You want to know the number of possible people you might date. These are "dateable candidates."
If that number is "n", then by the constraints given, you don't want to end up actually dating each and every one -- if the last one isn't a match, you're screwed.
We can try to ground this with an example. Suppose you're a female, and you know that you want to marry someone to conceive a child together. Now, [suppose] you have until you're ~40 years old to have a kid. Then you need to find your ideal suitor slightly before that.
So now, if you imagine you'll meet 10 "dateable candidates" per year, and you're just under 30, then you might estimate n to be 100.
Note, the method doesn't guarantee you'll stop shortly after the 37th dateable person you meet because it might take much longer until you find someone better than the first 37.
But at least you know that you've given yourself the best chance at finding the best person to have a kid with [under the dowry problem restrictions].
But then we are back to the initial problem: we are just guessing how many people we are going to date. So its still not really true that the math supports it when dating in actual reality. There is no reason to choose two, three, four, or any other number based on math alone.
There are other assumptions that this model of dating makes that also aren't well founded. For example, the probability distribution of the candidates probably isn't going to be uniform: a person who has dated one person versus someone who has dated fifty is going to have a lot of biases to the selection that the person who dated only one person didn't have at that time.
What I'm getting at here is that this isn't math giving an answer. There are many different places where a person has to make leaps of faith in order to accept this model. And a person also probably needs to make a definitively incorrect guess to start things off.
So if someone were to be wondering if they are being an idiot for not dumping the person they are with, who they like, for the sake of appeasing this math model? They could be prudent: and it wouldn't be going with what is supposedly going to give them a 37% shot at finding their best match. It would be not breaking up with the person they are dating.
It's a math problem. You make some assumptions, and then you solve the problem with respect to those assumptions.
Of course all models of the world are flawed. But some are useful. If you're wondering which restaurant you should stop at on your walk from a to b but aren't familiar with the area, you might assume you should pick the next place better than all previous after walking a third of the way home. That would be a reasonable application of this model.
Regarding your last point: I wouldn't base serious life decisions exclusively on an "optimal game theory" move. That would be nuts! This obviously doesn't perfectly model reality, so why act like it does?
You want to know the number of possible people you might date. These are "dateable candidates."
If that number is "n", then by the constraints given, you don't want to end up actually dating each and every one -- if the last one isn't a match, you're screwed.
We can try to ground this with an example. Suppose you're a female, and you know that you want to marry someone to conceive a child together. Now, [suppose] you have until you're ~40 years old to have a kid. Then you need to find your ideal suitor slightly before that.
So now, if you imagine you'll meet 10 "dateable candidates" per year, and you're just under 30, then you might estimate n to be 100.
Note, the method doesn't guarantee you'll stop shortly after the 37th dateable person you meet because it might take much longer until you find someone better than the first 37.
But at least you know that you've given yourself the best chance at finding the best person to have a kid with [under the dowry problem restrictions].