Wow . . . I got a very cool e-mail from Benjamin Fairydust, Magus Theurgist. In this e-mail he details how to simulate fizzle rates with the roll of two dice. I think I may use this for the advanced version of the game I'm making and point to this thread for more details on how fizzle rates are simulated with the dice.
Ok, so check out this email.
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I really like your TCG idea and was thinking of making my own deck. I recall someone’s comment regarding adding fizzling to the TCG with dice. Well after a semester or 2 of Statistics at school I’ve figured out a way to add fizzling to the game using only 2 die.
I’ve color-coordinated the TCG Fizzle Guide for simplicity: Red (NOTE: I went with a salmon color to make it easier to read on this blog) is all the mathematical and technical stuff, Blue is all the semi-technical stuff, and Green is all you really need to know (It's at the end).
This is the mathematics of it all.
If you just want how 2 die translates in fizzle accuracy skip to end:
So when you roll 2 die and take their sum (add both die together) you can get any number between 2-12 inclusive (including 2 and 12). There are 36 different combinations of numbers you could possibly get. And the chance (probability) of getting each sum (the #’s b/w 2-12) is different for each.
Below is a chart showing the sum of 2 die, the probability of each sum when both die are rolled, the different ways to get each sum, and the number of ways to get each sum:
To find the probability of each sum I simply took all the different ways of getting that sum and divided it by 36, the total number of combinations for the 2 die.
Now that we know the chance of getting each number we can use those probability to determine the accuracy for each card.
The following chart shows the accuracy of fizzling we want, the sums that get you that accuracy, and the accuracy we actually get.
So for example:
I play a Seraph card that has 90% accuracy. That means I have a 10% chance of fizzling. So I roll my 2 die.
According to the chart, we want 10% and the closest we can get is 11%. So when I roll, if I get a sum of 5 (That’s a 1,4; 2,3; 3,2; or 4,1) I fizzle.
This works for every accuracy. Just figure out what your chance of fizzling is, find the sums, roll the die, and if you get the sums listed you fizzle.
You can also do it vice versa, where the chart shows the accuracy instead of the fizzle.
Sticking to the Seraph example: Accuracy = 90% closest on chart is 91% so if we get any number that is not (3, 4, 5, 6, 7, 8, 9, 10, 12) then you fizzle.
I find using the chart to represent fizzle rate easier, but you might think differently.
For simplicity’s sake here’s a chart with the most common fizzle rates for each school:
The Fizzle #’s or Unlucky #’s (whichever you prefer) are the sums that if you get, you fizzle. So if I play a Skeletal Pirate (Accuracy = 85%), the fizzle chance is 15% so if I roll both die and they add up to 7, I fizzle.
Hope this is of some use to you.
whoa! Nice. That sounds solid enough to me! Any math people out there want to back Benjamin up? Those 3, 5, 6, and 7's are so DREADED! :-)