spades+182 of spades3 of diamonds4 of spades+9alone6 of diamondsjack of diamonds−17
Hand 10 seed 2028
2 of diamonds3 of spades3 of hearts4 of spades6 of spades7 of diamonds7 of clubs9 of clubsjack of heartsqueen of spades- Best −24
- 3 of spades3 of hearts+67 of diamonds7 of clubs+14alone2 of diamonds4 of spades6 of spades9 of clubsjack of heartsqueen of spades−44
- Greedy −24
- 7 of diamonds7 of clubs+143 of spades3 of hearts+6alone2 of diamonds4 of spades6 of spades9 of clubsjack of heartsqueen of spades−44
Hand 11 seed 2029
2 of clubs6 of diamonds8 of spades8 of clubs9 of clubsten of spadesten of clubsjack of heartsqueen of diamondsking of spades- Best −17
- 8 of spades8 of clubs+16ten of spadesten of clubs+20alone2 of clubs6 of diamonds9 of clubsjack of heartsqueen of diamondsking of spades−53
- Greedy −17
- ten of spadesten of clubs+208 of spades8 of clubs+16alone2 of clubs6 of diamonds9 of clubsjack of heartsqueen of diamondsking of spades−53
Hand 12 seed 2030
2 of hearts4 of spades5 of clubs7 of diamonds7 of clubs8 of hearts9 of spadesten of diamondsjack of diamondsking of diamonds- Best +6
- 8 of hearts9 of spadesten of diamonds+277 of diamonds7 of clubs+14alone2 of hearts4 of spades5 of clubsjack of diamondsking of diamonds−35
- Greedy −8
- 7 of clubs8 of hearts9 of spadesten of diamonds+34alone2 of hearts4 of spades5 of clubs7 of diamondsjack of diamondsking of diamonds−42
Hand 13 seed 2031
ace of diamonds2 of spades6 of hearts7 of hearts9 of clubsten of spadesten of diamondsjack of spadesqueen of spadesking of diamonds- Best +61
- ten of spadesace of diamondsqueen of spadesking of diamonds+469 of clubsten of diamondsjack of spades+30alone2 of spades6 of hearts7 of hearts−15
- Greedy +61
- ten of spadesace of diamondsqueen of spadesking of diamonds+469 of clubsten of diamondsjack of spades+30alone2 of spades6 of hearts7 of hearts−15
Hand 14 seed 2032
ace of spades2 of spades2 of hearts5 of diamonds6 of diamonds7 of clubs8 of spadesten of spadesqueen of diamondsking of clubs- Best −77
- 2 of spades2 of hearts+4aloneace of spades5 of diamonds6 of diamonds7 of clubs8 of spadesten of spadesqueen of diamondsking of clubs−81
- Greedy −77
- 2 of spades2 of hearts+4aloneace of spades5 of diamonds6 of diamonds7 of clubs8 of spadesten of spadesqueen of diamondsking of clubs−81
Hand 15 seed 2033
2 of diamonds3 of clubs4 of spades5 of hearts6 of clubs7 of diamonds8 of spades8 of clubsten of clubsking of spades- Best +10
- 4 of spades5 of hearts6 of clubs7 of diamonds+228 of spades8 of clubs+16alone2 of diamonds3 of clubsten of clubsking of spades−28
- Greedy −6
- 4 of spades5 of hearts6 of clubs7 of diamonds8 of spades+30alone2 of diamonds3 of clubs8 of clubsten of clubsking of spades−36
Hand 16 seed 2034
ace of spades2 of spades2 of hearts3 of spades5 of diamonds8 of spades8 of diamonds9 of clubsten of diamondsqueen of spades- Best −6
- 8 of diamondsace of spadesten of diamonds+272 of spades2 of hearts+4alone3 of spades5 of diamonds8 of spades9 of clubsqueen of spades−37
- Greedy −6
- 8 of diamondsace of spadesten of diamonds+272 of spades2 of hearts+4alone3 of spades5 of diamonds8 of spades9 of clubsqueen of spades−37
