Probabilities of Single EventsThe following are percentages (proportions) on scroll successes and failures of 1 event.
100% ScrollProbability of success, 1 event: 1.0, 100%
Probability of failure, no destruction, 1 event: 0.0, 0%
Probability of failure, destruction, 1 event: 0.0, 0%
90% Scroll - 60% used with Vega's Spell
Probability of success, 1 event: 0.9, 90%
Probability of failure, no destruction, 1 event: 0.1, 10%
Probability of failure, destruction, 1 event: 0.0, 0%
70% dark/cursed ScrollProbability of success, 1 event: 0.7, 70%
Probability of failure, no destruction, 1 event: 0.15, 15%
Probability of failure, destruction, 1 event: 0.15, 15%
60% ScrollProbability of success, 1 event: 0.6, 60%
Probability of failure, no destruction, 1 event: 0.4, 40%
Probability of failure, destruction, 1 event: 0.0, 0%
50% Scroll
Probability of success, 1 event: 0.5, 50%
Probability of failure, no destruction, 1 event: 0.50, 50%
Probability of failure, destruction, 1 event: 0.0, 0%
30% Scroll Probability of success, 1 event: 0.3, 30%
Probability of failure, no destruction, 1 event: 0.35, 35%
Probability of failure, destruction, 1 event: 0.35, 35%
30% dark/cursed Scroll - 10% used with Vega's SpellProbability of success, 1 event: 0.3, 30%
Probability of failure, no destruction, 1 event: 0.7, 70%
Probability of failure, destruction, 1 event: 0.0, 0%
10% ScrollProbability of success, 1 event: 0.1, 10%
Probability of failure, no destruction, 1 event: 0.9, 90%
Probability of failure, destruction, 1 event: 0.0, 0%
Apparently, there is some confusion on the destruction probabilities for Dark (Cursed) Scrolls:
"Every time I use a dark scroll, there is a 50% chance that the item will break."
Incorrect. This misconception is probably due to the unclear wording in the description of the scroll. In truth, there is a 50% chance that the item breaks if the scroll fails.
For example, a 30% scroll has a 70% chance of failure (1 - 0.3 = 0.7). 50% of the time it fails, which is 70% of the time, the item breaks.
Thus we conclude that each time you use a 30% scroll, there is a 35% chance the item will break (0.7 / 2 = 0.35).
Likewise, each time you use a 70% scroll, there is a 15% chance the item will break (0.3 / 2 = 0.15).
"Every time my dark scroll fails, my item is destroyed by 50%."
Incorrect. Again, this misconception is due to the unclear wording in the description of the scroll. Item breakage is an event, thus it is caused by one scrolling event. Also see above explanation.
Probabilities of Multiple EventsMultiple Events in Succession
To find out your chances of a certain grouping of events in a row, use the following method.
(probability)^n or (prob.)(prob.)(prob.), etc.
For example:
• What is the probability I will get 3 60% scrolls to work (in a row) ?
0.6 ^ 3, which equals 0.216.
There is a 21.6% chance that 3 consecutive 60% scrolls will work.
• What is the probability that I will get 1 30% and 2 70% scrolls to work (in a row) ?
0.3 x 0.7 ^ 2, which equals 0.147.
There is a 14.7% chance that 1 30% and 2 70% scrolls will work consecutively.
Table of Multiple Probabilities, Consecutive Events; Success
100% ScrollIt will always work! Go figure.
90% Scroll - 60% used with Vega's Spell
n = Number of scrolls used.
Decimal
Percentual
70% Scroll1 consecutive success: 0.7, 70%
2 consecutive success: 0.49, 49%
3 consecutive success: 0.343, 34.3%
4 consecutive success: 0.2401, 24.01%
5 consecutive success: 0.16807, 16.807%
6 consecutive success: 0.117649, 11.7649%
7 consecutive success: 0.0823543, 8.23543%
8 consecutive success: 0.05764801, 5.764801%
9 consecutive success: 0.040353607, 4.0353607%
10 consecutive success: 0.0282475249, 2.82475249%
The following are probabilities' percentages (proportions) on scroll successes and failures of 1 event.
