Optimal Stopping Strategy in Dating - Part 2

 

In April 2022, my post was about the optimal stopping strategy applied to dating and other life situations in which one must decide to choose a good option or to move on and continue looking. My son recently got married and while I didn’t expect him to be following my Math Blog, I was curious to know if his decision point was close to the optimal stopping point.

The original post of the Optimal Stopping strategy, suggests using the 37% rule. The approach used to maximize the probability of choosing the best option is to use a stopping rule. In the hiring problem, let n be the number of candidates and r as the stopping point. This means one automatically rejects the first r-1 candidates and then chooses the next candidate who is better than all the prior candidates. The term r can be either the number of choices or a time factor.

I don’t know how many women my son dated or plan to date, so I used time as the factor. As a rough guess, I estimated my son’s dating years to be between ages 18 and 60. One could make arguments for making either end of this range higher or lower, but this was just a starting point.

By the 37% rule, one dates, but does commit, 37% into this range. After that stopping point, one chooses the next candidate who is better than anyone dated prior to the stopping point.

For my son, the age of the stopping point would be 18 + .37 x (60 – 18), or 33.5 years. When my son announced to me that he was engaged, I asked if he was sure and he said, unequivocally, that this was his match. The reason I asked my son is because he started dating his spouse in August 2022 and was engaged to be married in December 2022.

My son was born in April 1989, so the age at which he met his spouse was 33.3 years and he was married at 33.7 years. As it turns out his decision matched the optimal stopping strategy nearly to the month. I wish him and his wife many, many happy years together.

Jacob and Carolina

Some readers may want to know if I followed this strategy. Fortunately, I didn't know about this when I got engaged at age 24, 9 years short of the optimal stopping point. However, my wife and I have been married for 39 years, so I'm glad I wasn't following the strategy - I relied on love and not math!

Digits, a daily puzzle on The New York Times

 

(Image: The New York Times)

Update 7/18/2023 - I was disappointed this morning when I went to the New York Times site to play Digits and it said the game would be no longer be available starting August 8, 2023. Here is a link to an article explaining the shut down of the game: The New York Times is shutting down Digits, its math-based puzzle game - The Verge. Perhaps fans might get to play Digits on another platform or play a similar game that will be developed by another site.

Original Post from 6/29/2023:

For over the past year, The New York Times has a popular on-line game called Wordle in which players guess what letters make up a five-letter word. It can best be described as a mix of Wheel of Fortune and the game, Hangman. 

About a year ago, The New York Times introduced a similar game called Digits. Players are presented with six clues (consisting of one-digit and two-digit numbers) and a target number. The object of the game is to combine any of the six clue numbers using the basic mathematical operations of addition, subtraction, multiplication, and division to reach the target number. Maximum points are achieved if one reaches the exact target number. One can also receive points for arriving at a final answer close to the final answer. 

I find the game to be similar in math challenge as the game Nerdle, which was reviewed in a prior post.

While I don't know the absolute best strategy for Digits, I generally use the larger number clues under the operation of multiplication to get close to the target number and then use the smaller number clues to fine-tune, under addition and subtraction, to reach the exact target number. 

Book Review: Fantastic Numbers and Where to Find Them by Antonio Padilla

 

(Image: Fantastic Numbers and Where to Find Them (macmillan.com))

In 2022, Antonio Padilla published Fantastic Numbers and Where to Find Them, A Cosmic Quest from Zero to Infinity. Padilla is a theoretical physicist and cosmologist at the University of Nottingham. You may know him from his frequent appearances on the Numberphile YouTube channel.

The fantastic numbers that Padilla explores are those numbers associated with physics. The book is divided into three parts: Big Numbers, Small Numbers, and Infinity. He provides explanations with a variety of examples and stories. For instance, how sprinter Usain Bolt ages less than spectators in a stadium watching him because of time dilation. I also liked the discussion of how we may be living in a holographic universe.

Padilla reviews many scientific concepts including entropy, the Higgs boson, symmetry, black holes, and the theory of everything (TOE) without burdening the reader with excessive equations. 

Pi Music

 

(Image: Vectopus FZ-LLC on Iconfinder)

    

I recently listened to an episode of Numberphile which featured data visualization guru Martin Krzywinski and composer Gregory Coles who composed music based on the mathematical constant, pi. I highly recommend listening to this episode: (66) The First and Last Digits of Pi - Numberphile Podcast - YouTube.

Some readers may be confused about the title including "...last digits of Pi." As a clarification, these last digits are based on the latest computation of Pi at the time of the composition. This was the 62.8 trillion digit computation of Pi.

Powers of Two

(Image: Phosphor Bold icons - Iconfinder)

I turned 64 today. As a math fan, this is likely my last power of two birthday (2 to the 6th power is 64). Today, I'm spending my birthday with my two children and their two partners. More powers of two - My wife, Mary Glezen McMahon, is about to compete in the Air Race Classic - https://www.airraceclassic.org/ and her race number is 32, another power of two (follow her progress beginning Tuesday morning as she races from Grand Forks ND to Homestead FL). My last power of two birthday, 32, I had recently become the father of my second child. On the power of two birthday prior, I started my first day as a Chicago Lifeguard on my 16th birthday. Near my 8th birthday, I shot my first rifle with my Father and uncle. Around my 4th birthday my family had just moved from Detroit to Chicago. I have no memories from being two, but my Mother once told me she was at her happiest when she was a young mother with two toddlers.