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

[Anonymous]

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.

[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.

You did not read the link nor do you understand the mathematical concept of independent events.

Dependent Events: one that affects the outcome of another. Picking a card from a deck (1:52), then picking a second card from that deck changes the oddds (1:51)

Independent events: One that does not affect the outcome of another. Picking a card from a deck (1:52) then picking another card from a SECOND deck (1:52).

Whether you are accepted to MIT does not affect the likelihood of whether or not you are accepted to Harvard. Independent events.

This is not debatable.

+100 . Love how simply you have explained dependent and independent events. Thanks.

[Anonymous]

Um, math no workey OP.

If college acceptance was like drawing names from a hat, 4% acceptance means a 1 in 25 chance. So argued, apply to 25 schools, winner chosen at random, might get into 1.

But names aren't randomly selected. The 4% chance simply means almost zero applicants meet the admission criteria

[Anonymous]

Still 4%

[Anonymous]

Anonymous wrote:Still 4%

It’s almost certainly NOT 4% for any given student, it’s just that the true number is not knowable by you in advance.

[Anonymous]

Anonymous wrote:Um, math no workey OP.

If college acceptance was like drawing names from a hat, 4% acceptance means a 1 in 25 chance. So argued, apply to 25 schools, winner chosen at random, might get into 1.

But names aren't randomly selected. The 4% chance simply means almost zero applicants meet the admission criteria

The reality is that far more applicants meet the admission criteria.

The reality is that it's very rare a single applicant sweep all top 20 schools.

The reality is that it's also very rare a single applicant who met the criteria got rejected by all top 20 schools.

The reality is that a typically applicant got waitlisted by a few and rejected by a few, but accepted by one or two.

[Anonymous]

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.

[Anonymous]

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.

Why don’t you quote the examples that are correct? Either the text or time/date sigs will work. Thanks!

[Anonymous]

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.

[Anonymous]

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.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Except that's not how it works, because each of those independent events is dependent on mostly the same factors.

This can't be true. JHU and Cornell are looking for different students, so are MIT and Yale.
Your reasoning reduces college admission to simple stats such as test score and gpa. However, that is not how it works!

Ummm. They are looking for the sane students.

[Anonymous]

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%).

But the math for getting accepted to at least one by applying to all T20s is very much in the students favor. Now whether the student wants to goto that T20 is another question

[Anonymous]

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.

Why don’t you quote the examples that are correct? Either the text or time/date sigs will work. Thanks!

Without intending to be dogmatic, I'd say that this contributor understands the importance of both math and social science (in this case the social science of college admission) in approaching the question:

Look, forecasters don't get the future inflation number or the USD-JPY rate correctly most of the time, but it doesn't stop them from using reason to arrive at a forecast , and they get the direction right most of the time even if not the exact number.

OP is similarly using reason. And the math is correct if you assume a set of qualified students whose stats put them in the range of these schools.

OP used 4% acceptance as an example. You can use Naviance to actually get a sense of probability of not being accepted to a school for your stats (calculate acceptance for that higher stat cluster). So let's say using the Naviance plot of GPA and SAT, your child has a 15% probability of admit at Cornell, and a 15% admit at Dartmouth, (that would be 85% probability of rejection at each). So the probability of rejection FROM BOTH is
0.85*0.85= 0.7225 , i.e. 72%.

If Harvard is a 8% admit probability for your stats, then the probability of reject from ALL THREE is
0.92*0.85*0.85= 0.6647 (66%).

The math is correct...and the correct interpretation is:
1. For those students whose stats put them within the range, applying to more elite schools lowers the likelihood of being rejected by all or put another way improves the probability of being accepted by at least one.
2. But that said , the resultant rejection probability is still high and for most of the best kids rarely gets better than a coin toss.

You don't get shattered when you lose a coin toss. Don't get shattered when your kid doesn't get into an elite.

To this, I'd add a general concept. Questions such as this are accessible to mathematical approaches. You can start with assumptions, however imperfect, in the form of assigned values. Then, with appropriate math, you can get closer than you were before. A feature of probability might even be the expectation that you often will be inaccurate until such time as all the information becomes available and the uncertainty reduces to zero.

On another note, events do not need to be either independent or dependent for probabilistic approaches to be effective. There are mathematical ways to adjust for degrees of dependence. I'd argue as well that there are different ways to define dependence.

Somewhat separately, I'm not understanding the game theory approaches to this question.

[Anonymous]

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.

[Anonymous]

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.

Why don’t you quote the examples that are correct? Either the text or time/date sigs will work. Thanks!

Without intending to be dogmatic, I'd say that this contributor understands the importance of both math and social science (in this case the social science of college admission) in approaching the question:

Look, forecasters don't get the future inflation number or the USD-JPY rate correctly most of the time, but it doesn't stop them from using reason to arrive at a forecast , and they get the direction right most of the time even if not the exact number.

OP is similarly using reason. And the math is correct if you assume a set of qualified students whose stats put them in the range of these schools.

OP used 4% acceptance as an example. You can use Naviance to actually get a sense of probability of not being accepted to a school for your stats (calculate acceptance for that higher stat cluster). So let's say using the Naviance plot of GPA and SAT, your child has a 15% probability of admit at Cornell, and a 15% admit at Dartmouth, (that would be 85% probability of rejection at each). So the probability of rejection FROM BOTH is
0.85*0.85= 0.7225 , i.e. 72%.

If Harvard is a 8% admit probability for your stats, then the probability of reject from ALL THREE is
0.92*0.85*0.85= 0.6647 (66%).

The math is correct...and the correct interpretation is:
1. For those students whose stats put them within the range, applying to more elite schools lowers the likelihood of being rejected by all or put another way improves the probability of being accepted by at least one.
2. But that said , the resultant rejection probability is still high and for most of the best kids rarely gets better than a coin toss.

You don't get shattered when you lose a coin toss. Don't get shattered when your kid doesn't get into an elite.

To this, I'd add a general concept. Questions such as this are accessible to mathematical approaches. You can start with assumptions, however imperfect, in the form of assigned values. Then, with appropriate math, you can get closer than you were before. A feature of probability might even be the expectation that you often will be inaccurate until such time as all the information becomes available and the uncertainty reduces to zero.

On another note, events do not need to be either independent or dependent for probabilistic approaches to be effective. There are mathematical ways to adjust for degrees of dependence. I'd argue as well that there are different ways to define dependence.

Somewhat separately, I'm not understanding the game theory approaches to this question.

The game theory question and formula, which is the title and main topic of this thread, requires events to be independent to work.

College admissions decisions are, in fact, independent events.

Despite this, the game theory formula which (again) is the title and main topic of this thread will not work because you cannot know the odds of any one student being admitted to any one school. Therefore the result of the formula - the only reason to use it - is useless, as you are guessing. This is how probability works. It's why you can't bet on counting cards in blackjack unless you know how many decks are in the shoe.

I guess we just need to keep repeating this.