Rules:Skill Check Table: Difference between revisions
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== Variable Skill Check Table == | |||
The following table lists the likelyhood to beat a certain score in [[Rules:Stats#Skills|variable skill checks]] at a given rank. It shall aid designers to balance those checks according to the stage of the game and difficulty of the situation. As a rule of thumb, one can assume higher ranks at later points in the game, but it should be noted that not all skills will necessarily be raised to 5th rank. | |||
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<br> | |||
== Calculating Probabilities == | |||
The following snippet of Python code has been used in calculating the probabilities above. | |||
# -- k: sides of die | |||
k = 6 | |||
def sum_dice (dice, sum, score): | |||
count = 0 | |||
if dice == 0: | |||
if sum >= score: count = 1 | |||
else: | |||
for x in range (1, k + 1): | |||
count = count + sum_dice (dice-1, x+sum, score) | |||
return count | |||
# -- x: number of dice (1-5) | |||
for x in range (1, 6): | |||
# -- n: scores possible with x dice | |||
for s in range (x*1, x*k+1): | |||
count = sum_dice (x, 0, s) | |||
p = (count*100.0)/(k**x) | |||
print "%id%i: p(%i) = %.2f%%" % (x, k, s, p) | |||
<!-- The following code was used to produce the nicely colored table: | |||
for n in range (1, 5*k+1): | |||
print "|- style=\"text-align:right\"\n| %i" % n | |||
# -- x: number of dice (1-5) | |||
for x in range (1, 6): | |||
count = sum_dice (x, 0, n) | |||
p = (count*100.0)/(k**x) | |||
col = int(p*2.55) | |||
g = 200 | |||
r = 200 | |||
if col > 128: r = r - col + 128 | |||
else: g = 72 + col | |||
print "| style=\"background:#%02x%02x2d\" | %.2f%%" % (r, g, p) | |||
//--> | |||
[[Category:Rules]] | |||
Revision as of 21:19, 23 August 2009
Variable Skill Check Table
The following table lists the likelyhood to beat a certain score in variable skill checks at a given rank. It shall aid designers to balance those checks according to the stage of the game and difficulty of the situation. As a rule of thumb, one can assume higher ranks at later points in the game, but it should be noted that not all skills will necessarily be raised to 5th rank.
| Score \ Rank | 1 | 2 | 3 | 4 | 5 |
| 1 | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% |
| 2 | 83.33% | 100.00% | 100.00% | 100.00% | 100.00% |
| 3 | 66.67% | 97.22% | 100.00% | 100.00% | 100.00% |
| 4 | 50.00% | 91.67% | 99.54% | 100.00% | 100.00% |
| 5 | 33.33% | 83.33% | 98.15% | 99.92% | 100.00% |
| 6 | 16.67% | 72.22% | 95.37% | 99.61% | 99.99% |
| 7 | 0.00% | 58.33% | 90.74% | 98.84% | 99.92% |
| 8 | 0.00% | 41.67% | 83.80% | 97.30% | 99.73% |
| 9 | 0.00% | 27.78% | 74.07% | 94.60% | 99.28% |
| 10 | 0.00% | 16.67% | 62.50% | 90.28% | 98.38% |
| 11 | 0.00% | 8.33% | 50.00% | 84.10% | 96.76% |
| 12 | 0.00% | 2.78% | 37.50% | 76.08% | 94.12% |
| 13 | 0.00% | 0.00% | 25.93% | 66.44% | 90.20% |
| 14 | 0.00% | 0.00% | 16.20% | 55.63% | 84.80% |
| 15 | 0.00% | 0.00% | 9.26% | 44.37% | 77.85% |
| 16 | 0.00% | 0.00% | 4.63% | 33.56% | 69.48% |
| 17 | 0.00% | 0.00% | 1.85% | 23.92% | 60.03% |
| 18 | 0.00% | 0.00% | 0.46% | 15.90% | 50.00% |
| 19 | 0.00% | 0.00% | 0.00% | 9.72% | 39.97% |
| 20 | 0.00% | 0.00% | 0.00% | 5.40% | 30.52% |
| 21 | 0.00% | 0.00% | 0.00% | 2.70% | 22.15% |
| 22 | 0.00% | 0.00% | 0.00% | 1.16% | 15.20% |
| 23 | 0.00% | 0.00% | 0.00% | 0.39% | 9.80% |
| 24 | 0.00% | 0.00% | 0.00% | 0.08% | 5.88% |
| 25 | 0.00% | 0.00% | 0.00% | 0.00% | 3.24% |
| 26 | 0.00% | 0.00% | 0.00% | 0.00% | 1.62% |
| 27 | 0.00% | 0.00% | 0.00% | 0.00% | 0.72% |
| 28 | 0.00% | 0.00% | 0.00% | 0.00% | 0.27% |
| 29 | 0.00% | 0.00% | 0.00% | 0.00% | 0.08% |
| 30 | 0.00% | 0.00% | 0.00% | 0.00% | 0.01% |
Calculating Probabilities
The following snippet of Python code has been used in calculating the probabilities above.
# -- k: sides of die
k = 6
def sum_dice (dice, sum, score):
count = 0
if dice == 0:
if sum >= score: count = 1
else:
for x in range (1, k + 1):
count = count + sum_dice (dice-1, x+sum, score)
return count
# -- x: number of dice (1-5)
for x in range (1, 6):
# -- n: scores possible with x dice
for s in range (x*1, x*k+1):
count = sum_dice (x, 0, s)
p = (count*100.0)/(k**x)
print "%id%i: p(%i) = %.2f%%" % (x, k, s, p)