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[quote=Anonymous][quote=Anonymous][quote=Anonymous]
I guess the take home here from this thread is: yes, reasoning about probability and stochastic processes is hard.  [/quote]

No, the takeaway is you are a stubborn person. You got an idea into your head. You find it impossible to believe your idea is wrong, so you go on all sorts of logical excursions -- and throw in insults to those who try to set you straight, to boot.

Your logical fallacy is in this paragraph, in the bolded part:
[quote]
What you want to do instead is calculate the [b]VARIANCE of outcomes with 1 roll or 100 rolls for 100 schools[/b]. You are correct that the number of seats does not change so the number of students given a seat does not change. [b]What changes is the ordering and the waitlist positions[/b]. To see this, look at the kid with the lowest 1-roll master number. They are last on all their waitlists. That situation does not happen if there are multiple rolls.[/quote]

Having more rolls doesn't affect the variance of outcomes. It affects the variance of the numbers used to determine the outcomes. With a single roll you get a linear distribution, with more rolls you get more of a normal distribution. But when you take those numbers are rank the participants, the outcome is the same: someone is first, someone is last, and only some of the participants get a seat because there are more participants than seats.

The ordering and waitlist positions aren't important, what's important is whether you get a seat or not. It does you no good to have a good waitlist position if the waitlist doesn't move. You seem to be obsessed with the idea that the lottery lets those with good number "hoard" good fortune, which could more equitably be distributed to the less fortunate. But that's not how it works. Everyone gets either one seat, or no seat. There is no way to distribute them more granularly.

I'm assuming you're obsessing over this because you got a bad lottery number and just can't accept that you're unlucky rather than the system being broken. I'm sorry you got a bad number, better luck next time. But this is a strange thing to obsess over. As another poster pointed out, the lottery is one of the best-functioning things in all of public education in DC. And it has consistently gotten better in recent years. If you want to get upset, there are lots of bigger issues to get upset about. [/quote]

“Linear distribution” (not a thing; try Bernoulli distribution for a coin or discrete uniform for a die)
“More normal distribution” (?)
“One seat” (ignoring waitlists)

Again: I recommend a stochastic processes class.  I think where you’re being tripped up is that a statistical model should be thought of as having an ensemble of outcomes.  This idea is what links the variance of die rolls with the variance of outcomes.  Cheers![/quote]

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