Hand 17 seed 2035
ace of diamonds2 of spades3 of spades5 of hearts5 of diamonds5 of clubs7 of heartsten of heartsjack of spadesking of spades- Best +64
- ten of heartsjack of spadesace of diamondsking of spades+465 of hearts5 of diamonds5 of clubs+30alone2 of spades3 of spades7 of hearts−12
- Greedy +64
- ten of heartsjack of spadesace of diamondsking of spades+465 of hearts5 of diamonds5 of clubs+30alone2 of spades3 of spades7 of hearts−12
Hand 18 seed 2036
ace of spades6 of hearts6 of diamonds8 of hearts9 of spades9 of heartsten of diamondsten of clubsjack of spadesjack of diamonds- Best +751 of 6 optima
- 6 of heartsace of spades8 of hearts9 of spadesten of diamondsjack of spades+519 of heartsten of clubsjack of diamonds+30alone6 of diamonds−6
- Greedy +75
- 6 of heartsace of spades8 of hearts9 of spadesten of diamondsjack of spades+519 of heartsten of clubsjack of diamonds+30alone6 of diamonds−6
Hand 19 seed 2037
ace of clubs2 of spades3 of spades5 of spades7 of clubs8 of diamonds9 of spadesjack of heartsqueen of heartsking of diamonds- Best +38
- 7 of clubs8 of diamonds9 of spades+24jack of heartsace of clubsking of diamonds+36alone2 of spades3 of spades5 of spadesqueen of hearts−22
- Greedy +38
- jack of heartsace of clubsking of diamonds+367 of clubs8 of diamonds9 of spades+24alone2 of spades3 of spades5 of spadesqueen of hearts−22
Hand 20 seed 2038
2 of diamonds4 of diamonds5 of spades6 of diamonds6 of clubs8 of spades8 of hearts9 of hearts9 of diamondsjack of diamonds- Best +30
- 4 of diamonds5 of spades6 of diamonds+158 of spades8 of hearts+169 of hearts9 of diamonds+18alone2 of diamonds6 of clubsjack of diamonds−19
- Greedy +30
- 9 of hearts9 of diamonds+188 of spades8 of hearts+164 of diamonds5 of spades6 of diamonds+15alone2 of diamonds6 of clubsjack of diamonds−19
Hand 21 seed 2039
ace of clubs2 of diamonds3 of spades3 of hearts3 of diamonds4 of spades5 of clubs7 of hearts9 of spadesking of diamonds- Best −42
- 3 of spades3 of hearts3 of diamonds+18aloneace of clubs2 of diamonds4 of spades5 of clubs7 of hearts9 of spadesking of diamonds−60
- Greedy −42
- 3 of spades3 of hearts3 of diamonds+18aloneace of clubs2 of diamonds4 of spades5 of clubs7 of hearts9 of spadesking of diamonds−60
Hand 22 seed 2040
4 of hearts5 of hearts5 of diamonds7 of spades7 of clubs8 of spadesten of heartsjack of clubsqueen of heartsqueen of diamonds- Best +331 of 2 optima
- ten of heartsjack of clubsqueen of hearts+335 of hearts5 of diamonds+107 of spades7 of clubs+14alone4 of hearts8 of spadesqueen of diamonds−24
- Greedy +33
- ten of heartsjack of clubsqueen of hearts+337 of spades7 of clubs+145 of hearts5 of diamonds+10alone4 of hearts8 of spadesqueen of diamonds−24
Hand 23 seed 2041
ace of spadesace of diamondsace of clubs3 of hearts4 of diamonds5 of clubs9 of spades9 of diamondsqueen of diamondsking of hearts- Best +22
- 9 of diamondsace of spadesace of diamondsace of clubsking of hearts+55alone3 of hearts4 of diamonds5 of clubs9 of spadesqueen of diamonds−33
- Greedy +22
- 9 of diamondsace of spadesace of diamondsace of clubsking of hearts+55alone3 of hearts4 of diamonds5 of clubs9 of spadesqueen of diamonds−33
Hand 24 seed 2042
