Trying to make various dicepool TNs generate similar curves.
Here, what I care about is mostly the high P areas.
So, formulas:
For d20, 2d10, and 3d6, I hardcoded the relative probabilities, and divided by the sum of relative probabilities. I actually counted out the number of permutations that yield each number for 3d6.
[*] PDF(z) = (# permutations)/(total permutations)
[*] CDF(z) = CDF(z-1) - PDF(z-1)
For the XdY TN V (dicepool),
[*] PDF(Z successes) = (X nCr Z) * (1-(V-1)/Y)^(Z) * ((V-1)/Y)^(X-Z)
[*] CDF(Z) = CDF(Z-1) - PDF(Z-1)
I have been trying to think of ways to flatten the bell curve from rolling multiple dice and summing them. By flatter I mean that the probability of getting the average result is closer to the probability of getting either the maximum or minimum. The only practical ideas I've had where to use smaller die or use less die. Both of those have the problem of increasing granularity.
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@Juton: The way GURPS fattens up the tails on 3d6 is to say all results of 3-5 (crit fail) or 16-18 (crit success) are normally the same. Which makes it very similar to 1d10+5 on those graph thingies (individual results vary by less than 5%).
Other things you can do include different size dice. 1d20+1d6 is fairly flat while still having little tails, though it's hard to tell the different between that and 1d20+3 in play.
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Juton wrote:I have been trying to think of ways to flatten the bell curve from rolling multiple dice and summing them. By flatter I mean that the probability of getting the average result is closer to the probability of getting either the maximum or minimum. The only practical ideas I've had where to use smaller die or use less die. Both of those have the problem of increasing granularity.
You could try multiplying some of the dice, but then you'd need different colored dice or something.
Tussock wrote:Other things you can do include different size dice. 1d20+1d6 is fairly flat while still having little tails, though it's hard to tell the different between that and 1d20+3 in play.
Tussock wrote:Other things you can do include different size dice. 1d20+1d6 is fairly flat while still having little tails, though it's hard to tell the different between that and 1d20+3 in play.
I'm curious what the distribution looks like when the variables are "# of fair coins flipped" (or xd6 at or above target number 4) vs. "required number of heads" (required number of successes).
Last edited by vermithrx on Sat Dec 29, 2012 1:31 am, edited 1 time in total.
It looks like a 3 variable graph. Within that, it looks like progressive binomial distributions.
Vebyast wrote:Here's a fun target for Major Creation: hydrazine. One casting every six seconds at CL9 gives you a bit more than 40 liters per second, which is comparable to the flow rates of some small, but serious, rocket engines. Six items running at full blast through a well-engineered engine will put you, and something like 50 tons of cargo, into space. Alternatively, if you thrust sideways, you will briefly be a fireball screaming across the sky at mach 14 before you melt from atmospheric friction.
Huh, so N must be greater than or equal to 2R - 1 for CDF(N,R) to be greater than or equal to 0.5 (50%).
I can't tell just looking at the charts; are there similarly simple formulas for 12.5%, 25%, 75%, and 87.5%? I'm hoping to see a pattern between them in order to develop easy to remember rules of thumb. If there are such, you can point them out explicitly in your game and thus gain the benefits of 'relatively' easy chance deduction while still using binomial distributions.
