I promised to look in on psychic powers and so I will. The psychic powers are really cool but how likely are you to get them during play? This we will find out. We will also find out if beer and math go together. This section is math heavy so it will likely be a little boring therefore consider yourself warned. My task will be to provide an estimate, not churn through all the permutations since that would make it even more boring then it already is.
Righto, so Carcosa’s much lauded psychic powers rules, that rock and are easy to use, mention every character with a mental stat over 15 has a chance of getting psychic powers at char generation. This chance is not high. In fact, I suspect this chance might be utterly negligable. Its been a while since I had a proper statistics course but calculating probabilities was in it so I might remember enough to get by, be sure to correct me if I don’t. I’m rounding shit off also because I am lazy.
Righto, first thing we do is figure out what the chance of getting a 16 on a 3d6 is.
We can get a 16 as follows: 5, 5, 6. (x3 because the six can be the first or the second dice instead of the third one).
4, 6, 6. (again times 3, [6-4-6] and [6-6-4]).
Thats six possible combos out of 6 * 6 * 6 = 216 possibilities. 6/216 = .028 or 2.8 % of getting a sixteen. (we assume you roll in order as per OD&D and Lamentations of the flame princess standard procedure, allowing players to assign stats massively increases the chance of psionic powers if you are aiming for that).
Therefore, the chance of getting a 16 on any single mental stat is 2.8%.
We do the same for 17. So 6, 6, 5. Times 3. 3/216 = 1.4 %
And 18. 6, 6, 6. 1/216. = 0.5 %
And 15 too, the triksiest one.
6-6-3. Times three.
6-5-4. 6-4-5. 5-6-4. 5-4-6. 4-5-6. 4-6-5. 6 possibiliites.
For a total of 10/216. = 4.6%
Easy so far. Next part is trickier. We want the chance of just a single 15 among the 3 stats that generate psychic powers(Int, wis, cha). We cannot simply take the chance of rolling a single 15, since the probabilities are not independent(if we had two 15s this would alter our starting chance of getting psychic powers. The chance of getting psychic powers changes depending on what the other two stats are. So, in order to get the result we want, we want the odds of a single 15, with the other two stats fourteen or lower. I am adding more notes then I have to so its easier to see whether I have made a mistake or not.
P(Single 15) = P(15) * P(14 or lower) * P(14 or lower) = .046 * (1-P(15 or higher) * P (1- 20/216) = .046 * .91 * .91 = .038
15 Int means the chance of getting psychic powers is 1%. So adding 2 more zeros to the equation will suffice. P = .00038 All these probabilities are added to the “probability pool” which is P(starting with psychic powers).
15 wis means your chance is .5% so we divide .00038 by 2 P = .00019
15 cha means your chance is 1.5% so we simply add the two prior ones together. P = .00057
Combined they are P = .00114. Since the chance of higher numbers becomes increasingly less likely I suspect this might be the single highest probability. If this is true, the chance of a psychic character is something like 1 in 300.
This is but the first step in a very lengthy and drawn out process. P(2 15s) = P(15) * P(15) * P(14 or lower) = .0019. You don’t multiply because in this case the order in which the dice end up is important and will change the outcome. Chances for getting psychic powers stack.
P(15 int/15 wis) = .0019 * .015 = .000028. Utterly insignificant.
P (15 int/15 cha) = .0019* .025 = .000047.
P(15 wis/15 cha) = .0019 * .02 = .000038.
For a whopping combined .000113. Add to the total of .00114 makes .00121
Repeat for 3 15s. Even smaller. (.046) ^ 3 = .000097. Chance is .000097 * .045 = .0000043. So little it cant be added to my figure the way I portray it now. We can ignore it since it does nothing.
Single 16. Probability makes its comeback. The chance of single 16 is .028, a little more then half the previous chance. The Probability of getting psychic powers for 16 is double that of 15. 16 is like the probability sweet spot. P(psychic powers single 16) = .028 * .91 * .91 = .023 We multiply by the percentile chance of getting psychic powers like so, and notice the chance of getting them seems to have doubled. The chance of a 17 is exactly half that of a sixteen unfortunately, and the probability of psychic powers does not double from a 16 to a 17, so from 17 on shits starts nosediving.
P(16 int) = .02 * .028 = .00056
P(16 wis) = .01 * .028 = .00028
P(16 cha) = .03 * .028 = .00084
For a very impressive .00168. Added to the total this makes for a promising .00289.
We can repeat for 2 16s. (.028) ^2 * .91 = .000713. Already very low.
P(16 int/16 wis) = .000713 * .03 = .000021
P(16 int/16 cha) = .000713 * .05 = .000036
P(16 wis/16 cha) = .000713 * .04 = .000028
a whopping .000085. Added to .00289 yields us .00297.
We could calculate the chance for 3 16s but we wont since the chance of 3 sixteens is (.028) ^ 3 and multiplying that by the pooled psychic power chance(6%) yields us something like .000001 so basically nothing. You could pool all the probabilies of having 2 15s and a 16 or two 15s and a sixteen and you would get comparable probabilities. you’d get more because there are many possible combinations. But not enough to make a fucking difference. .00001 or maybe something along the lines of .00002 or even the optimistic .00005. Would not change shit.
The only really interesting one is P(15 and 16). .028 * .046 * .91 = .0011
P (15 int 16 wis) .0011 * .02 = .000022
P(16 int 15 wis) .0011 * .025 = .0000275
P(15 int 16 cha) .0011 * .04 = .000044
P(16 int 15 cha) .0011 * .035 = .000038
P(15 wis 16 cha) .0011 * .035 = .000038
P(15 cha 16 wis) .0011 * .025 = .0000275
For a very unimpressive grand total of .000197. Added to the p-pool, we see a promising climb from .00297 to .00316. But as we are about to see its ascent, already hampered, will slow down to a crawl. I dont think the chance of getting a psychic character will even hit the 1%.
Quick and dirty P(17). .014 * (.91) ^2 yields us .011. This where we are going to run out of steam. We do our habitual multiplication for 17 int, wis cha and add .00033, .000165 and .000495. We sigh as we add .00069 to the total of .00316 for .00385. Why does this happen? The chance of getting a 17 is half the chance of getting a 16 but the chance of getting psychic powers has increased by a half only. This trend actually continues with 18, with the chance being a third of that of getting a 17 and the chance of getting psychic powers only 1/3 more then 17.
Quick and dirty P(2 17s). We experience despair as we gaze blankly at the chance of 2 17s. .00017. Odds of psychic powers hover around .06 so we would get results along the lines of .000008. Multiply times three for a stunning.000024. Three seventeens or any combination of seventeens and sixteens will simply not amount to very much, even with a lot of permutations.
With 18 it becomes .0038 times 3 times average chance of getting p powers .03 so something like .000342. We are at .0041something.
I would estimate the combined chance of getting psychic powers will be lucky to rise above .005. That means that in laymans terms, you have about a 1 in 200 shot of getting psychic powers. The powers might be very well written, but you will be very lucky indeed if you ever get to see them in action. Note that these calculations assume 3d6 in order and do not take into account the fact that in Loftp it is recommended you reroll ‘hopeless’ characters.
In final, bitter irony, one of the finest, most streamlined psychic powers rulesets will see less use then the old 17 cha paladin class. This problem can be easily fixed by simply multiplying the chance of getting psychic powers during character creation by 2 or even 3.