Does the Tiefling mutation manifest at a greater probability per child in later generations?

Question

In a comment thread elsewhere on RPG.SE, someone asserted that tiefling features manifest increasingly down the generations, citing the following text as his evidence:

Tiefling says

Most tieflings never know their fiendish sire, as the coupling that produced their curse occurred generations earlier. The taint is long-lasting and persistent, often manifesting at birth or sometimes later in life, as a powerful, though often unwanted, boon.

Does this text in fact mean that the probability that any given descendant will manifest the taint grows over time?

Does it mean that the chance of the very first generation manifesting the taint is small?

Answer 1

The quoted sentence is not enough to imply that the the chance of manifesting the taint starts low, or that the chance of an individual getting it increases with latter generations. In fact, the chance of it manifesting can go down significantly over time and still make that sentence true. Let's look at an example.

To simplify the math, let's imagine that:

• The probability that the taint manifests in any first generation child is 70%,
• The probability that it manifests in any given child of the next 4 generations is 10%,
• That it drops to 0% after 5 generations,
• And that each generation has 2 children.

This means that our hypothetical fiend has 2 children, 4 grand, 8 great-grand, 16 great-great-grand, and 32 great-great-great-grand children. On average, how many first generation tiefling children will come from this union?

2 * 0.7 = 1.4

And on average, how many latter generation tiefling children will come of this union?

(2+4+8+16+32) * 0.1 = 6.2

Note that I'm not suggesting that these are the probabilities, only that the quoted sentence holds true even under these probabilities. There may be evidence elsewhere that first generation tieflings are rare...but this sentence isn't sufficient evidence to claim it.

Answer 2

That passage doesn't make any statement about probability in the first place, making the whole consideration moot. This wording:

Most tieflings never know their fiendish sire, as the coupling that produced their curse occurred generations earlier.

Is trivially transformed into this:

Most tieflings never know their fiendish sire because the coupling that produced their curse occurred generations earlier.

Or in much simpler words, "Most people never know their great-great-...-grandparents," which is not controversial at all.

It's comparable to World of Darkness vampires: most of them don't know the progenitor of their curse because most vampires aren't Antediluvians who have met Caine.

Answer 3

No.

Firstly, many "first gen" half-breeds are half-demons or the like. You tend to get tieflings farther down, and that can be from tiefling+tiefling or tiefling+non-tiefling or non-tiefling with recessive tiefling trait+non-tiefling. You seem to be mostly focused on the latter but even with the former you don't know your "fiendish sire" except by family history.

There's always going to be more in later generations, because generations tend to increase geometrically. Even if the rate goes down the numbers catch up (as @JeffFry calculates for you).

Answer 4

The description seems to indicate a classic description of an Autosomal recessive gene.

Which indicates that a mating of "fiendish sire" and non-carrier mother will 100% be a carrier of the "taint" only (i.e. no Tiefling children) and only sire children that express the taint with a 25% chance with another carrier.

Even a paring of a carrier and the "fiendish sire" will produce 50/50 Tifling/carrier only children.

So populations of predominantly Teiflings will often have Tiefling children (compare the blonde hair/blue eyes recessive trait in scandinavian countries).

That said, the description of dominant recessive traits is somewhat archaic given the extensive complications mapping the human genome has discovered in what actually happens at the level of expression of individual proteins. The large difference of the Tiefling phenotype would suggest a complex genetic inheritance structure (or most probably a supernatural element), so feel free to make up what you want.

Answer 5

The question might be re-phrased:

Given this short piece of canon, can we say anything about related probabilities?

The basic answer to that is "yes". We can say that taking all tieflings as a group, the majority of them are at a far-removed generation from where the Fiendish taint was introduced to the bloodline. This rules out fiendish inheritence schemes where the probability of manifesting the taint (i.e. being a tiefling) falls off very rapidly after the first generation.

However, that is only a small proportion of all possible schemes you could invent.

Does that mean that the probability that any given descendant will manifest the taint grows over time?

No, because generation size grows over time, a fixed probability will produce higher numbers in each generation.

However, it doesn't rule it out, either. A scheme where the probability grew on each generation (e.g. 0.1, 0.2, 0.3, 0.4...0.9, 0.91, 0.92...) would fit canon.

Does it mean that the chance of the very first generation manifesting the taint is small?

No, again because the first generation is outnumbered by members in future generations. It is very easy to construct schemes that have high probability in generation 1, much lower in generation 2 onwards, which fit canon. For example, a probability of 1.0 in first generation and 0.25 in subsequent generations would easily result in the bulk of all tieflings being in a far-removed generation.

However, it doesn't rule it out, either. A scheme with probability 0.01 in first 3 generations, and 0.25 in all future generations would fit the canon.

In short, the quoted canon says very little about probabilities, and even if you are concerned about running a game adhering strictly to this small piece of text, then you have huge leeway on how to interpret it.

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For further pedantic-ness, this answer is making an assumption that the rate of ongoing tainting is small compared to the size of current tiefling population. A large amount recent Fiendish love affairs in an adventure background would complicate things - and if you wanted to have that in a world background, plus stick to canon as written, plus remain self-consistent in a purely mathematical sense, you would indeed need to have a lower initial probability.

Answer 6

My original point was that the statement didn't assert an increasing chance of mutation occurring over time, but because over generations there are more people there is a greater chance of it occurring. The actual chance is still the same for an individual person, but the chance of one in a group getting the mutation increases as the group size increases.

Lets assume for the moment that the chance of becoming a tiefling is 1 in 10. Every single child born with demon blood has that 1 in 10 chance. Now lets also assume that every person has 2 children, so we have exponential growth. In our first generation we have 2 children sired by a demon, each child having a 1 in 10 chance of being a tiefling. The formula for working the statistical chance of one of the group getting the mutation is 1 - (9/10)ⁿ where n is the number of children in that generation (it's 9/10 in the formula because there is a 9 in 10 chance of not gaining the mutation). That means in this generation we have a total of 0.19 chance of a tiefling appearing in the group, just slightly under a 2 in 10 chance.

Take the second generation, each of the two children in the first generation has two children of their own. That gives us 4 children of the second generation in total, each with a 1 in 10 chance of being a tiefling. So the total chance of a tiefling occurring in this generation is 0.3439, almost twice as likely as the previous generation.

We can keep going:

Generation | Num Children | Chance of Tiefling
    1      |    2         |    0.19
    2      |    4         |    0.3439
    3      |    8         |    0.5695
    4      |    16        |    0.8147
    5      |    32        |    0.9657

So as you can see, by the time we get to the 5th generation, there is an almost 100% chance of one of the 32 children being a tiefling. Obviously the statistical chance will be much smaller than 1 in 10, and the number of children will not be a smooth exponential increase, but I just used those numbers to simplify things for this example. The maths still holds true with more realistic numbers.