The Pool — any natural 1 succeeds
At the table
In James V. West’s The Pool, you roll a pool of d6. If any die shows a 1, the action succeeds; otherwise it fails. Pool size depends on how much you stake on the attempt.
Try it
In the playground, open this recipe in the playground and click Run. Output shows success probabilities for pool sizes 1d through 10d.
The script
↗for dice in range(1, 11):
p = dice_pool(dice, 6).p_any(1)
output("{}d".format(dice), p)
1d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 1d | 16.7 | 1/6 | 0.167 |
2d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 2d | 30.6 | 11/36 | 0.306 |
3d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 3d | 42.1 | 91/216 | 0.421 |
4d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 4d | 51.8 | 423/817 | 0.518 |
5d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 5d | 59.8 | 637/1065 | 0.598 |
6d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 6d | 66.5 | 425/639 | 0.665 |
7d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 7d | 72.1 | 1320/1831 | 0.721 |
8d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 8d | 76.7 | 1640/2137 | 0.767 |
9d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 9d | 80.6 | 703/872 | 0.806 |
10d · Prob
| outcome | % | frac | X |
|---|---|---|---|
| 10d | 83.8 | 1002/1195 | 0.838 |