Steve Jackson Games Forums Condensing Multiple Rolls with a Chart? [Math Help Needed]
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 08-21-2018, 12:21 AM #1 GreatWyrmGold   Join Date: Oct 2011 Condensing Multiple Rolls with a Chart? [Math Help Needed] I decided I'd like to hack together a quick mass combat system, one for fights between groups too small and individuals too varied for the default mass combat system to work well (e.g. supervillain gangs). I figured that a good first step would be to have a way to simulate multiple rolls with one. For instance, if someone made 10 attacks with skill 12 in a given timeframe, they would hit (on average) with seven or eight of them, but would hit with all 10 roughly 5% of the time. Since there's a roughly 5% chance of rolling 3-5 on 3d6, you could make it so rolling 3-5 means they hit with all ten...and, conversely, that 16-18 means they miss with all ten. And so on for every number between 1 and 9 as well. But, of course, I want a way to easily calculate that sort of table for any combination of skill level and number of rolls. Ideally, I'd like a big chart, with 3-18 on both edges, with the cells containing the percentage of rolls which succeed for a given die roll and skill level. It seems like the kind of thing there should be a simple formula I can plug into each square to figure out; stick in the probabilities for rolling each number on the die, multiply or exponent them in the right way, and fill the table. But I haven't been able to figure out what. Or if that's not an option, I guess other options for not-quite-mass-combat rules could be helpful. But this is the kind of problem that keeps bugging certain types of people until they have a solution, and I am one of those types...even though probability isn't really my forte. I hope I didn't nerd-snipe anyone.

 Tags math, probability