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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]

Still, the one-number-per-year thing is a real bummer of the current system.[/quote]

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people. [/quote]

In this hypothetical, you are correct.  Only one flip is the best procedure.

But your hypothetical is flawed.  The true situation is that there are many schools.  So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die.  Would you rather have one roll, and if it turned up badly you got shut out of all your choices?  Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

[/quote]

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way. [/quote]

^^ Failure to understand mathematics

I’m done here.  Take a stats or applied math class please.  Pay attention in sections on “correlated outcomes”[/quote]

I have a degree in mathematics from Harvard and the PP is exactly right -- the odds are exactly the same. Show your work or don't call names.

Proof by induction:

Assume every participant in the lottery can pick one school. You are competing against only people who picked the same school as you. Regardless of whether it is one roll per school or one roll for the whole lottery, you have one roll and you get the spot if you roll the highest in your group. So the odds are exactly the same.

Assume that it is true that if everyone picks n schools the odds are the same for one roll or 100 rolls. Does that imply that they are the same for n+1? The outcome we are assessing is whether you get shut out, so we are looking at whether the odds of getting the seat at your n+1 choice change depending on whether there are 100 rolls or one roll. In either case the pool of competitors is the same, and the person with the highest roll in that group gets the seat. So again the odds are exactly the same.

Since the hypothesis is true when n=1, and it has been shown that the hypothesis being true for n implies it is true for n+1, the hypothesis is proved.[/quote]

Look you too are making a hash of this math and making Harvard look bad.

Your discrete-math arguments do not apply to reasoning about probabilities.  Your induction argument fails because the n case is statistically dependent on the n+1 case, so you cannot assume the n case to be true when proving the n+1.

What you want to do instead is calculate the VARIANCE of outcomes with 1 roll or 100 rolls for 100 schools.  You are correct that the number of seats does not change so the number of students given a seat does not change.  What changes is the ordering and the waitlist positions.  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.

Again, it’s been discussed above that the situation above is suboptimal from a lottery point of view (it is unstable).  So don’t take it too seriously.  But the posts above about fixed number of seats are just missing the point.

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

OMG. I am not even the PP and you are driving me insane. You are wrong. You can only get into one school in the end. Getting a number so bad you are shut out of every school you apply to is statistically the same thing/just as likely as getting the number of independent rolls required to shut you out of every school. That's the whole point. Many people don't end up at their #1 school or shut out entirely, they get into a school somewhere in the middle of their list... akin to getting the combo of independent rolls that gets them into some schools and not others w/ a rule that you can only take the seat at the school you preferred most. THAT'S THE WHOLE POINT OF THE LOTTERY. Yes, there is only one master number, but it essentially enters you into independent lotteries for each school. Whether you get different master numbers for each independent lottery or one master number does not affect your odds of getting into a school. [/quote]

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