Lightweight Memory Tables
I'm looking for a weather table with a memory.
Edward Mitchell Bannister, Approaching Storm, 1886, Smithsonian American Art Museum
Existing Solutions
Fortunately this problem has been solved a bunch of times.
Goblin's Henchman did it once with Hexflowers.
Mindstorm Press did it again with ladder tables.
Fedmar's weather is built off the 3 axes of heat, wind and cloud cover.
There's no memory here, but I'd be remiss if I didn't mention Ktrey's 100 weathers.
They're all great, but I want something light.
Lightweight Memory
How's this for a basic idea:
2d6 | WEATHER
2. TOO DAMN COLD
3. Real cold
4. Cold
5. Chilly
6. Mild
7. Pleasant
8. Warm
9. Balmy
10. Hot
11. Real hot
12. TOO DAMN HOT
There's our table. Now the rolling procedure will provide the memory.
- If the previous roll was below 7, roll 3d6 and drop the highest roll
- If the previous roll was above 7, roll 3d6 and drop the lowest roll
- Roll 2d6 on the first roll and on a roll of 7.
It won't be as in-depth as the memory systems above, but remember - this is just a toy memory. We need to evoke this feeling: if you've had a hot day recently, chances are, you'll have more hot days coming up. But not always!
Distributions
Let's have a quick look at the distributions on anydice. Play along at home with these parameters:
output [highest 2 of 3d6] named "3d6 drop lowest"
output [lowest 2 of 3d6] named "3d6 drop highest"
Here's the graph for hot weather - 3d6 drop lowest:
Looks nice. Hot weather begets hot weather, and vice versa. Roughly 70 percent of the time a hot day will be followed by another. This feels good - you have a 30% chance to escape a hot weather cycle into a cold weather cycle.
For curiosity's sake I asked around the Prismatic Wasteland discord for anyone with some smarts to model the system's odds for me. To Be Resolved was kind enough to generate a histogram. Turns out that the system still roughly resembles a bell curve, with a peak at the number 7.\
Thanks dadstep
One other detail that is nice here - this setup allows more exploration of the shoulders of the distribution than a flat 2d6 roll. As a comparison, rolling 2 or 12 on a 2d6 has a probability under 3%. But on a drop-lowest roll, you have almost a 7.5% chance to roll a 12.
As Joel at Silverarm Press discussed in his radical d12 manifesto, the most interesting results on a table are often hidden behind extremely low odds. I wonder if lightweight memory tables could be applied elsewhere to dig out some of the further reaches of other 2d6 tables.
Variants
Broader Shoulders - Dig in to the far reaches of the distribution: roll [4d6 drop lowest 2] for rolls over 7 and [4d6 drop highest 2] for rolls under 7.
3 Bands - Have a middle band of flat probability: roll [3d6 drop lowest] for rolls over 9 and [3d6 drop highest] for rolls under 5.
Deep Gutters - Make it extra hard to go from one end of the distribution to the other: roll [4d6 drop lowest 2] for rolls over 9, [3d6 drop lowest] for rolls of 8 & 9, [4d6 drop highest 2] for rolls under 5, and [3d6 drop highest] for rolls of 5 & 6.
Ping Pong - Make it unlikely to stay on one side of the distribution: roll [3d6 drop lowest] for rolls under 7 and [3d6 drop highest] for rolls over 7.
Trend Low, Sweet Chariot - Always roll [3d6 drop highest].
Variable Trend - Roll [3d6 drop highest] in Winter, [3d6 drop lowest] in Summer and flat 2d6 in the shoulder seasons.
Premonition - Allow a player to roll one of your dice the day before. (Or 2, if rolling 3d6.) - Thanks for the suggestion Ktrey!
Don't be married to the d6, either. Longer or shorter dice will change the distributions of your graph. Mix and match dice shapes for some really weird distributions. Get funky with it.