100% ScrollProbability of success, 1 event: 1.0, 100%
Probability of failure, no destruction, 1 event: 0.0, 0%
Probability of failure, destruction, 1 event: 0.0, 0%
90% Scroll - 60% used with Vega's Spell
Probability of success, 1 event: 0.9, 90%
Probability of failure, no destruction, 1 event: 0.1, 10%
Probability of failure, destruction, 1 event: 0.0, 0%
70% dark/cursed ScrollProbability of success, 1 event: 0.7, 70%
Probability of failure, no destruction, 1 event: 0.15, 15%
Probability of failure, destruction, 1 event: 0.15, 15%
60% Scroll1 consecutive success: 0.6, 60%
2 consecutive success: 0.36, 36%
3 consecutive success: 0.216, 21.6%
4 consecutive success: 0.1296, 12.96%
5 consecutive success: 0.07776, 7.776%
6 consecutive success: 0.046656, 4.6656%
7 consecutive success: 0.0279936, 2.79936%
8 consecutive success: 0.01679616, 1.679616%
9 consecutive success: 0.010077696, 1.0077696%
10 consecutive success: 0.0060466176, 0.60466176%
50% Scroll
n = Number of scrolls used.
Decimal
Percentual
30% Scroll1 consecutive success: 0.3, 30%
2 consecutive success: 0.09, 9%
3 consecutive success: 0.027, 2.7%
4 consecutive success: 0.0081, 0.81%
5 consecutive success: 0.00243, 0.243%
6 consecutive success: 0.000729, 0.0729%
7 consecutive success: 0.0002187, 0.02187%
8 consecutive success: 0.00006561, 0.006561%
9 consecutive success: 0.000019683, 0.0019683%
10 consecutive success: 0.0000059049, 0.00059049%
20% Scroll
n = Number of scrolls used.
Decimal
Percentual
10% Scroll1 consecutive success: 0.1, 10%
2 consecutive success: 0.01, 1%
3 consecutive success: 0.001, 0.1%
4 consecutive success: 0.0001, 0.01%
5 consecutive success: 0.00001, 0.001%
6 consecutive success: 0.000001, 0.0001%
7 consecutive success: 0.0000001, 0.00001%
8 consecutive success: 0.00000001, 0.000001%
9 consecutive success: 0.000000001, 0.0000001%
10 consecutive success: 0.0000000001, 0.00000001% (Yikes!)
5% Scroll
n = Number of scrolls used.
Decimal
Percentual
3% Scroll
n = Number of scrolls used.
Decimal
Percentual
1% Scroll
n = Number of scrolls used.
Decimal
Percentual
Table of Multiple Probabilities, Consecutive Events; Failure
100% Scroll
It will never fail! Go figure.
90% Scroll - 60% used with Vega's Spell
n = Number of scrolls used.
Decimal
Percentual
70% Scroll1 consecutive failure: 0.3, 30%
2 consecutive failure: 0.09, 9%
3 consecutive failure: 0.027, 2.7%
4 consecutive failure: 0.0081, 0.81%
5 consecutive failure: 0.00243, 0.243%
6 consecutive failure: 0.000729, 0.0729%
7 consecutive failure: 0.0002187, 0.02187%
8 consecutive failure: 0.00006561, 0.006561%
9 consecutive failure: 0.000019683, 0.0019683%
10 consecutive failure: 0.0000059049, 0.00059049%
60% Scroll1 consecutive failure: 0.4, 40%
2 consecutive failure: 0.16, 16%
3 consecutive failure: 0.064, 6.4%
4 consecutive failure: 0.0256, 2.56%
5 consecutive failure: 0.01024, 1.024%
6 consecutive failure: 0.004096, 0.4096%
7 consecutive failure: 0.0016384, 0.16384%
8 consecutive failure: 0.00065536, 0.065536%
9 consecutive failure: 0.000262144, 0.0262144%
10 consecutive failure: 0.0001048576, 0.01048576%
30% Scroll1 consecutive failure: 0.7, 70%
2 consecutive failure: 0.49, 49%
3 consecutive failure: 0.343, 34.3%
4 consecutive failure: 0.2401, 24.01%
5 consecutive failure: 0.16807, 16.807%
6 consecutive failure: 0.117649, 11.7649%
7 consecutive failure: 0.0823543, 8.23543%
8 consecutive failure: 0.05764801, 5.764801%
9 consecutive failure: 0.040353607, 4.0353607%
10 consecutive failure: 0.0282475249, 2.82475249%
20% Scroll
n = Number of scrolls used.
