Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap

[Anonymous]

The application strategy is , apply to all the colleges that you would want to attend. Don't limit yourself to x reachs, y targets and z safeties

[Anonymous]

Anonymous wrote:

Anonymous wrote:Look at it another way. Do you really think that an applicant those stats are in the top 25% of accepted applicants to T20 and checks most boxes, has less than a coin flip chance (55% assuming 4% at each) of getting into at least one of the T20, assuming they apply to all 20?

You have no idea what that person’s odds are of getting into a top 20 college is the fn point. No formula can tell you.

If it were as simple as you make it, advisors would tell kids “You don’t need reach-match-safety, just apply to all top 20 and you’ll likely get into one!”

They don’t do that. Why do you think that is?

Because even applying to all top 20, assuming 4%, it is still basically a coin flip. But the odds of getting into one when applying to all 20 are significantly better than applying to 10.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.

This one (04/06/2025 06:00) correctly highlighted the difference between dependent and independent events. But I have not seen anyone point out the fact that game theory cannot work because the people in the selection pool do not have equal chances of being selected.

Applications are read and the selection of any candidate for any particular school is a curated event. Selection is deterministic based on the reading of an application; it is not random. Game theory does not work in this instance.

Yes, I feel like this is what OP is missing. OP’s math only works if admissions are all random lotteries of applicants.

Every time this board had a high stats kid rejected from all t20, every one jumped out to say, oh but college admission is a lottery!

Is it? Is it not? Feels like catch 22.

compare to getting into a car crash. A car crash is simply physics of one car hitting another for whatever reason. You don't have someone pulling numbers out of a hat. But you can model the probability and insurance companies do it all the time.

Yes, they do it all the time, for a large group of people, not just for one person. College applicants are one person. Why is this so hard to understand?

Do you think every applicant with the stats for Harvard has the same 4% chance of admission?

Do you realize how low of chance 4% already is? It is the same as having 1 thru 25 numbered balls in a binding and picking the right one on the first try. Very hard.

No no no no no no no.

You have essentially said that every applicant has the same chance of admission.

They don’t. And no applicant knows the difference. Certainly not enough to use a probability formula to develop an application strategy.

It is not the same as picking a number from a finite set. You have no idea how many balls are in the jar, so you don’t know what the odds are of you picking the right one. It’s a useless number with no practical application.

no one is trying to determine an actual probability , to calculate insurance premiums or whatever

It is enough to point out

1) they are independent events
2) there is enough randomness
3) that only one acceptance is sufficient

OK now I am being gaslighted.

Yes some are trying to determine actually probability.

In fact the title of this thread explicitly mentions 33%.

Are you reading THIS thread?

[Anonymous]

It's early, but this could be the dumbest post of the year.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.

This one (04/06/2025 06:00) correctly highlighted the difference between dependent and independent events. But I have not seen anyone point out the fact that game theory cannot work because the people in the selection pool do not have equal chances of being selected.

Applications are read and the selection of any candidate for any particular school is a curated event. Selection is deterministic based on the reading of an application; it is not random. Game theory does not work in this instance.

Yes, I feel like this is what OP is missing. OP’s math only works if admissions are all random lotteries of applicants.

Every time this board had a high stats kid rejected from all t20, every one jumped out to say, oh but college admission is a lottery!

Is it? Is it not? Feels like catch 22.

compare to getting into a car crash. A car crash is simply physics of one car hitting another for whatever reason. You don't have someone pulling numbers out of a hat. But you can model the probability and insurance companies do it all the time.

Yes, they do it all the time, for a large group of people, not just for one person. College applicants are one person. Why is this so hard to understand?

Do you think every applicant with the stats for Harvard has the same 4% chance of admission?

Do you realize how low of chance 4% already is? It is the same as having 1 thru 25 numbered balls in a binding and picking the right one on the first try. Very hard.

No no no no no no no.

You have essentially said that every applicant has the same chance of admission.

They don’t. And no applicant knows the difference. Certainly not enough to use a probability formula to develop an application strategy.

