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I cannot believe it. Finally someone has actually broken down the process into comprehensible logical game strategies. All these years of confusion, only to realize that it is as simple as a game of Risk. Whether you choose to start your army in South America or Europe and whether you are waging war on Kamachatka or Brazil - strategy is the key. I'm not sure why people say Risk and Game Strategy is complicated. Too bad, I'm already married.😛 But for others - anyways here goes
Source: https://www.associatedcontent.com/article/465911/the_mathematics_of_dating_applying.html?singlepage=true&cat=41
Of all the things mathematicians ought to keep their rational hands off of, you'd think searching for a spouse would near the top of the list. But then, you'd miss out on these excellent strategies for winning the Game of Love.
The object of the Game of Love is to marry the best mate you can. The only rule is that everyone can choose to accept or decline a marriage proposal (the following strategic analysis doesn't apply to arranged marriages or "shotgun" marriages). I make a few assumptionsto begin with.
The First: Free will trumps fate in this model. I assume there are a vast number of people that a given person (a.k.a. "player") could marry and be happy with. Some would make the player happier than others, but there certainly isn't a single "Soul Mate" that each person must find - less they be doomed to loneliness forever. I think this assumption make this model more realistic.
The Second: no one will accept a marriage proposal from anyone who doesn't meet their standards (ie: no one will say "yes" to anyone who isn't at least "okay" in their book. Mary would rather stay single forever than accept a proposal from Mr. Wrong).
The Third: everyone will accept a marriage proposal from the best person they think will marry them (ie: Mary will always say "yes" to the current man of her dreams).
The Fourth: everyone will decline a marriage proposal if they know they will get a better offer (ie: Mary will say "no" to Mr. Okay if she knows Mr. Perfect will propose to her tomorrow).
The Fifth: there is no way for one person to be sure the other person will accept or reject their marriage proposal, aside from actually proposing.
The Sixth: no one is waiting around in this game. Everyone is busy looking for the best mate they can find. Just because someone would accept your marriage proposal today, doesn't mean they'll accept it tomorrow.
Finally: in this model of the Game of Love, any player may propose to any other player any number of times. When two players get married, they are both "out of the game."
With these seven assumptions, let's begin our analysis.
The more people a player dates, the more likely they are to find their Best Possible Mate. In fact, if a player were to date every single other player before making or accepting a proposal, that player would have, without a doubt, met their Best Possible Mate (They also would have met their Worst Possible Mate, and everyone in between). They could then list every person they dated in the order that they would choose to marry them. Their favorite choice would be first, their second choice second, and so on... with the "just okay, barely above my standards" people at the bottom of the list, and the people that fell below their standards not on their list at all.
Of course, no one can date everyone, that's just impractical. We'll deal with that in a minute. First, let's make some notation.
Let's say Mary has dated 10 people that met or exceeded her standards. She can then, through thoughtful introspection and consulting with her heart, decide which one is her favorite amongst them. Let's call him "Mary's M1", for "Mate Choice 1." Her second choice will be called "Mary's M2," and so on and so forth.
Remember, Mary's goal is to marry the best mate she can. As of now, her best choice is M1. If she wants to find someone better than M1, she's going to have to date more people. In fact, the more people she dates, the better chance she has at finding a new, better M1. Furthermore, the more people she dates, the longer her list will get, and the more "backups" she will have in case her M1 doesn't marry her. So, at first, Mary's best strategy - and in fact all players' best strategy - seems to be "date as many people as I can, then propose to M1. If M1 rejects me, propose to M2, and so on."
But there is a problem with this. Though dating as many people as possible is the best strategy for meeting the best mate, it is not necessarily the best strategy for marrying the best mate. After all, let's say Mary found her M1 on date#10, and at that time her M1 decided that Mary was his M1 too - a match made in heaven. Let's further say that Mary went off and continued dating many other people just to see if there was anyone better - and found no one better. The problem, then, is that her M1 may not take her back - being hurt that she dumped him to go on dating other people.
You see, on date #10, when Mary finds her new M1 - her favorite man yet - she has to make a decision. She has to decide weather to continue searching - in hopes of finding yet a better man - or to settle and propose to this one - and wonder for the rest of her life if there could have been someone better for her. How does she know what decision to make?
She has to find out what kind of player she is dating. If the player Mary is dating is okay with Mary leaving to look for another mate, and will accept her back if she finds no one better than him, then he will be called an "Open Player", or just an "OP" for short. If he is not okay with her leaving a good thing in search of a better thing, and will not take her back if she leaves him, then he will be called a "Closed Player", or just a "CP" for short. If he is unsure how he feels and doesn't know whether he'll take her back or not, she should play it safe and regard him as a CP.
(It's worth noting that in life, though CPs will always refuse a player for having dumped them, some CPs will take a past player back if it was the CP that did the dumping. Thus, if you find that you are dating one of these "double standard" CPs, you can consider them an OP if you can get them to initiate the break-up. Note that by doing this you will likely put yourself further down on their ordered list of mates. For this reason it is best to just consider them a regular CP. If you are a CP yourself, just know that your odds of finding your Best Mate increase drastically if you become a "double standard" CP, and increase even more if you become an OP.)
Mary needs to find out, on every date, which of these two kinds of players she is dating. How she does this is beyond the scope of mathematics, but we assume here that she can. (Perhaps she could just ask him outright, "If I left you to search for someone better, would you take me back if my search failed?"... In softer words, of course, and probably after a few glasses of wine.)