Decimal
Percentual
60% Scroll1 consecutive success: 0.6, 60%
2 consecutive success: 0.36, 36%
3 consecutive success: 0.216, 21.6%
4 consecutive success: 0.1296, 12.96%
5 consecutive success: 0.07776, 7.776%
6 consecutive success: 0.046656, 4.6656%
7 consecutive success: 0.0279936, 2.79936%
8 consecutive success: 0.01679616, 1.679616%
9 consecutive success: 0.010077696, 1.0077696%
10 consecutive success: 0.0060466176, 0.60466176%
50% Scroll
n = Number of scrolls used.
Decimal
Percentual
30% Scroll1 consecutive success: 0.3, 30%
2 consecutive success: 0.09, 9%
3 consecutive success: 0.027, 2.7%
4 consecutive success: 0.0081, 0.81%
5 consecutive success: 0.00243, 0.243%
6 consecutive success: 0.000729, 0.0729%
7 consecutive success: 0.0002187, 0.02187%
8 consecutive success: 0.00006561, 0.006561%
9 consecutive success: 0.000019683, 0.0019683%
10 consecutive success: 0.0000059049, 0.00059049%
20% Scroll
n = Number of scrolls used.
Decimal
Percentual
10% Scroll1 consecutive failure: 0.9, 90%
2 consecutive failure: 0.81, 81%
3 consecutive failure: 0.729, 72.9%
4 consecutive failure: 0.6561, 65.61%
5 consecutive failure: 0.59049, 59.049%
6 consecutive failure: 0.531441, 53.1441%
7 consecutive failure: 0.4782969, 47.82969%
8 consecutive failure: 0.43046721, 43.046721%
9 consecutive failure: 0.387420489, 38.7420489%
10 consecutive failure: 0.3486784401, 34.86784401%
5% Scroll
n = Number of scrolls used.
Decimal
Percentual
3% Scroll
n = Number of scrolls used.
Decimal
Percentual
1% Scroll
n = Number of scrolls used.
Decimal
Percentual
Multiple Probabilities Events not in SuccessionThis is the most important statistical tool in determining scroll outcomes over a span of multiple scrolls. From this, we can determine the probability of x number of successes or failures out of n total, the expected outcome, and the expected yield. The equation to find this is complicated, and for one thing, I can't write it with correct notation here on the Basil forums because of the lack of a mathematics key set. However, if you own a TI-83 or higher model calculator, you can find these statistics using binompdf(n,prob.,x) (Credits to yoshidude65)
To find out your chances of a number of successes or fails from a group of scrolls, use the following method.
[n! / ((n-k)!k!)] x p^k x (1-p)^(n-k); whereas n represents the total scrolls used, k represents the number of successes or failures being questioned, and p represents the probability of the success or failure.
For example:
• What is the probability I will get 3 60% scrolls to work out of 5 total 60% scrolls?
[5! / ((5-3)!3!)] x (0.6)^3 x (0.4)^2, or binompdf(5,0.6,3) on your TI-83+ calculator.
There is a 34.56% chance that 3 60% scrolls will work out of 5 total 60% scrolls.
• What is the probability that I will get 1 10% scroll to work out of 7 total 10% scrolls?
[7! / ((7-1)!1!)] x (0.1)^1 x (0.9)^6, or binompdf(7,0.1,1) on your TI-83+ calculator.
There is a 37.2% chance that 1 10% scroll will work out of 7 total 10% scrolls.
Table of Multiple Probabilities Events, k successes out of n trials
I realize that only some of the scroll percent types are listed below - they are the most popular. If you would like to find the probability of another set of occurrences, please use this tool.
