Ed Thorp is one of the fathers of blackjack card counting. Recently he made a nice donation to the Blackjack Ball, which ensures the continuance of the ball even after it’s founder, Max Rubin, passes away. As a partial thank you, Max told Thorp that he could invite his entire family to this year’s Blackjack Ball if he wanted, totally complimentary.
This year, Thorp brought his wife, three children, one son-in-law, and two grandchildren. Slightly before the dinner started, I sat down at a random table. One of my goals at the ball was to find guests for the podcast. Before dinner I was writing up notes before I forgot who the people on my list were and what made them interesting.
It turned out that the table where I had sat down was the one that the Thorps were planning on reserving for themselves. As there are only eight chairs at the table, I told them I would move. They graciously said that wasn’t necessary and they’d just go find another chair, which they did. So, I ended up sitting between his granddaughter, who had just graduated from Dartmouth College, and his wife, Catherine.
While I conversed with both ladies, as well as others at the table, I had the longest conversation with Catherine. She had married Ed Thorp, who is now in his mid-80s and still quite sharp, about seven years ago. Since I married Bonnie five years ago, there were certain similarities.
Catherine said Ed chose her mathematically! He had some mathematical model that told him that she was the one! I found that fascinating. I’m happy with my choice of Bonnie, but certainly did not use any mathematical formula to pick her out. So, I decided to ask Ed to tell me more about his methodology.
He smiled and said it’s not original with him and Wikipedia addresses this as the “Secretary Problem.” My explanation below is going to be highly simplified, but you can look it up in Wikipedia should you like.
The Secretary Problem was originally derived in the context of determining how many potential secretaries you should interview before deciding on which one to hire. The problem requires that you know the number of interviewees in the pool, n, and that you are able to rank each secretary relative to the others.
The key number for the optimal number of secretaries (or candidates for marriage) turns out to be n / e, where e is a mathematical constant whose value is approximately 2.718.
That is, when Ed was looking for a wife, if he thought he would have five years to find one and would meet eight potential mates a year, that would be 40 candidates. Doing the math, we have 40 / 2.718 = 14.7. This means that with the first 14 women Ed meets, no matter how desirable they are, he does not propose. He merely ranks each one relative to the others.
Starting with the 15th woman, he should propose to the first one he meets who exceeds the others in ranking. Assuming she accepts, that’s the one he should marry. If none of the last 26 women outrank the best one in the first 14, he should simply marry the last one.
(Presumably in the real world, if the 40th one was totally inappropriate, he would continue until he found one that’s reasonably appropriate.)
So, I told Catherine that I might forget her name before next year, but I was probably going to remember that she was Ms. 15, because she couldn’t have been in the first 14! She and Ed were both fine with that!
This was a pleasant chat and “intellectual” discussion with two charming people, but I have my doubts that this was actually the method Ed Thorp used to select his wife. Why? Because it’s extremely difficult to rank people.
Let’s say he’s met Karen, Linda, and Mary and assume they are all “reasonably” acceptable. One will be prettier, one will be smarter, one will make better lasagna, one will be more responsible financially (a definite consideration because Thorp is, I believe, a billionaire or close to it), one will be more compatible on religious and political issues, one will be better liked by his family members, etc.
How can you possibly give a unique ranking for these three women — let alone 14? It’s virtually impossible that one woman could be superior in every aspect to the others. So, you’re going to have to make some kind of formula that tells you which attribute is most important. And these are real live women, who each come with lots and lots of attributes, each of whom have good days and bad days. This is not a catalog where you can pick and choose.
So, this strikes me as an apocryphal story that Ed and Catherine like to tell but was not actually used in real life. However he actually chose her, he did well. She appears to be quite charming and they are clearly very fond of one another.
The Secretary Problem, however, is an interesting theoretical concept about when to stop your searching. I’m glad I was introduced to it.
Author’s note: After I wrote the above, I sent it to Dr. Thorp to get his feedback before I published. It’s possible I misrepresented the problem, and I was, after all, suggesting that he wasn’t being entirely truthful in saying he used this technique to find Catherine. He is one of my heroes and I didn’t want to insult him. He responded:
Hi Bob,
We enjoyed your company. Yes, a math model like this is fun to think about but the real world is so much more complex in this instance that one shouldn’t, and we didn’t, follow it.
Best,
Ed