A best strategy for the Game of Love must take this into consideration. She needs to maximize her search area and minimize the loss of good players within it. Lets look at some common strategies, ending with the optimal one.
Strategy 1 - Idealistic Love Strategy
"I'm going to search the earth forever, refusing every proposal, until I find the Best. If that person won't marry me I'll ask the second best, and so on."
This strategy's ultimate outcome is bleak. "The Best" can only be determined by dating every player - an impossible task. The player dies long before ever even making a proposal.
Strategy 2 - Idealistic Love Strategy w/ Time Restriction
"I'm going to search the earth until I'm X years old, refusing every proposal until then. Then I'll propose to my M1, then M2, then M3, and so on, until someone accepts."
This strategy works, but it eliminates any chance of marrying a CP (unless your very last date before you turn X years old is both your new M1 and a CP). It also takes so long that many of those possible companions that are high on your list often get married before you can get back to them and propose.
Strategy 3 - Passive Acceptance Strategy
"I'm accepting the first proposal I get from a player who at least meets my standards. I think the search for someone better is a slippery slope."
This search is often for those who are afraid of rejection. Notice that they themselves never actually make a proposal, so there is no chance of being rejected. The problem is, their M1 may be using the same strategy, in which case neither would ever propose to the other. What a sad situation that would be!
Strategy 4 - Active Acceptance Strategy
"If my current companion at least meets my standards I will propose. If they reject, I will propose to the next person that at least meets my standards."
This strategy encourages a quick marriage. However, it doesn't allow for any comparison. It does not attempt to get the player the best spouse... rather, it just attempt to get the player a spouse.
Strategy 5 - Simple Young Love Strategy
"I'm proposing to my M1. If my M1 rejects, I'll date until I find a new M1 and repeat until someone accepts."
This strategy is great, especially for the young. It ensures that you will never marry anyone whom you've ever considered second best, and it doesn't neglect CPs. The only problem is that, over time, finding a new M1 becomes more and more difficult - as each new M1 must be even better than the last. It also doesn't give previous M1s the chance to change their mind. If you want to ensure that you will marry, you may want to abandon this strategy shortly after you start "feeling the clock tick", and take up another strategy.
Strategy 6 - Advanced Young Love Strategy
"I'm going to be an OP that lies to convince all other players that I'm a CP. I'm going to date until I find a new M1. If my new M1 is a CP I will propose. If they reject, I will start over. Else, if my new M1 is an OP I will continue searching for a better mate for a short period of time. If my search fails I will propose to my M1. If they reject I'll start over."
The lying in this strategy is to make other players think twice before leaving you to look for a better partner, while still being open to receiving your M1 back if they deny your initial proposal. This strategy is also similar to the Simple Young Love Strategy in that you will never marry anyone you have ever considered to be less than the best, but has the added benefit of exploiting OPs' openness to look for another, better partner for a short period of time. The downside to this strategy is that, just like the Simple Young Love Strategy, finding new M1s gets more difficult each time.
Strategy 6 - Desperation Strategy
"I'm asking my current M1, then my M2, then my M3, etc. If none of them accept, then I'll ask my next acceptable date, then the next, until someone - anyone - accepts."
This is almost an optimal strategy. However, it does not allow for other players changing their minds. Just because you propose to your M1 and s/he rejects you now, that doesn't mean s/he will reject you next year. Other players' options and M1s change just like yours do. So, unless they are a strict CP, there is a chance that a "no" today could in fact be a "yes" next year.
Strategy 7 - The Stalker's Strategy
"I'm going to propose to my M1 over and over again until either s/he accepts my proposal or is removed from the game (gets married). If s/he leaves the game I'll recalculate my ordered list and start over with my new M1."
Unless you are high up on your M1's list, you are likely to die, or end up in prison before this strategy pays out.
Strategy 8 - The Nagger's Strategy (Optimal Strategy)
"I'm going to propose my M1. If they reject, I'll propose to M2. If they reject I'll propose to my M1 again. If rejected I'll propose to M2 again. Then M3. Then M1, M2, M3, and then M4. Then again, M1, M2, M3, M4, and then M5. And so on. When I'm out of M's, I'll date a new player and recalculate my ordered list. Then I'll repeat from the beginning."
Notice how this strategy gives all your favorite players a chance to change their minds. Many times, in fact. Also, unlike the Stalker's Strategy, it allows you to focus on other players than your M1, vastly improving your odds of having a proposal accepted. It should be mentioned that, to avoid unnecessary rejection, you should remove from your ordered list all CPs after they have rejected you for the first time, as they will not - by definition - give you a second chance. You should also remove any players that give you a strong indication that they will never consider marrying you, even if they are Ops.
The Nagger's Strategy is the optimal strategy, as it gives you the best chances of marrying the best person that will marry you. If no one on your list will marry you, it allows for you to expand your list, without abandoning hope that one day you'll tie the knot with your M1.
In conclusion, if you go with The Nagger's Strategy and do not get your M1, it's because your M1 didn't want you, and you weren't going to get him/her anyway. Same goes with your M2. Whoever you do end up with is the highest person on your list that wants you back. And to be sure you are giving yourself a fair chance, make sure you date at least a handful of people without strategy before looking for a possible spouse at all. Besides keeping you sane, this will help mathematically too: you'll start out with a wider search area!
Good luck tying the knot!
Source: https://www.associatedcontent.com/article/465911/the_mathematics_of_dating_applying.html?singlepage=true&cat=41
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