70% Scroll1 success out of 2 trials: 0.42, 42%
1 success out of 3 trials: 0.189, 18.9%
1 success out of 4 trials: 0.0756, 7.56%
1 success out of 5 trials: 0.02835, 2.835%
1 success out of 6 trials: 0.010206, 1.0206%
1 success out of 7 trials: 0.0035721, 0.35721%
1 success out of 8 trials: 0.00122472, 0.122472%
1 success out of 9 trials: 0.000413343, 0.0413343%
1 success out of 10 trials: 0.000137781, 0.0137781%
2 success out of 3 trials: 0.441, 44.1%
2 success out of 4 trials: 0.2646, 26.46%
2 success out of 5 trials: 0.1323, 13.23%
2 success out of 6 trials: 0.059535, 5.9535%
2 success out of 7 trials: 0.0250047, 2.50047%
2 success out of 8 trials: 0.01000188, 1.000188%
2 success out of 9 trials: 0.003857868, 0.3857868%
2 success out of 10 trials: 0.0014467005, 0.14467005%
3 success out of 4 trials: 0.4116, 41.16%
3 success out of 5 trials: 0.3087, 30.87%
3 success out of 6 trials: 0.18522, 18.522%
3 success out of 7 trials: 0.0972405, 9.72405%
3 success out of 8 trials: 0.04667544, 4.667544%
3 success out of 9 trials: 0.021003948, 2.1003948%
3 success out of 10 trials: 0.009001692, 0.9001692%
4 success out of 5 trials: 0.36015, 36.015%
4 success out of 6 trials: 0.324135, 32.4135%
4 success out of 7 trials: 0.2268945, 22.68945%
4 success out of 8 trials: 0.1361367, 13.61367%
4 success out of 9 trials: 0.073513818, 7.3513818%
4 success out of 10 trials: 0.036756909, 3.675690%
5 success out of 6 trials: 0.302526, 30.2526%
5 success out of 7 trials: 0.3176523, 31.76523%
5 success out of 8 trials: 0.25412184, 25.412184%
5 success out of 9 trials: 0.171532242, 17.1532242%
5 success out of 10 trials: 0.1029193542, 10.29193542%
6 success out of 7 trials: 0.2470629, 24.70629%
6 success out of 8 trials: 0.29647548, 29.647548%
6 success out of 9 trials: 0.266827932, 26.6827932%
6 success out of 10 trials: 0.200120949, 20.0120949%
7 success out of 8 trials: 0.19765032, 19.765032%
7 success out of 9 trials: 0.266827932, 26.6827932%
7 success out of 10 trials: 0.266827932, 26.6827932%
8 success out of 9 trials: 0.155649627, 15.5649627%
8 success out of 10 trials: 0.2334744405, 23.34744405%
9 success out of 10 trials: 0.121060821, 12.1060821%
60% Scroll1 success out of 2 trials: 0.48, 48%
1 success out of 3 trials: 0.288, 28.8%
1 success out of 4 trials: 0.1536, 15.36%
1 success out of 5 trials: 0.0768, 7.68%
1 success out of 6 trials: 0.036864, 3.6864%
1 success out of 7 trials: 0.0172032, 1.72032%
1 success out of 8 trials: 0.00786432, 0.786432%
1 success out of 9 trials: 0.003538944, 0.3538944%
1 success out of 10 trials: 0.001572864, 0.1572864%
2 success out of 3 trials: 0.432, 43.2%
2 success out of 4 trials: 0.3456, 34.56%
2 success out of 5 trials: 0.2304, 23.04%
2 success out of 6 trials: 0.13824, 13.824%
2 success out of 7 trials: 0.0774144, 7.74144%
2 success out of 8 trials: 0.04128768, 4.128768%
2 success out of 9 trials: 0.021233664, 2.1233664%
2 success out of 10 trials: 0.010616832, 1.0616832%
3 success out of 4 trials: 0.3456, 34.56%
3 success out of 5 trials: 0.3456, 34.56%
3 success out of 6 trials: 0.27648, 27.648%
3 success out of 7 trials: 0.193536, 19.3536%
3 success out of 8 trials: 0.12386304, 12.386304%
3 success out of 9 trials: 0.074317824, 7.4317824%
3 success out of 10 trials: 0.042467328, 4.2467328%
4 success out of 5 trials: 0.2592, 25.92%
4 success out of 6 trials: 0.31104, 31.104%
4 success out of 7 trials: 0.290304, 29.0304%
