Wanna learn how to travel hack like an actuary on FIRE? I betcha!

Wanna learn the secrets of credit card travel rewards, and how to maximize the value of those travel points? Yeah?

Well, this ain’t the place.

There are dozens and dozens of sites that can help you with travel hacking with credit cards and I’ve got nothing to add there. I’ve dabbled in that area, but as you should know by now, I like to do things differently. So let’s paddle this canoe of travel hackability up a different creek.

*Have you read the special conditions for reading this blog?*

# Travel Hacking and Where to Sit?

When you fly where do you like to sit? I’m a tall guy and so extra legroom for me is a must. I don’t know anybody that requests a middle seat, but for me, I would even go with a middle seat if it meant space to stretch out. My secondary consideration to extra space would be a seat close to the front of the plane; I need to get off that sucker in a hurry!

But, if you were to ask my mother, she would insist on a window seat with the additional rider of an adjacent empty seat. In fact she is prepared to go right to the back of the plane in order to claim that prize.

As a long-time traveler I have observed that everyone has their own preferences for airline seats.

Most of the time I don’t get a whole lot of choice, unless it’s an airline where I have status. So the choice can often be out of my hands, but flying Southwest provides a whole new area of choice optimization. Southwest does not assign seats, you simply take the first seat that you like the look of and claim it for yourself. Some other airlines in Europe also have this system.

This means that when I fly Southwest I engage in a game of chicken where I make my way slowly down the aisle eyeing up potential sites and quickly evaluate them against the row that I am currently on. My choice is between a seat in the current aisle or the promise of a potentially more favorable seat further down the plane. If I pull the trigger too soon then I might forgo the perfect seat in a few rows, or if I wait too long I may be left with some poor choices at the end of the plane.

The choice is not reversible and this creates a constraint on my strategy; when I have passed a vacant seat I can no longer return, I need to keep moving down the aisle pushed by the inexorable flow of passengers entering the aircraft. This is assuming I don’t flout social norms and clamber back over seats elbowing fellow passengers out the way in order to claim the perfect seat. I guess that could solve the problem, but flouting social conventions on a plane with strange, and, slightly aggressive, behavior usually doesn’t end well.

## Optimal stopping problem

This is the perfect example of an *Optimal Stopping Problem*. The key problem we are trying to solve is – how many examples should I examine before I make a decision, in order to maximize my chance of choosing the best available option?

Other examples include how many potential partners you should date before settling down to marriage (or other committed partnership of your choosing), or how many apartments you should view before making a decision to rent? These are all examples of *optimal stopping problems*.

However travel seems to provide for numerous situations where a knowledge of optimal stopping could give me an edge. When walking through the terminal looking for a place to sit, do I choose the place near a power outlet but next to the kid having a tantrum, or proceed on to a potentially better place? (I guess if it’s my kid having the tantrum then I can’t really abdicate my parental responsibilities and have to settle for that seat!) When boarding a ferry do I hold out for a table somewhere that doesn’t smell of diesel, or take the best looking seat near the restaurant? These are all choices that I can somehow optimize to make the travel experience incrementally more enjoyable.

*You know what I like to do at airports? Read. So why not sign up for email updates and get every post straight to your inbox. Follow the main menu and use the email signup form and also follow me on Twitter @actuaryonfire*

## A solution

You’ll be relieved to hear that those clever mathematicians have found a solution to this problem.

**The optimal strategy is to monitor the first 37% of cases before making a decision. After that, you should choose the option that is better than any you have seen before. **

A typical Southwest plane seats 137 passengers, so I need to walk past around 50 empty seats, or over eight rows, before I start to assess each new seat. At this point, I evaluate each new seat and if it is better than any of the 50 I passed by, then I take it there and then.

What’s the probability that my choice is optimal? It’s actually the same number of 37%! So I evaluate 37% of options before making a choice, and this strategy will give me a 37% chance that I get the best option for me. It’s not a great probability but it has been proven to be the optimal strategy. There is no better strategy.

You can thank math for that, and the math can get pretty hairy – see below!

There are different versions of the problem. For example there are variants where you can go backwards and select a previously rejected case. For these problems the optimal strategy involves looking at a larger sample before deciding, but the principle is the same.

## Curmudgeon

As I get older I try to do new activities, experience new places, sample new dishes and meet new people. There seems to be a generally accepted fact that in order to keep feeling young I need to keep pushing myself out of my comfort zone. I also think the FI community promotes the view that financial independence will facilitate all these new and wonderful activities, allowing a life rich with continual excitement.

But optimal stopping theory tells me the opposite.

I’m now at a point in my life where I have probably met over 37% of the people I ever will, have been to over 37% of the places I’m likely to go, and sampled over 37% of the dishes I will ever taste. Optimal stopping theory says that my optimal lifestyle is potentially very close, and maybe only a couple of choices away.

Suppose you leave a comment below and I decide I like you. I mean really like you – more than all the other people that I’ve ever met. Then that’s it. I’m done. We are besties for life! There is no point in me trying to meet others, we will be friends for life!

