2022-10-10 Restocking 2W6

Just 20min to go before the next game starts.

In 2013-08-21 One Roll Dungeon Stocking and 2022-03-29 Restocking I suggested we should replace the Moldvay dungeon stocking procedure using two d6 with a single d20 roll for restocking. But then it turns out the dungeon grew out of control if I did that.

2013-08-21 One Roll Dungeon Stocking

2022-03-29 Restocking

+-----+--------------------------------+
| 1d6 |             Result             |
+-----+--------------------------------+
|   1 | Monster                        |
|   2 | Monster & Treasure             |
| 3–6 | Empty with a 1-in-6 chance of  |
|     | unguarded treasure             |
+-----+--------------------------------+

So actually, the chances are ⅙, ⅙, and ⅑ (⅔×⅙). If we use a single roll of 2d6, we can pick appropriate rows:

+-------+--------------------------+
|  2d6  |          Result          |
+-------+--------------------------+
| 2–4   | Monster without treasure |
| 5–8   | Empty                    |
|     9 | Unguarded treasure       |
| 10–12 | Monster with treasure    |
+-------+--------------------------+

The distribution of 2d6

(This based on 2d6 Math.)

2d6 Math

For those interested in how to pick the rows, here’s how I like to explain it. Let’s start with a table with all the possible results of the two dice and their sums.

||⚀|⚁|⚂|⚃|⚄|⚅| ||:--:|:--:|:--:|:--:|:--:|:--:| |⚀|2|3|4|5|6|7| |⚁|3|4|5|6|7|8| |⚂|4|5|6|7|8|9| |⚃|5|6|7|8|9|10| |⚄|6|7|8|9|10|11| |⚅|7|8|9|10|11|12||

Now, let’s count how often the various sums show up. I like how the numbers form diagonal “lines”. Check out 7, for example: from the bottom left to the top right. Anyway, here are the occurrences: sum above, count below.

+---+---+---+---+---+---+---+---+----+----+----+
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+---+---+---+---+---+---+---+---+----+----+----+
| 1 | 2 | 3 | 4 | 5 | 6 | 5 | 4 |  3 |  2 |  1 |
+---+---+---+---+---+---+---+---+----+----+----+

In total, we have 6×6 results, that is 36. So the chances of rolling a sum of 2 is 1 in 36, the chances of rolling a sum of 3 is 2 in 36, and the chances of rolling a sum of 3 or less is 1 in 36 plus 2 in 36, that is 3 in 36, or 1 in 12.

So now you know how to find the ranges. If you need a 1 in 6 chance, that is the equivalent of 6 in 36, so any of the following would do: 7, 2 or 6, 3 or 5, 4 or 10, 2 to 4, 10 to 12, and so on. In my case, I also needed a 1 in 9, or 4 in 36. Both at 5 or a 9 have the correct chances of showing up.

​#RPG