4 success out of 8 trials: 0.2322432, 23.22432%
4 success out of 9 trials: 0.167215104, 16.7215104%
4 success out of 10 trials: 0.111476736, 11.1476736%
5 success out of 6 trials: 0.186624, 18.6624%
5 success out of 7 trials: 0.2612736, 26.12736%
5 success out of 8 trials: 0.27869184, 27.869184%
5 success out of 9 trials: 0.250822656, 25.0822656%
5 success out of 10 trials: 0.2006581248, 20.06581248%
6 success out of 7 trials: 0.1306368, 13.06368%
6 success out of 8 trials: 0.20901888, 20.901888%
6 success out of 9 trials: 0.250822656, 25.0822656%
6 success out of 10 trials: 0.250822656, 25.0822656%
7 success out of 8 trials: 0.08957952, 8.957952%
7 success out of 9 trials: 0.161243136, 16.1243136%
7 success out of 10 trials: 0.214990848, 21.4990848%
8 success out of 9 trials: 0.060466176, 6.0466176%
8 success out of 10 trials: 0.120932352, 12.0932352%
9 success out of 10 trials: 0.040310784, 4.0310784%
30% Scroll1 success out of 2 trials: 0.42, 42%
1 success out of 3 trials: 0.441, 44.1%
1 success out of 4 trials: 0.4116, 41.16%
1 success out of 5 trials: 0.36015, 36.015%
1 success out of 6 trials: 0.302526, 30.2526%
1 success out of 7 trials: 0.2470629, 24.70629%
1 success out of 8 trials: 0.19765032, 19.765032%
1 success out of 9 trials: 0.155649627, 15.5649627%
1 success out of 10 trials: 0.121060821, 12.1060821%
2 success out of 3 trials: 0.189, 18.9%
2 success out of 4 trials: 0.2646, 26.46%
2 success out of 5 trials: 0.3087, 30.87%
2 success out of 6 trials: 0.324135, 32.4135%
2 success out of 7 trials: 0.3176523, 31.76523%
2 success out of 8 trials: 0.29647548, 29.647548%
2 success out of 9 trials: 0.266827932, 26.6827932%
2 success out of 10 trials: 0.2334744405, 23.34744405%
3 success out of 4 trials: 0.0759, 7.59%
3 success out of 5 trials: 0.1323, 13.23%
3 success out of 6 trials: 0.18522, 18.522%
3 success out of 7 trials: 0.2268945, 22.68945%
3 success out of 8 trials: 0.25412184, 25.412184%
3 success out of 9 trials: 0.266827932, 26.6827932%
3 success out of 10 trials: 0.266827932, 26.6827932%
4 success out of 5 trials: 0.02835, 2.835%
4 success out of 6 trials: 0.059535, 5.9535%
4 success out of 7 trials: 0.0972405, 9.72405%
4 success out of 8 trials: 0.1361367, 13.61367%
4 success out of 9 trials: 0.171532242, 17.1532242%
4 success out of 10 trials: 0.200120949, 20.0120949%
5 success out of 6 trials: 0.010206, 1.0206%
5 success out of 7 trials: 0.0250047, 2.50047%
5 success out of 8 trials: 0.04667544, 4.667544%
5 success out of 9 trials: 0.073513818, 7.3513818%
5 success out of 10 trials: 0.1029193452, 10.29193452%
6 success out of 7 trials: 0.0035721, 0.35721%
6 success out of 8 trials: 0.01000188, 1.000188%
6 success out of 9 trials: 0.021003948, 2.1003948%
6 success out of 10 trials: 0.036756909, 3.6756909%
7 success out of 8 trials: 0.00122472, 0.122472%
7 success out of 9 trials: 0.003857868, 0.3857868%
7 success out of 10 trials: 0.009001692, 0.9001692%
8 success out of 9 trials: 0.000413343, 0.0413343%
8 success out of 10 trials: 0.0014467005, 0.14467005%
9 success out of 10 trials: 0.000137781, 0.0137781%
10% Scroll1 success out of 2 trials: 0.18, 18%
1 success out of 3 trials: 0.243, 24.3%
1 success out of 4 trials: 0.2916, 29.16%
1 success out of 5 trials: 0.32805, 32.805%
1 success out of 6 trials: 0.354294, 35.4294%
1 success out of 7 trials: 0.3720087, 37.20087%
1 success out of 8 trials: 0.38263752, 38.263752%
