Forum: Author Hangout

Except that only works if every draw is fully independent, which means to use your example, you have to put the peas back in the bag and mix them back up.

The op is talking about a human population forming couples. Once a couple forms, those two are no longer available to form new couples.

So to go back to your example of peas in a bag, after each pair is drawn, you have to throw those two peas away, there are now one fewer pea of each color drawn (or two fewer of one color if you draw two peas of the same color).

This means that since each draw reduces the remaining population, the draws are not fully independent as each draw has some small effect on the probability of the next draw.

A better way to look at it is in raw numbers.

150 Green, 300 red and 550 Yellow.

if they form couples at random, how many couples will have a green person, ~150. It won't be exactly 150 because you will get some GG couples, but I don't know of any good way to estimate how many.

So you start with 150/1000 green people = 15%

After forming couples, you effectively cut the population in half to 500 couples.

You will get a minimum of 75 green couples if all greens pair with another green and a maximum of 150 green couples if no you get no GG couples.

That's a minimum of 75/500=15% and a maximum of 150/500=30%

If you average the min and max, that gives 112.5 rounding up since you can't have half a couple and the extra green person goes somewhere, 113/500 = 22.6%

It would work out a bit differently on the other end, since Yellow has the highest population, you would get a minimum of (550-300-150)/2 = 50 YY couples

Except that only works if every draw is fully independent, which means to use your example, you have to put the peas back in the bag and mix them back up.

If a population is sufficiently large it doesn't matter. If the population is very small, you're right, the events wouldn't be independent and can lead to different outcomes depending on the sequence of events.

In your example with just a thousand, there's a nonzero chance no green-green or red-red pair would form at all, and only few yellow-yellow pairs are guaranteed to form because all yellows can't be exhausted by other color pairings.

But that is complexity that is unnecessary for global averaging, unless, it is indeed stated this happens within confines of a single school or very small village, and even then the independent averages are informative.

If a population is sufficiently large it doesn't matter.

That depends on how many "draws" you intend to make.

If you start with a large population, the effect of individual draws will initially be insignificant. However, after enough draws, the cumulative effect will be significant.

In your example with just a thousand, there's a nonzero chance no green-green or red-red pair would form at all, and only few yellow-yellow pairs are guaranteed to form because all yellows can't be exhausted by other color pairings.

Actually, the second half of that would hold true no matter how large the population is. As long as the relative percentages are held constant, the majority group can't be exhausted by pairings with the other two groups. It doesn't matter if the population is 1,000, 1,000,000, or 100,000,000,000.

And as long as pairings are truly random, there will be a non zero probability of no in sub-group pairings for the smallest sub-group. The probability of such an out come might approach zero as the population increases, but it will never get there.

Sure, for any N there would be 1/N! chance of any specific combination. Only that's a rapidly shrinking number as N grows.

Only that's a rapidly shrinking number as N grows.

Yes, but it never quite reaches zero, so it's always non-zero as long as N is finite.

Yes, but we're not talking about exact outcomes, but about likelihood of any given color combination to exist.

I'm not saying exactly 4.5% of all couples must necessarily be Red-Green, I'm saying the unbiased chance to roll a Red-Green couple is 4.5%. For that chance to realize you would necessarily need quite a few rolls.

And, of course, some couples are already formed. Those will presumably stick together

Not necessarily. Depends on the relationship and, apparently, how magic is presented to the resisting spouse. I say apparently because the first couple to face this split up, but the circumstances were extreme. As one of my characters keeps suggesting, they have to avoid drawing conclusions until they have a larger sample size.

And there are other relationships, parents, siblings, employers.
it's easy to say, "Head for the hills," but few of us could support ourselves in the hills, and fewer still could support ourselves comfortably.

Yup. The original entry point is a small town near Huntsville, Alabama in 1973. I'm expecting a significant turnover in the town's population. And living in the hills is different as humanity's control over electricity and explosions fails. Of course, the concentration in urban areas of those who are attracted to using magic for power over others could make cities into post-apocalyptic horrors. Depends on how well the team does in carrying out their guidance.

Sorry. Couldn't resist a little teaser. (At least I hope it's a teaser. If you hate it, please be kind and don't tell me now! I'm not to that point yet.) Now, I need to get back to working on the story to see if I can get it to a point where I'd be willing to post it.