2 of diamonds3 of spades3 of clubs4 of clubs6 of diamonds7 of hearts9 of heartsten of heartsjack of clubsking of spades- Best −56
- 3 of spades3 of clubs+6alone2 of diamonds4 of clubs6 of diamonds7 of hearts9 of heartsten of heartsjack of clubsking of spades−62
- Greedy −56
- 3 of spades3 of clubs+6alone2 of diamonds4 of clubs6 of diamonds7 of hearts9 of heartsten of heartsjack of clubsking of spades−62
Hand 25 seed 2043
ace of spadesace of hearts2 of hearts3 of spades3 of diamonds4 of clubs5 of diamonds6 of diamonds9 of clubsqueen of diamonds- Best +43
- 9 of clubsace of heartsace of spadesqueen of diamonds+423 of diamonds4 of clubs5 of diamonds+12alone2 of hearts3 of spades6 of diamonds−11
- Greedy +43
- 9 of clubsace of heartsace of spadesqueen of diamonds+423 of diamonds4 of clubs5 of diamonds+12alone2 of hearts3 of spades6 of diamonds−11
Hand 26 seed 2044
5 of spades7 of spades7 of hearts8 of hearts9 of diamonds9 of clubsten of spadesjack of heartsqueen of diamondsking of diamonds- Best +17
- 7 of spades8 of hearts9 of clubs+249 of diamondsten of spadesjack of hearts+30alone5 of spades7 of heartsqueen of diamondsking of diamonds−37
- Greedy +17
- 9 of diamondsten of spadesjack of hearts+307 of spades8 of hearts9 of clubs+24alone5 of spades7 of heartsqueen of diamondsking of diamonds−37
Hand 27 seed 2045
2 of diamonds4 of hearts8 of hearts8 of diamonds9 of heartsten of clubsjack of diamondsqueen of spadesking of spadesking of hearts- Best +78
- 9 of heartsten of clubsjack of diamondsqueen of spades+428 of hearts8 of diamonds+16king of spadesking of hearts+26alone2 of diamonds4 of hearts−6
- Greedy +52
- 9 of heartsten of clubsjack of diamondsqueen of spadesking of hearts+558 of hearts8 of diamonds+16alone2 of diamonds4 of heartsking of spades−19
Hand 28 seed 2046
ace of spadesace of hearts2 of spades2 of clubs3 of hearts4 of diamonds5 of diamonds9 of clubsjack of spadesking of diamonds- Best +29
- 3 of heartsace of spades5 of diamonds+129 of clubsace of heartsjack of spades+302 of spades2 of clubs+4alone4 of diamondsking of diamonds−17
- Greedy +25
- 9 of clubsace of heartsjack of spades+302 of spades3 of heartsace of spades5 of diamonds+14alone2 of clubs4 of diamondsking of diamonds−19
Hand 29 seed 2047
ace of spadesace of hearts2 of spades3 of hearts4 of hearts6 of spadesjack of spadesjack of diamondsjack of clubsqueen of diamonds- Best +70
- 2 of spades3 of heartsace of spadesace of hearts6 of spades+20jack of spadesjack of diamondsjack of clubs+66alone4 of heartsqueen of diamonds−16
- Greedy +70
- jack of spadesjack of diamondsjack of clubs+662 of spades3 of heartsace of spadesace of hearts6 of spades+20alone4 of heartsqueen of diamonds−16
Hand 30 seed 2048
ace of heartsace of diamonds2 of clubs4 of hearts6 of spades7 of diamonds8 of spadesjack of spadesjack of heartsqueen of diamonds- Best −21 of 2 optima
- 6 of spadesace of hearts8 of spades+21jack of spadesjack of hearts+22aloneace of diamonds2 of clubs4 of hearts7 of diamondsqueen of diamonds−45
- Greedy −2
- jack of spadesjack of hearts+226 of spadesace of hearts8 of spades+21aloneace of diamonds2 of clubs4 of hearts7 of diamondsqueen of diamonds−45