Algorithms to live by -The optimal stopping problem

 I have read about this book for  a while now, before I have chosen to read it , it is about some algorithms that may have encountered most of us with some algorithms that may be helpful to solve them, so this pots would be mainly some brief notes about it. 
for example the main hiring dilemma, when should we stop interviewing candidates and get the best so far, the same goes for the finding an apartment , or even for marriage seeking !!!.

all of these had the same problems, that we may stop early so we are missing a better candidate/apartment that we have not see yet, or we can stop late , meaning we have already met the best candidate/seen the best apartment but we have bypassed this one in hope of finding a better candidate/apartment. 

The optimal strategy is to find the balance between the two, which was introduced as look then leap rule, you do not choose anyone no matter how good/impressive are they . Then you are in the leap phase where you are to choose anyone who outshine the best applicant so far. 

Then they introduce the optimal point to move from the look phase to the leap phase, that is as the pool grows look to 37% of the pool of candidates size then choose anyone who is better than all you have seen so far.This is why they named it the 37% rule. Following this optimal strategy gives us 37% chance of hiring the best applicant.

The book has also mentioned how this is also similar to searching for a a bride and how a researcher tries  

to follow the same rule for marriage and found that since the suitable age for this is between 18-40 , then the 37% rule here means to choose after reaching 26.1 years of age, however when he has done so he was rejected by the girl he proposed to .

There is also something worth noting that is , this specific number of 37% is  only valid if you can not return to previous options. so for example if half of the previous options can reject your belated offering, then there is a twist to this very rule which is the period to wait before taking decision in this case become 61%.

Worth a note also how the book mentions that this very specific problem might appear have appeared with different names through different times , but it is all about the same concept, in the 19th century it was described by women choosing male suitors , in the early 20th century by holiday motorist searching for hotels or by male suitors searching for brides then by mid 20th century-which has been dominated by male workforce mainly- by male bosses searching for female assistants.

There was also a valid idea , that is consider the secretary problem , but you do have sort of a full information like an objective criterion based upon which we can choose an applicant , an example for this was an exam -consider that this exam can decisively show the real capabilities of the candidates- like SAT or GRE , then if the first applicant was in the 95th percentile , then hire him directly. But if you want the best candidate in general then one the next candidate might have even a higher score , but also in this case we would have a certain exact probability of what are the odds of having an applicant who would score higher than a certain percentile. This whole idea of full information has been called a threshold rule , like if an applicant exceeded a certain threshold then you should accept him immediately.

One concrete example to the threshold rule is when you are selling a house , in this case you have a range of offers once you have an offer above a certain threshold you can accept that , or there might be some variants to this case when we are limited by time or the waiting have a cost effect on us , in this case we would be limited by this waiting cost.