OK, so first of all, what is the basic probability of psionics? According to the Player's Handbook 1e, if you have an ability score of 16 or higher in INT, WIS, or CHA, you have a base 1% chance of having psionic powers. So the question then becomes, what percentage of people have ability scores that high?

First of all, from the basic odds of rolling dice: The odds of having a score of 16 is 6/216, or 1/36.

So, 1 in 36 people will have a 16 in, say, INT. 1 in 100 of them will have psionic power. Thus, 1 in 3600 people will have 16 INT and a psionic power. Think about what that means:

--In a city of 36,000 people, 10 of them will have 16 INT and a psionic power.

Now given that the base chance of having a 16 WIS or 16 CHA is the same as having a 16 INT, the 1% chance of psionics gives us the same number as well. Thus 1 in 3600 peole will have 16 WIS and a psionic power, and 1 in 3600 people will have a CHA of 16 and a psionic power.

--In a city of 36,000, 10 of them will have a 16 WIS and psionics, and 10 of them will have 16 CHA and psionic power.

**Thus, in our city of 36K, we can expect 30 people to have psionic powers because of their single 16 ability score.**

So what about people with scores higher than 16? It gets a little more complicated here because the Players Handbook gives different bonuses for high scores in the three different abilities. First, the basic probability of the dice: The odds of having an ability score of 18 is 1/216, and the odds of having an ability score of 17 is 3/216, or 1/72.

*INT = 17*

The score of 17 INT gives the person a +2.5% chance of having psionic powers. 1/72 has a 17 INT, and 3/100 of them will have psionics. Thus 1 in 2400 will have both. In our city of 36,000, we would expect to have 15 people to have INT 17 and psionic power.

*WIS = 17*

The score of 17 WIS gives the person a +1.5% chance of having psionic powers. 1/72 has a 17 WIS, and 2/100 of them will have psionics. Thus, 1 in 3600 will have both. In our city of 36,000, we would expect to have 10 people to have WIS 17 and psionic power.

*CHA = 17*

The score of 17 CHA gives a person a +0.5% chance of having psionic powers, but unfortunately, fractions are rounded down, so it remains the base 1/100 chance. 1/72 has 17 CHA, and 1/100 will have psionics. Thus, 1 in 7200 will ahve both. In our city of 36,000, we would expect to have 5 people to have CHA 17 and psionic power.

**Thus, in our city of 36K, we can expect 30 people to have psionic powers because of their single 17 ability score.**

*INT = 18*

The score of 18 INT gives the person a +5% chance of having psionic powers. 1/216 has a 18 INT, and 6/100 of them will have psionics. Thus 1 in 3600 will have both. In our city of 36,000, we would expect to have 10 people to have INT 18 and psionic power.

*WIS = 18*

The score of 18 WIS gives the person a +3% chance of having psionic powers. 1/216 has a 18 WIS, and 4/100 of them will have psionics. Thus, 1 in 5400 will have both. In our city of 36,000, we would expect to have 6.7 people to have WIS 18 and psionic power.

CHA = 18

The score of 18 CHA gives a person a +1% chance of having psionic powers. 1/216 has a 18 CHA, and 2/100 of them will have psionics. Thus, 1 in 10,800 will ahve both. In our city of 36,000, we would expect to have 3.3 people to have CHA 18 and psionic power.

**Thus, in our city of 36K, we can expect 20 people to have psionic powers due to their one ability score of 18.**

****In sum, because of single ability scores of 16, 17, or 18,

**we can expect a city of 36K to have 80 people with psionic powers**. ****

*Combinations of Ability Scores*

Having multiple scores that are in the high range gives you a slightly higher chance of having psionic powers. The problem is, people are far LESS likely to have multiple high ability scores than just one high ability score. Thus, the people who have high scores in 2 or 3 abilities and a psionic power are much more rare.

17 INT (+2.5%) + 17 CHA (+0.5%) = 1/72 x 1/72, 4% base chance = 1 in 129,600

17 INT (+2.5%) + 18 CHA (+1%) = 1/72 x 1/216, 4% base chance = 1 in 388,800

18 INT (+5%) + 17 CHA (+0.5%) = 1/216 x 1/72, 6% base chance = 1 in 259,200

18 INT (+5%) + 18 CHA (+1%) = 1/216 x 1/216, 7% base chance = 1 in 666,514

17 INT (+2.5%) + 17 WIS (+1.5%) = 1/72 x 1/72, 5% base chance = 1 in 103,680

17 INT (+2.5%) + 18 WIS (+3%) = 1/72 x 1/216, 6% base chance = 1 in 259,200

18 INT (+5%) + 17 WIS (+1.5%) = 1/216 x 1/72, 7% base chance = 1 in 222,171

18 INT (+5%) + 18 WIS (+3%) = 1/216 x 1/216, 9% base chance = 1 in 518,400

17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/72 x 1/72, 3% base chance = 1 in 172,800

17 WIS (+1.5%) + 18 CHA (+1%) = 1/72 x 1/216, 3% base chance = 1 in 518,400

18 WIS (+3%) + 17 CHA (+0.5%) = 1/216 x 1/72, 4% base chance = 1 in 388,800

18 WIS (+3%) + 18 CHA (+1%) = 1/216 x 1/216, 5% base chance = 1 in 933,120

--17 INT (+2.5%) + 17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/72 x 1/72 x 1/72, 5% base chance = 1 in 7,464,960

--17 INT (+2.5%) + 17 WIS (+1.5%) + 18 CHA (+1%) = 1/72 x 1/72 x 1/216, 6% base chance = 1 in 18,662,400

--17 INT (+2.5%) + 18 WIS (+3%) + 17 CHA (+0.5%) = 1/72 x 1/216 x 1/72, 7% base chance = 1 in 15,996,342

--17 INT (+2.5%) + 18 WIS (+3%) + 18 CHA (+1%) = 1/72 x 1/216 x 1/216, 7% base chance = 1 in 47,989,029

--18 INT (+5%) + 17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/216 x 1/72 x 1/72, 8% base chance = 1 in 13,996,800

--18 INT (+5%) + 17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/216 x 1/72 x 1/72, 8% base chance = 1 in 13,996,800

--18 INT (+5%) + 17 WIS (+1.5%) + 18 CHA (+1%) = 1/216 x 1/72 x 1/216, 8% base chance = 1 in 41,990,400

--18 INT (+5%) + 18 WIS (+3%) + 17 CHA (+0.5%) = 1/216 x 1/216 x 1/72, 9% base chance = 1 in 37,324,800

--18 INT (+5%) + 18 WIS (+3%) + 18 CHA (+1%) = 1/216 x 1/216 x 1/216, 10% base chance = 1 in 100,776,960

## 2 comments:

interestingly according to 0d&d and arneson's fyrd (militia) numbers a city of 45,000 will have 81 magic-users. 54 low level ones and 27 of at least 7th level.

I wonder if he was working from a similar ratio?

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