Here is a chart summarizing the best/smallest sets known for various player counts. Entries in red are known to be the best (lowest) possible values achievable (generally through exhaustive computer search).
| Players | Smallest LCM | Fewest Total Sides | Smallest Largest Die | Fewest Sides (“Nice”* Set) |
|---|---|---|---|---|
| 2 | 2 (2d2) | 3 (aba) | 2 (aba) | 8 (2d4) |
| 3 | 6 (3d6) R. Ford | 12 (d2+d4+d6) | 6 (various) | 14 (2d4+d6) |
| 4 | 12 (4d12) R. Ford | 30 (d4+d6+d8+d12) E. Harshbarger | 9 (d6+2d8+d9) E. Harshbarger | 30 (d4+d6+d8+d12) |
| 5 | 60 (5d60) P. Meyer | 164 (d20+4d36) B. Cohen | 36 (d20+4d36) B. Cohen | 222 (d30+4d48) P. Meyer |
| 6 | 360 (d20+5d360, d36+5d360, d20+d120+4d360) M. Purcell | 746 (d80+d90+4d144) E. Harshbarger | 144 (d80+d90+4d144) E. Harshbarger | ? |
| 7 | 10080 (7d10080) P. Meyer | 5316 (d480+d540+d840+4d864) E. Harshbarger | 864 (d480+d540+d840+4d864) E. Harshbarger | Impossible |
| 8 | ? | 32736 (d840+d2880+d3240+d5040+4d5184) E. Harshbarger/B. Hearn | 5184 (d840+d2880+d3240+d5040+4d5184) E. Harshbarger/B. Hearn | Impossible |
| 9 | ? | 3844224 (d7560 + d25920 + d29160 + d45360 + 4d46656 + d89600) B. Hearn | 89600 (d7560 + d25920 + d29160 + d45360 + 4d46656 + d89600) B. Hearn | Impossible |
* A “nice” set comprises dice that are all isohedral shapes that are not lenses or rolling logs (“nice” is definitely subjective, since 2n-lens-shaped dice with small n values are definitely functional and pleasing enough for some folks' tastes). Also, a d2 (a coin) is not considered “nice”, but that is purely the opinion of this author (Eric). “Nice” side counts, therefore, are the following: 4, 6, 8, 12, 20, 24, 30, 48, 60, and 120.