It is not the same as picking a number from a finite set. You have no idea how many balls are in the jar, so you don’t know what the odds are of you picking the right one. It’s a useless number with no practical application.

no one is trying to determine an actual probability , to calculate insurance premiums or whatever

It is enough to point out

1) they are independent events
2) there is enough randomness
3) that only one acceptance is sufficient

OK now I am being gaslighted.

Yes some are trying to determine actually probability.

In fact the title of this thread explicitly mentions 33%.

Are you reading THIS thread?

I think OP is just trying to make a point of how probability and independent events works

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Look at it another way. Do you really think that an applicant those stats are in the top 25% of accepted applicants to T20 and checks most boxes, has less than a coin flip chance (55% assuming 4% at each) of getting into at least one of the T20, assuming they apply to all 20?

You have no idea what that person’s odds are of getting into a top 20 college is the fn point. No formula can tell you.

If it were as simple as you make it, advisors would tell kids “You don’t need reach-match-safety, just apply to all top 20 and you’ll likely get into one!”

They don’t do that. Why do you think that is?

Because even applying to all top 20, assuming 4%, it is still basically a coin flip. But the odds of getting into one when applying to all 20 are significantly better than applying to 10.

You are contradicting yourself. Is it a “coin flip” or are the odds significantly better?

Assuming you used “coin flip” to not mean 50-50 but rather that it is an unknown quantity.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.

This one (04/06/2025 06:00) correctly highlighted the difference between dependent and independent events. But I have not seen anyone point out the fact that game theory cannot work because the people in the selection pool do not have equal chances of being selected.

Applications are read and the selection of any candidate for any particular school is a curated event. Selection is deterministic based on the reading of an application; it is not random. Game theory does not work in this instance.

Yes, I feel like this is what OP is missing. OP’s math only works if admissions are all random lotteries of applicants.

Every time this board had a high stats kid rejected from all t20, every one jumped out to say, oh but college admission is a lottery!

Is it? Is it not? Feels like catch 22.

compare to getting into a car crash. A car crash is simply physics of one car hitting another for whatever reason. You don't have someone pulling numbers out of a hat. But you can model the probability and insurance companies do it all the time.

Yes, they do it all the time, for a large group of people, not just for one person. College applicants are one person. Why is this so hard to understand?

Do you think every applicant with the stats for Harvard has the same 4% chance of admission?

Do you realize how low of chance 4% already is? It is the same as having 1 thru 25 numbered balls in a binding and picking the right one on the first try. Very hard.

No no no no no no no.

You have essentially said that every applicant has the same chance of admission.

They don’t. And no applicant knows the difference. Certainly not enough to use a probability formula to develop an application strategy.

It is not the same as picking a number from a finite set. You have no idea how many balls are in the jar, so you don’t know what the odds are of you picking the right one. It’s a useless number with no practical application.

no one is trying to determine an actual probability , to calculate insurance premiums or whatever

It is enough to point out

1) they are independent events
2) there is enough randomness
3) that only one acceptance is sufficient

OK now I am being gaslighted.

Yes some are trying to determine actually probability.

In fact the title of this thread explicitly mentions 33%.

Are you reading THIS thread?

I think OP is just trying to make a point of how probability and independent events works

I don’t care what you think the op meant, I care what the op wrote. It’s clear and explicit, and there is a freakin’ number and a percent sign.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.

This one (04/06/2025 06:00) correctly highlighted the difference between dependent and independent events. But I have not seen anyone point out the fact that game theory cannot work because the people in the selection pool do not have equal chances of being selected.

Applications are read and the selection of any candidate for any particular school is a curated event. Selection is deterministic based on the reading of an application; it is not random. Game theory does not work in this instance.

Yes, I feel like this is what OP is missing. OP’s math only works if admissions are all random lotteries of applicants.

Certainly the exact probability may be lower or higher than 4%. But if a students scores are in the top 50% for a colleges accepted students, and they check most of the boxes, it would be a reasonable estimate to assume at least half (2%).

