Thursday, December 20, 2012

Zappadan, Days 16: The Odds Ain't 50/50

Well, I'm a bad Zappan. Due to an incredibly long and difficult work day, I missed my Zappadan update, yesterday. I have a good one too, I think. So, I'll do this in two installments today. One for Day 16 an one for Day 17.

Frank figures the odds be 50/50.

Let's talk about dice and odds, particularly for those die rolls that produce a non-linear result.

First, thanks to Adam for the inspiration for this post, especially his discussion of probability distributions. Now, please understand, I am NOT a math guru. I did get through three quarters of calculus in college (got a B, a C, and a D+, then changed to a non-engineering major, thanks very much...). However, I've always been interested in probability and dice rolls.

In this case, I want to look at a new way to do skill rolls, substituting for the linear d20 mechanic a different non-linear mechanic. In this case, we're talking about using multiple dice to produce results with a "central tendency." A roll of 2d6, for example, does not produce equal odds of getting any result between 2 and 12. Instead, because of the way the dice themselves are built, rolling a 7 is more likely than any other result. When one looks at the curve for the distribution of probabilities, it is decidedly bell-shaped. It also moderates the very wild swings we see with using a straight d20 mechanic, where a 1 and a 20 are equally likely, and both have the same probability of coming up as any other result. They're extreme results, so I've never liked how that works. They should be relatively rare. We can harness this tendency to change the way skill or characteristic checks work, and have a very, very simple mechanic.

When making a skill check, you could instead roll 2 dice instead of just a d20. I thought at first that 2d6 would be fine, but then started thinking about how attribute modifiers might be brought in. They could, for example, shift the resulting number up or down to fudge the results toward or away from rolled number. So, if I'm playing DCC and have a 14 Agility, I have a +1 modifier. I can use it to shift the roll upward by 1. If I have a negative mod, it shifts down. No mod, and I can't shift it at all. With 2d6, this shift is pretty radical. However, if I move to 3d6, the upper limit of 18 is not only very close to the 20 on a d20 roll, it also follows the same distribution as the roll for PC attributes. What a lovely bit of symmetry. If a PC's characteristic is very high or very low, then he or she can shift the roll up to 3.

For example, let's say I have a character whose Stamina is 18. This is a pretty tough PC. If the PC has to make a DC 10 Fortitude save, using this mechanic, then it's very likely that the PC will be able to do so, and only a very low roll (which is less likely using at 3d6 mechanic) will result in a failure. This makes a lot of sense to me, as we're dealing with a badass character. Of course he or she will shrug off what would affect most PCs. If that same PC's Agility was 3, then then an Agility check would always be tough. The most likely results are a 10 or 11. For a target of 10 with a a minus 3 modifier, that would make it fairly unlikely that the DC 10 result could be achieved. This, again, makes sense. Klutzy McStumble with his 3 Agility would tend to fuck up any challenging Agility check. Only under the most unlikely scenarios would he have wild successes. This is very different than a straight d20 roll, which grants an equal probability of an extremely high or extremely low roll.

So, does this make sense to you as well? Do you see any obvious holes in my idea?

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