Hit Points
Comparison of different ways of rolling hit points for Swords & Wizardry White Box.
Add die: When you gain a Hit Die, roll just new the new hit die and add it to your previous hit point total. A common technique in Dungeons & Dragons.
Reroll dice: The official method in Swords & Wizards White Box. At every level, even ones in which your Hit Dice remain the same, reroll all Hit Dice. If larger than your previous hit point total, replace your hit point total. Otherwise keep your old hit point total.
Avg: Average or expected hit points at this level.
SD: Standard deviation from the average.
Ratio: Difference from the "Add die" and "Reroll dice" methods.
Charts: The X-axis is hit points, the Y-axis is percentage chance. The black line is "Reroll dice" while the grey line is "Add die".
Cleric
| Add die | Reroll dice | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Level | HD | Avg | SD | Avg | SD | Ratio | Notes | ||||
| 1 | 1 | 3.5 | ±1.7 | 3.5 | ±1.7 | 100.0% |  | ||||
| 2 | 2 | 7.0 | ±2.4 | 7.2 | ±2.2 | 102.3% |  | ||||
| 3 | 3 | 10.5 | ±3.0 | 10.9 | ±2.6 | 103.5% |  | ||||
| 4 | 3+1 | 11.5 | ±3.0 | 12.8 | ±2.4 | 111.2% |  | ||||
| 5 | 4 | 14.0 | ±3.4 | 15.1 | ±2.6 | 108.0% |  | ||||
| 6 | 5 | 17.5 | ±3.8 | 18.4 | ±3.1 | 105.1% |  | ||||
| 7 | 6 | 21.0 | ±4.2 | 22.0 | ±3.4 | 104.9% |  | ||||
| 8 | 6+1 | 22.0 | ±4.2 | 24.2 | ±3.2 | 109.9% |  | ||||
| 9 | 7 | 24.5 | ±4.5 | 26.6 | ±3.3 | 108.4% |  | ||||
| 10 | 8 | 28.0 | ±4.8 | 29.7 | ±3.7 | 106.0% |  | ||||
Fighter
| Add die | Reroll dice | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Level | HD | Avg | SD | Avg | SD | Ratio | Notes | ||||
| 1 | 1+1 | 4.5 | ±1.7 | 4.5 | ±1.7 | 100.0% |  | ||||
| 2 | 2 | 7.0 | ±2.4 | 7.3 | ±2.1 | 104.6% |  | ||||
| 3 | 3 | 10.5 | ±3.0 | 10.9 | ±2.6 | 103.6% |  | ||||
| 4 | 4 | 14.0 | ±3.4 | 14.6 | ±2.9 | 104.2% | Elf, Halfling Max |  | |||
| 5 | 5 | 17.5 | ±3.8 | 18.3 | ±3.2 | 104.6% |  | ||||
| 6 | 6 | 21.0 | ±4.2 | 22.0 | ±3.4 | 104.9% | Dwarf Max |  | |||
| 7 | 7 | 24.5 | ±4.5 | 25.7 | ±3.6 | 105.1% |  | ||||
| 8 | 8 | 28.0 | ±4.8 | 29.5 | ±3.8 | 105.2% |  | ||||
| 9 | 9 | 31.5 | ±5.1 | 33.2 | ±4.0 | 105.3% |  | ||||
| 10 | 10 | 35.0 | ±5.4 | 36.9 | ±4.2 | 105.4% |  | ||||
Magic-User
| Add die | Reroll dice | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Level | HD | Avg | SD | Avg | SD | Ratio | Notes | ||||
| 1 | 1 | 3.5 | ±1.7 | 3.5 | ±1.7 | 100.0% |  | ||||
| 2 | 1+1 | 4.5 | ±1.7 | 5.1 | ±1.4 | 112.3% |  | ||||
| 3 | 2 | 7.0 | ±2.4 | 7.4 | ±2.0 | 105.7% |  | ||||
| 4 | 2+1 | 8.0 | ±2.4 | 9.0 | ±1.9 | 112.2% |  | ||||
| 5 | 3 | 10.5 | ±3.0 | 11.3 | ±2.3 | 107.4% |  | ||||
| 6 | 3+1 | 11.5 | ±3.0 | 12.9 | ±2.3 | 112.1% |  | ||||
| 7 | 4 | 14.0 | ±3.4 | 15.1 | ±2.6 | 108.2% |  | ||||
| 8 | 4+1 | 15.0 | ±3.4 | 16.8 | ±2.5 | 111.9% | Elf Max |  | |||
| 9 | 5 | 17.5 | ±3.8 | 19.0 | ±2.8 | 108.6% |  | ||||
| 10 | 5+1 | 18.5 | ±3.8 | 20.6 | ±2.8 | 111.6% |  | ||||
Elf-Synthetic
This assumes that the Elf rolls Fighter Hit Dice at first level, adventures as a Fighter until second level, then alternates classes thereafter until hitting the Fighter cap of 4. So at level "5", the Elf is a level 3 Fighter and level 2 Magic-User. The "Add die" columns and grey line in the charts are nonsensical.
| Add die | Reroll dice | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Level | HD | Avg | SD | Avg | SD | Ratio | Notes | ||||
| 1 | 1+1 | 4.5 | ±1.7 | 4.5 | ±1.7 | 100.0% |  | ||||
| 2 | 2 | 7.0 | ±2.4 | 7.3 | ±2.1 | 104.6% |  | ||||
| 3 | 1+1 | 4.5 | ±1.7 | 7.5 | ±1.9 | 166.8% |  | ||||
| 4 | 3 | 10.5 | ±3.0 | 10.9 | ±2.6 | 103.7% |  | ||||
| 5 | 2 | 7.0 | ±2.4 | 11.1 | ±2.4 | 158.7% |  | ||||
| 6 | 4 | 14.0 | ±3.4 | 14.6 | ±2.9 | 104.4% |  | ||||
| 7 | 2+1 | 8.0 | ±2.4 | 14.7 | ±2.8 | 183.1% |  | ||||
| 8 | 3 | 10.5 | ±3.0 | 15.0 | ±2.6 | 142.5% |  | ||||
| 9 | 3+1 | 11.5 | ±3.0 | 15.4 | ±2.4 | 133.5% |  | ||||
| 10 | 4 | 14.0 | ±3.4 | 16.4 | ±2.4 | 117.4% |  | ||||
| 11 | 4+1 | 15.0 | ±3.4 | 17.5 | ±2.3 | 116.5% |  | ||||