This also works with food. I like to take the family to the Italian restaurant down the street, and my kids bitterly complain that I’m a curmudgeon and moan “*we always go there*”. This should not worry me, it is probably the optimal choice and the chance of improving on this familiar option is now getting vanishingly small. Why bother trying a new restaurant when it’s getting less and less likely that I will stumble upon a more optimal choice of great food, reasonable price, walkability and cold beer?

So… I finally have the mathematical justification to enjoy a financially independent, but curmudgeonly, early retirement.

*Did you find this a useful tool to prevent analysis paralysis from making a decision? Let me know if you think you might use this in your everyday life. Also let me know if you’re happy being a curmudgeon and settled on your optimal outcome. *

Technical note: the ratio 37% is not an accident. It is actually the ratio 1/e. The irrational number e pops up in all sorts of places, but it’s kind of surprising that it is here.

Want to read some popular posts? Check out this one on Sequence of Returns Risk and this one on valuing a pension.

GasemFascinating topic

There is a view in experimental psychology that the brain is Bayeseian:

https://en.wikipedia.org/wiki/Bayesian_approaches_to_brain_function

This is to say the biology creates a statistical engine which is constantly predicting a range of probable outcomes based on perceived inputs. (Al Franken reckoned the thrill of a lil tush squeeze would result in no blowback) There is even a state theory that keys off the state equations of 19th century physical scientist J Willard Gibbs:

https://en.wikipedia.org/wiki/Gibbs_sampling

This means people make choices based on internally calculated probabilities not certainties. Curmudgeon is how your brain is wired. According to the Gibbs energy model Your choice is based on optimized energy expenditure. Hence the inertia to go to the same restaurant. To go elsewhere would require extra energy with unlikely superior result. It also clues you into what your up against if you try to change somebody’s mind, and why you wouldn’t want to try and go back and take a seat you already passed. YOU WOULD BE TOTALLY SCREWING WITH EVERYBODY’S BAYESIAN CALCULATIONS! There may be sudden death involved in that choice.

So the question is what came first the above hairy math equation or the neurology?

This knowledge is not trivial. It pretty much means you have 37% of the time to select the optimum lifelong investment strategy, so in a 30 year work horizon you better be well on your way by year 11 with the majority of your portfolio, because after that the inertia will eat you alive. A change will likely result in sub-optimal return. Does this predict a Bogelhead portfolio as most efficient because it has least DRAG? There are all kind of questions that drop out of “optimal shopping”.

The constant e was given to us by 17th century mathematician Jacob Bernoulli when he was studying interest compounding. He found e is the limit of profit if you take an investment and compound it continuously.

actuary on FIREThat information about the Internal Bayesian model created by the brain was a fascinating rabbit hole. I was not aware of that at all. But feels like a reasonable hypothesis to me.

I didn’t touch at all on the investment implications of this work, but you highlight a real area of interest.

I had also forgotten that e features in continuous compounding,so thanks for reminding me! It’s still not my favorite irrational number – that would have to be pi!

kiwiandkeweenawWhat pi? Not tau? Clearly tau is a better option. I guess we can’t be besties for life!

Mrs GroovyWow! I”m a bit intimidated by your post and Gasem’s informative comment. All I have to say is fluff, but really, I wanted to tell you I’m a middle-seater. Mr. Groovy likes to look out the window and we prefer sitting together — so I get the middle.Luckily, on our past few flights I had an empty aisle seat beside me.

I’m curmudgeonly too, and if I’m good with one planned activity a day (that’s our retirement style) I think I’m also good with the 37% guideline.

Can we be besties?

actuary on FIREOh no! The last thing I want is for any readers to be intimidated by my blog! Urgh. (And don’t worry about Gasem, he doesn’t bite!)

We will certainly be besties, I know it! And if I’m in your neck of the woods I will swing by to pick trash.

Mrs GroovyMr. Groovy did his first remote Talking Trash with the WoWs (Mr. & Mrs. Waffles on Wednesday). They were in LA picking up trash, taping themselves and talking to Mr. Groovy. He needsto see how it looks when he edits and publishes — but barring any issues he should be able to do more remotes. Get that picker ready!

GasemMrs. G No need to be intimidated by me. I’m just saying there may be a very strong biological mechanism for statistical choice. AoF’s blog is original in its content compared to other fire blogs. Sometime you’ll be down the road in your life and see something and the light will click on: oh ya I read about that on AoF. A genuine diamond in the ruff

baldthoughtsI’m a finance guy, so we round vs. calculate to the penny, so I’ll just say 1 out of 3 ain’t bad. If you played professional baseball, you’d be a Hall of Famer hitting .333.

Definitely appreciate your approach and logic behind it. I agree with you on food as well. I know what I like and already know what I’m going to eat based on which restaurants we visit. Super time savings!