No, it would NOT be. You have no idea if that student's chances are 0%. Multiple posters have told you this.

I guess it needs to be repeated again - you can't use game theory without knowing the actual odds. It does not work and is a TERRIBLE way to design an application strategy.

Why would the students chances be 0% if their scores are in top 25% of accepted students and check most or all the boxes?

A variety of possibilities. Sometimes an admissions office has a list of high schools that they aren’t accepting from that year. Not to mention that “all of the boxes” can vary over the course of an admissions season, and the day an application is read and the person reading it can make the difference between a chance and no chance.

that makes it more random, not less

Yes sir or ma'am.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.

This one (04/06/2025 06:00) correctly highlighted the difference between dependent and independent events. But I have not seen anyone point out the fact that game theory cannot work because the people in the selection pool do not have equal chances of being selected.

Applications are read and the selection of any candidate for any particular school is a curated event. Selection is deterministic based on the reading of an application; it is not random. Game theory does not work in this instance.

Yes, I feel like this is what OP is missing. OP’s math only works if admissions are all random lotteries of applicants.

Every time this board had a high stats kid rejected from all t20, every one jumped out to say, oh but college admission is a lottery!

Is it? Is it not? Feels like catch 22.

compare to getting into a car crash. A car crash is simply physics of one car hitting another for whatever reason. You don't have someone pulling numbers out of a hat. But you can model the probability and insurance companies do it all the time.

Yes, they do it all the time, for a large group of people, not just for one person. College applicants are one person. Why is this so hard to understand?

Do you think every applicant with the stats for Harvard has the same 4% chance of admission?

Do you realize how low of chance 4% already is? It is the same as having 1 thru 25 numbered balls in a binding and picking the right one on the first try. Very hard.

No no no no no no no.

You have essentially said that every applicant has the same chance of admission.

They don’t. And no applicant knows the difference. Certainly not enough to use a probability formula to develop an application strategy.

It is not the same as picking a number from a finite set. You have no idea how many balls are in the jar, so you don’t know what the odds are of you picking the right one. It’s a useless number with no practical application.

no one is trying to determine an actual probability , to calculate insurance premiums or whatever

It is enough to point out

1) they are independent events
2) there is enough randomness
3) that only one acceptance is sufficient

Yes some are trying to determine actually probability.

I'm among those who believe this is certainly possible. This might be thought of along the lines of attaching a probably to an outcome rather than determining "actual probability."

[Anonymous]

"attaching a probability," above.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.

This one (04/06/2025 06:00) correctly highlighted the difference between dependent and independent events. But I have not seen anyone point out the fact that game theory cannot work because the people in the selection pool do not have equal chances of being selected.

Applications are read and the selection of any candidate for any particular school is a curated event. Selection is deterministic based on the reading of an application; it is not random. Game theory does not work in this instance.

Yes, I feel like this is what OP is missing. OP’s math only works if admissions are all random lotteries of applicants.

Every time this board had a high stats kid rejected from all t20, every one jumped out to say, oh but college admission is a lottery!

Is it? Is it not? Feels like catch 22.

compare to getting into a car crash. A car crash is simply physics of one car hitting another for whatever reason. You don't have someone pulling numbers out of a hat. But you can model the probability and insurance companies do it all the time.

Yes, they do it all the time, for a large group of people, not just for one person. College applicants are one person. Why is this so hard to understand?

Do you think every applicant with the stats for Harvard has the same 4% chance of admission?

Do you realize how low of chance 4% already is? It is the same as having 1 thru 25 numbered balls in a binding and picking the right one on the first try. Very hard.

No no no no no no no.

You have essentially said that every applicant has the same chance of admission.

They don’t. And no applicant knows the difference. Certainly not enough to use a probability formula to develop an application strategy.