1 success out of 9 trials: 0.387420489, 38.7420489%
1 success out of 10 trials: 0.387420489, 38.7420489%
2 success out of 3 trials: 0.027, 2.7%
2 success out of 4 trials: 0.0486, 4.86%
2 success out of 5 trials: 0.0729, 7.29%
2 success out of 6 trials: 0.098415, 9.8415%
2 success out of 7 trials: 0.1240029, 12.40029%
2 success out of 8 trials: 0.14880348, 14.880348%
2 success out of 9 trials: 0.172186884, 17.2186884%
2 success out of 10 trials: 0.1937102445, 19.37102445%
3 success out of 4 trials: 0.0036, 0.36%
3 success out of 5 trials: 0.0081, 0.81%
3 success out of 6 trials: 0.01458, 1.458%
3 success out of 7 trials: 0.0229635, 2.29635%
3 success out of 8 trials: 0.03306744, 3.306744%
3 success out of 9 trials: 0.044641044, 4.4641044%
3 success out of 10 trials: 0.057395628, 5.7395628%
4 success out of 5 trials: 0.00045, 0.045%
4 success out of 6 trials: 0.001215, 0.1215%
4 success out of 7 trials: 0.0025515, 0.25515%
4 success out of 8 trials: 0.0045927, 0.45927%
4 success out of 9 trials: 0.007440174, 0.7440174%
4 success out of 10 trials: 0.011160261, 1.1160261%
5 success out of 6 trials: 0.000054, 0.0054%
5 success out of 7 trials: 0.0001701, 0.01701%
5 success out of 8 trials: 0.00040824, 0.040824%
5 success out of 9 trials: 0.000826686, 0.0826686%
5 success out of 10 trials: 0.0014880348, 0.14880348%
6 success out of 7 trials: 0.0000063, 0.00063%
6 success out of 8 trials: 0.00002268, 0.002268%
6 success out of 9 trials: 0.000061236, 0.0061236%
6 success out of 10 trials: 0.000137781, 0.0137781%
7 success out of 8 trials: 0.00000072, 0.000072%
7 success out of 9 trials: 0.000002916, 0.0002916%
7 success out of 10 trials: 0.000008748, 0.0008748%
8 success out of 9 trials: 0.000000081, 0.0000081%
8 success out of 10 trials: 0.0000003645, 0.00003645%
9 success out of 10 trials: 0.000000009, 0.0000009% (Good luck!)
Clean Slate Scrolls
Clean slate scrolls are an addition to the variety of scrolls in Patch 0.56. With a small success rate, they regain lost slots.
Probability of the Clean Slate Scroll as a Single Event
1% Clean Slate ScrollProbability of success, 1 event: 0.01, 1%
Probability of failure, no destruction, 1 event: 0.97, 97%
Probability of failure, destruction, 1 event: 0.02, 2%
3% Clean Slate ScrollProbability of success, 1 event: 0.03, 3%
Probability of failure, no destruction, 1 event: 0.91, 91%
Probability of failure, destruction, 1 event: 0.06, 6%
5% Clean Slate ScrollProbability of success, 1 event: 0.05, 5%
Probability of failure, no destruction, 1 event: 0.85, 85%
Probability of failure, destruction, 1 event: 0.1, 10%
20% Clean Slate ScrollProbability of success, 1 event: 0.2, 20%
Probability of failure, no destruction, 1 event: 0.4, 40%
Probability of failure, destruction, 1 event: 0.4, 40%
Probability of the Clean Slate Scroll as Multiple Events
1% Clean Slate Scroll1 consecutive success: 0.01, 1%
2 consecutive success: 0.0001, 0.01%
3 consecutive success: 0.000001, 0.0001%
4 consecutive success: 0.00000001, 0.000001%
5 consecutive success: 0.0000000001, 0.00000001%
6 consecutive success: 0.000000000001, 0.0000000001%
7 consecutive success: 0.00000000000001, 0.000000000001%
8 consecutive success: 0.0000000000000001, 0.00000000000001%
9 consecutive success: 0.000000000000000001, 0.0000000000000001%
10 consecutive success: 0.00000000000000000001, 0.000000000000000001%
The following are probabilities for consecutive failure with NO destruction.
