Nuclear Beasts Blog
Friday, October 31, 2003
Alternative Damage Calculation
Found an interesting artifact of probability recently. I may change how Reliability tests are performed because of it.
If you treat every die rolled as a separate Performance test, then you get from zero to three successes per die. A roll that meets or beats the target nets 1 success, a roll that beats it by 4-7 nets 2, 8+ gives you 3.
If you measure the average result of every die type vs the standard difficulty of 4, you get:
- A d4 has a one-in-four chance of giving one success, so its average is 0.25
- d6 is 0.50
- d8 is 0.75 (because it can produce 2 successes on a roll of 8)
- d10 is 1.00
- d12 is 1.25 (and nets 3 successes on a 12)
Now if the difficulty drops below 4 (meaning a particularly easy check) then the average favors the d4s. If it goes above 4, then the average favors the d12s (particularly since d4s can never succeed at a check of difficulty 5+).
Now, the way I had been intending to calculate the results of a Reliability test, each die either gave you zero or one successes and could never produce multiple successes. Vs difficulty 4, that looks like:
- d4 0.25
- d6 0.50
- d8 0.625
- d10 0.70
- d12 0.75
This particularly applies for damage because I can say that a regular hit against an unarmored opponent is difficulty 4... where all weapons are balanced. Armor might move the difficulty up as high as 8 (and 12 is potentially possible with high-tech powered armor, just really rare) while critical hits might move it down as low as 2... or even lower. Since the number of wounds inflicted is based on the difference between the number rolled and the difficulty, it should support even negative difficulties just fine. If you roll vs a difficulty of -2, you'll get a one success on a 1, two on a result of 2-5 and three on a result of 6-9. I might even extend it to 4 on 10+, whereas the normal system maxes out at 3 successes. I'll probably leave it maxed out at 3 for right now. Negative difficulties will be very rare, anyway.
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