It is not the same as picking a number from a finite set. You have no idea how many balls are in the jar, so you don’t know what the odds are of you picking the right one. It’s a useless number with no practical application.

no one is trying to determine an actual probability , to calculate insurance premiums or whatever

It is enough to point out

1) they are independent events
2) there is enough randomness
3) that only one acceptance is sufficient

Yes some are trying to determine actually probability.

I'm among those who believe this is certainly possible. This might be thought of along the lines of attaching a probably to an outcome rather than determining "actual probability."

You want to determine a probability without determining a probability?

Then just pick a random number out of your behind, because that is of the exact same value as an odds calculation from a formula where the factors are all pulled out of your behind.

[Anonymous]

To the poster above, that's not worth quoting back. To be clear, though, I wasn't suggesting that you can determine anything. I'm pretty sure you can't, actually.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:They are not totally independent, but also not totally dependent. But your point is taken.

The takeaway is that college admission is NOT a lottery system like some posters claimed.

If your stats puts on in the game, you want to apply to AS MANY top 20 as possible!!!

In mathematical terms, related to game theory, they are totally independent events, in that the outcome of one does not affect the outcome of another.

https://mathematicalmysteries.org/independent-and-dependent-events/

But as noted, despite that you cannot use game theory because you can’t know the starting odds of your admission the way you can know that you have a 1 in 52 chance of drawing the 8 of hearts from a full deck of cards.

The occurrence of one does affect the probability of the others also occurring. If a student is in at MIT and Harvard, there is a greater than 4% chance of them also being in at Princeton.

What was the student’s odds at Princeton before they were accepted to MIT and Harvard? How did they change AFTER acceptance to MIT and Harvard? (They didn’t).

That is what dependent events are - that change the likelihood. If the likelihood does NOT change, they are independent events. Game Theory requires independent events for the formula shown to work.

You are speaking about correlation. https://en.m.wikipedia.org/wiki/Correlation.

Do not use game theory when developing a college application strategy.

Correlation is a type of dependence. Two events that are correlated can not be independent.

https://stats.stackexchange.com/questions/509141/correlation-vs-dependence-vs-causality/509221#509221

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:They are not totally independent, but also not totally dependent. But your point is taken.

The takeaway is that college admission is NOT a lottery system like some posters claimed.

If your stats puts on in the game, you want to apply to AS MANY top 20 as possible!!!

In mathematical terms, related to game theory, they are totally independent events, in that the outcome of one does not affect the outcome of another.

https://mathematicalmysteries.org/independent-and-dependent-events/

But as noted, despite that you cannot use game theory because you can’t know the starting odds of your admission the way you can know that you have a 1 in 52 chance of drawing the 8 of hearts from a full deck of cards.

The occurrence of one does affect the probability of the others also occurring. If a student is in at MIT and Harvard, there is a greater than 4% chance of them also being in at Princeton.

What was the student’s odds at Princeton before they were accepted to MIT and Harvard? How did they change AFTER acceptance to MIT and Harvard? (They didn’t).

That is what dependent events are - that change the likelihood. If the likelihood does NOT change, they are independent events. Game Theory requires independent events for the formula shown to work.

You are speaking about correlation. https://en.m.wikipedia.org/wiki/Correlation.

Do not use game theory when developing a college application strategy.

Correlation is a type of dependence. Two events that are correlated can not be independent.

https://stats.stackexchange.com/questions/509141/correlation-vs-dependence-vs-causality/509221#509221

Your own link is entitled correlation-vs-dependence-vs-causality. vs stands for VERSUS. Meaning they are different.

More importantly, this article has nothing to do with dependent events and independent events in probability. A link explaining that was posted above. You choose to ignore it.

You need to do better at this. This is awful.

[Anonymous]

https://www.stat.cmu.edu/~cshalizi/uADA/13/reminders/uncorrelated-vs-independent.pdf

If X and Y are independent, then they are also uncorrelated. Therefore, if X and Y are correlated, they are also dependent.

I read the Wikipedia article (which you couldn't even link correctly), I don't see how this supports your point that the two events are independent, or where on earth your use of the term "game theory" came from.