Thanks for the tag on Twitter. Maybe I’ll make it to the best buddies for life list ?

actuary on FIREThanks for dropping by Baldthoughts, really appreciate the comments. For any of my readers seeking some real travel hacks then I hope they visit your site.

earlyretirementnow.comInteresting post. I guess this all depends on the setup of the problem. Are you assuming that you have to first “learn” the distribution of the quality of seats? That’s why you create a burn-in of 37% of the sample and then accept anything better than the maximum of the burn-in?

For example, if you knew the distribution ex ante, you’d solve this through backward induction, i.e., a Bellman equation. The final seat, you have to take. That gives you a cutoff point for accepting or rejecting the second to last seat. That gives you a cutoff for accepting/rejecting the third-to-last seat. And so on. Using backward induction I get a value function and policy function = a cutoff that’s increasing in the number tries I still have left. In that case, I would not rule out taking the first seat I see. For example, if the quality can take values 1-10 and the first seat I find has a 10 I take it. I don’t have to sample 37% of seats before making a decision.

Oh well, it depends on the setup. I have definitely taken Southwest seats after sampling a lot less than 37% of the plane. ๐

actuary on FIREYou’re right,there are all sorts of assumptions I swept under the carpet to keep it simple. (And you just lifted the corner of the carpet and revealed my mess! Heh heh. Watch your step Big ERN or I’ll revoke your free coffee privileges in the AoF lounge! ?)

The simplest form of the problem that I used was a finite homogenously distributed set off choices. They can all be ‘ranked’ but there is no absolute measure. So you can’t look at a choice and determine its a ’10’ you can only assert it’s either better or worse than others you have seen. So the plane analogy is not that great, and potential marriage partners is a better example.

There are versions of the problem with scoring and also versions that take into account the time-cost of searching. Expirements revealed that people pull the trigger much earlier than 37% but when you factor in a cost function of searching then you get better agreement between theory and reality.

There is also a version of the marriage problem that factors in a certain happiness level in staying single and not going with a sub-optimal partner. The optimal strategy here is a burn rate much larger than 37%.

Good luck with your Southwest trips! I’m an American guy.

Revanche @ A Gai Shan LifeBy this math, my life expectancy must be around 90-100 because I once decided that I’d made all the friends I was going to make at age 20, and couldn’t afford any more because of weddings and bridesmaiding, but it turns out that I’ve continued to make great friends for another decade. Did I do that right? ๐

actuary on FIREHeh heh you got it!

catfishwizardThe formula is simpler for me. I don’t need to review 37% of the seats for every flight because I already know what’s available and can immediately assess what’s occupied as soon as I board the plane.

My right knee is bad and starts to hurt if I can’t stretch it out. So that leaves three acceptable seat options: the first row, the newer planes have an emergency row window seat with no seat in front of it, or a port-side aisle seat. As an A-Lister who never pays the extra $20 for business select or early check in , I’m boarding between the middle and the end of the A group, which is usually a little late for the special emergency row. The first row typically only has middle seats by that point, which would be acceptable but a deeper aisle is preferable, so 9 times out of 10 I’m just taking the first available port-side aisle seat. Usually ends up between rows 8 and 12.

actuary on FIRESounds like a tried and tested optimization method. Can’t beat empirical methodology!

GasemAOF. Since you been through this countless times do you now just go to the same seat, much like going to the same restaurant?

actuary on FIREActually I don’t often fly Southwest a lot so I end up near the end of the line. My choice is then trying to get an aisle seat as close to the front as possible and avoiding sitting in front of a kid who will kick me. (If anyone has had to sit in front of my kids, then sorry about that…)

GasemI was thinking about this, can the 37% rule be used to predict the outcome of a retirement plan? If you have a typical 30 year 4% WR 25x plan (or any plan for that matter) when you get to 11.1 years should you have at least 63% of your money left in order to be successful?

actuary on FIREI’m not sure that would work, but I thought you were going to go in a different direction on that. I’ve been wondering whether you should use the Optimal Stopping Theorem to decide *when* to retire. Ideally you want to choose a point in time where you have sufficient funds to maximize your chance of staying solvent, whilst also maximizing your time in retirement. You could retire super early and risk running out of money, or you could wait and have a large pot, but then eat into your retirement time.

To use optimal stopping you would look at your future life expectancy and then wait 1/3 of the years. After that point you monitor each additional year and if it is the best one yet in terms of meeting your dual criteria, then you pull the trigger and retire!

I might write a post on this….

GasemIf you fly a plane, it has a reserve tank just in case. Simply plan in a “separate portfolio reserve tank” into the equation. The question then would be whether to use a 100% stock reserve tank or a Harry Browne permanent portfolio reserve tank. The tank would only have to cover a few years supplemental, say 2-5 years re-balanced every 5 years. The Harry Browne tank would add diversity since it would not follow the main portfolio and has a very low risk of failure. As your time runs out it would the tank that provide an equivalent amount of “work” in case you were too old to work Then pull the trigger any time you want and you wouldn’t have to worry about side gigs and stuff like that which also rob you of your time.

GasemThere is a lot of data on the Harry Browne portfolio so it should be easy to analyze.