1 consecutive failure: 0.97, 97%
2 consecutive failure: 0.9409, 94.09%
3 consecutive failure: 0.912673, 91.2673%
4 consecutive failure: 0.88529281, 88.529281%
5 consecutive failure: 0.8587340257, 85.87340257%
6 consecutive failure: 0.8329720049, 83.29720049%
7 consecutive failure: 0.8079828448, 80.79828448%
8 consecutive failure: 0.7837433594, 78.37433594%
9 consecutive failure: 0.7602310587, 76.02310587%
10 consecutive failure: 0.7374241269, 73.74241269%
3% Clean Slate Scroll1 consecutive success: 0.03, 3%
2 consecutive success: 0.0009, 0.09%
3 consecutive success: 0.000027, 0.0027%
4 consecutive success: 0.00000081, 0.000081%
5 consecutive success: 0.0000000243, 0.00000243%
6 consecutive success: 0.000000000729, 0.0000000729%
7 consecutive success: 0.00000000002187, 0.000000002187%
8 consecutive success: 0.0000000000006561, 0.00000000006561%
9 consecutive success: 0.000000000000019683, 0.0000000000019683%
10 consecutive success: 0.00000000000000059049, 0.000000000000059049%
The following are probabilities for consecutive failure with NO destruction.
1 consecutive failure: 0.91, 91%
2 consecutive failure: 0.8281, 82.81%
3 consecutive failure: 0.753571, 75.3571%
4 consecutive failure: 0.68574961, 68.574961%
5 consecutive failure: 0.6240321451, 62.40321451%
6 consecutive failure: 0.567869252, 56.7869252%
7 consecutive failure: 0.5167610194, 51.67610194%
8 consecutive failure: 0.4702525276, 47.02525276%
9 consecutive failure: 0.4279298001, 42.79298001%
10 consecutive failure: 0.3894161181, 38.94161181%
5% Clean Slate Scroll1 consecutive success: 0.05, 5%
2 consecutive success: 0.0025, 0.25%
3 consecutive success: 0.000125, 0.0125%
4 consecutive success: 0.00000625, 0.00625%
5 consecutive success: 0.0000003125, 0.0003125%
6 consecutive success: 0.000000015625, 0.0000015626%
7 consecutive success: 0.00000000078125, 0.000000078125%
8 consecutive success: 0.0000000000390625, 0.00000000390625%
9 consecutive success: 0.000000000001953125, 0.0000000001953125%
10 consecutive success: 0.00000000000009765625, 0.000000000009765625%
The following are probabilities for consecutive failure with NO destruction.
1 consecutive failure: 0.85, 85%
2 consecutive failure: 0.7225, 72.25%
3 consecutive failure: 0.614125, 61.4125%
4 consecutive failure: 0.52200625, 52.200625%
5 consecutive failure: 0.4437053125, 44.37053125%
6 consecutive failure: 0.3771495156, 37.71495156%
7 consecutive failure: 0.3205770883, 32.05770883%
8 consecutive failure: 0.272490525, 27.2490525%
9 consecutive failure: 0.2316169463, 23.16169463%
10 consecutive failure: 0.1968744043, 19.68744043%
20% Clean Slate Scroll1 consecutive success: 0.2, 20%
2 consecutive success: 0.04, 4%
3 consecutive success: 0.008, 0.8%
4 consecutive success: 0.0016, 0.16%
5 consecutive success: 0.00032, 0.032%
6 consecutive success: 0.000064, 0.0064%
7 consecutive success: 0.0000128, 0.00128%
8 consecutive success: 0.00000256, 0.000256%
9 consecutive success: 0.000000512, 0.0000512%
10 consecutive success: 0.0000001024, 0.00001024%
The following are probabilities for consecutive failure with or without destruction.
1 consecutive failure: 0.4, 40%
2 consecutive failure: 0.16, 16%
3 consecutive failure: 0.064, 6.4%
4 consecutive failure: 0.0256, 2.56%
5 consecutive failure: 0.01024, 1.024%
6 consecutive failure: 0.004096, 0.4096%
7 consecutive failure: 0.0016384, 0.16384%
8 consecutive failure: 0.00065536, 0.065536%
9 consecutive failure: 0.000262144, 0.0262144%
10 consecutive failure: 0.0001048576, 0.01048576%
Chaos Scrolls 60%| Chaos Scroll 60% |
Alters the equipment for better or worse with a 60% success rate. Dropped by Zombie Mushroom, Annoyed Zombie Mushroom, Jr. Necki, Cold Eye, Lioner, Copper Drake, Drumming Bunny, Panda Teddy, Wild Kargo, Seruf, Strong Stone Goblin, Red Slime, Cube Slime, Balrog 1, Grizzly, Tae Roon, Jar, Homun, Ginseng Jar, Bone Fish, Balrog 2, Captain, Red Slime, Cold Shark, Hankie, Zakum 3, Iruvata, Dragon Rider, Griffey, Snowman, Papulatus, Ravana 4, Dark Cornian, Horned Tail's Head B, Lyka |
Probability of the Chaos Scroll as a Single Event
Probability of success, (Any change), 1 event: 0.6, 60%
Probability of success, Net (overall) Positive change, 1 event: 0.3, 30%
• Probability of success, +5 stat points, 1 event: 0.06, 6%
• Probability of success, +4 stat points, 1 event: 0.06, 6%
• Probability of success, +3 stat points, 1 event: 0.06, 6%
• Probability of success, +2 stat points, 1 event: 0.06, 6%
• Probability of success, +1 stat points, 1 event: 0.06, 6%
Probability of success, Net (overall) Negative change, 1 event: 0.3, 30%
• Probability of success, -5 stat points, 1 event: 0.06, 6%
• Probability of success, -4 stat points, 1 event: 0.06, 6%
• Probability of success, -3 stat points, 1 event: 0.06, 6%
• Probability of success, -2 stat points, 1 event: 0.06, 6%
• Probability of success, -1 stat points, 1 event: 0.06, 6%
Probability of failure, destruction, 1 event: 0.4, 40%
Deviations of Success Effects
The distribution of effects upon scroll success are integers from -5 to 5, excluding 0, which is a failure and subsequent destruction.
Assuming that each deviation has an equal probability of occurrence, each deviation has a probability of 0.06, 6%, meaning that your Chaos Scroll has a 30% chance of adding or subtracting stat points on an overall basis. (See above)
Probability of Change(s) by Categories
1 Stat Category
Probability of an increase or decrease of 5 stat points, 1 event: 0.06, 6%
Probability of an increase or decrease of 4 stat points, 1 event: 0.06, 6%
Probability of an increase or decrease of 3 stat points, 1 event: 0.06, 6%
Probability of an increase or decrease of 2 stat points, 1 event: 0.06, 6%
Probability of an increase or decrease of 1 stat point, 1 event: 0.06, 6%
2 Stat Categories
Probabilities for an Increase or Decrease of 5 Stat Points
Increase or Decrease of 5 on first category, 0 on second category, 1 event: 0.01, 1%
Increase or Decrease of 4 on first category, 1 on second category, 1 event: 0.01, 1%
Increase or Decrease of 3 on first category, 2 on second category, 1 event: 0.01, 1%
Increase or Decrease of 2 on first category, 3 on second category, 1 event: 0.01, 1%
Increase or Decrease of 1 on first category, 4 on second category, 1 event: 0.01, 1%
Increase or Decrease of 0 on first category, 5 on second category, 1 event: 0.01, 1%
Probabilities for an Increase or Decrease of 4 Stat Points
Increase or Decrease of 4 on first category, 0 on second category, 1 event: 0.01, 1%
Increase or Decrease of 3 on first category, 1 on second category, 1 event: 0.01, 1%
Increase or Decrease of 2 on first category, 2 on second category, 1 event: 0.02, 2%
Increase or Decrease of 1 on first category, 3 on second category, 1 event: 0.01, 1%
Increase or Decrease of 0 on first category, 4 on second category, 1 event: 0.01, 1%
Probabilities for an Increase or Decrease of 3 Stat Points
Increase or Decrease of 3 on first category, 0 on second category, 1 event: 0.015, 1.5%
Increase or Decrease of 2 on first category, 1 on second category, 1 event: 0.015, 1.5%
Increase or Decrease of 1 on first category, 2 on second category, 1 event: 0.015, 1.5%
Increase or Decrease of 0 on first category, 3 on second category, 1 event: 0.015, 1.5%
Probabilities for an Increase or Decrease of 2 Stat Points
Increase or Decrease of 2 on first category, 0 on second category, 1 event: 0.015, 1.5%
Increase or Decrease of 1 on first category, 1 on second category, 1 event: 0.03, 3%
Increase or Decrease of 0 on first category, 2 on second category, 1 event: 0.015, 1.5%
Probabilities for an Increase or Decrease of 1 Stat Point
Increase or Decrease of 1 on first category, 0 on second category, 1 event: 0.03, 3%
Increase or Decrease of 0 on first category, 1 on second category, 1 event: 0.03, 3%
Credits to:
charismatic for Probabilities of scrolls
Source: http://www.basilmarket.com/forum/8109/0/Complete_Scrolling_Guide_and_Reference.html
