How to Outsmart a Smart Ass: a Story of Travel and Mathematics
A couple of days ago, I came back from holiday with my wife. We spend some amazing time in the Maldives to warm up from the cold Korean winter.
In flip flops and comfortable summer clothes for airplane travel, we landed at Incheon airport in Seoul, got through customs and picked up our luggage at the carousel and eager to go home after nearly two days without sleep. Time to put on our winter coat and normal shoes so we can brave the sub-zero Seoul weather.
We just need to get them out of our Suitcase.
The password for our suitcase was still set to factory settings (who actually changes it after purchase?), 000. I also remember I didn’t bother jumbling the numbers after closing the suitcase. My bad.
Weird. It’s not on 000, but on 444 now. No problem, let’s roll it back.
Even weirder. It does not open at 000. Did we break the mechanism?
I quickly concluded we got tricked by someone who handled our luggage. He opened the suitcase maybe, didn’t find anything valuable (arguably… I consider that old t-shirt I’ve had for 10 years very valuable), got frustrated and changed the code for revenge.
All speculation, of course.
What a pickle.
- Try out all the 1000 combinations at the airport? About 1–2 seconds per try, 1000–2000 seconds or up to half an hour of meaningless work on an empty stomach.
- Break the lock by brute force?
- Complain at the support counter and ask for financial compensation?
- Go home in our slippers in the freezing cold and deal with it at home?
I often resolve things using time as my ally. I was ready to go with the last option.
My wife went to the bathroom. She later admitted she hoped I would resolve it magically in the meanwhile.
Got a couple of minutes to wait for her, why not start trying.
Here my sequence.
- Try all 3 same number combinations.
- Try the sequence of numbers 001 up to 030. No luck.
- Think to myself. What would I do if I were that other guy and really wanted to annoy these tourists?
- I’m stupid, I take 999. It will take him 999 tries to get there. Ok, not that stupid, I already tried 999.
- I’m reasonably smart, I take something slightly below 999, but not low so the pain remains maximized.
- I’m very smart, I take something close to 500. Assuming most people would start going up from 000 or down from 999, I’ll optimize the outcome of my evil revenge lusts.
998–997–996–995–994–994–993–992–991–990… No luck. Smarter than I thought. Or is he?
2 minutes, you rascal! You thought I would try 987 numbers before getting yours, right. Beat you!
My wife comes back from the bathroom. I’m all smiling looking at our dirty laundry. She’s happy, I’m happy. We partake in a victory dance and go home.
- I am smarter than a random guy in the world. Statistically speaking, that could just mean I’m average.
- Maybe I’m just lucky.
- Assuming one would only start counting up or counting down, had the criminal known about game theory, and assuming most tourists don’t, he should have settled with 500. Most secure way for maximum pain.
- Same assumptions, but with changed given that this one tourist knows a bit more about Nash’s theory, 250 or 750 would have been nice alternatives.
- Assuming I distribute the numbers from 1 to 333 as group 1, 334 to 666 as group 2 and 667 to 999 as group 3, I guess that the right number must be in group 2. I get to call the criminal (because he left me a note with his phone number, duh) and tell him I think the right number is in group 2. He immediately and magically proceeds with flipping through all the numbers from group 3 to show me the final number is not in group 3. I then confidently tell him I will try out all the numbers from group 1 rather than my initial guess of group 2 first because he just helped me increase my odds of opening the suitcase faster. He is impressed and invites me to a next viewing of Let’s Make a Deal. Monty Hall paradox, anyone?
- My wife’s frequent bathroom breaks are a blessing in disguise.
Or wait? Did he actually Outsmart me by giving both him and I maximal satisfaction (rather than optimal Nash equilibrium)?
He knew he’d never meet me to find out how I fared. So he knew he could choose the number that gives him maximal satisfaction using whatever reasoning he settled on. Right now, he is still under the illusion that it took me close to 1000 tries to get it right. Illusion, but he does not know it’s an illusion.
So he is maximally satisfied.
At the same time here, I beat him. He gave me a number that could be found easily with only a few elementary tries. Trial and error with a bit of brains. So, I feel like I beat him.
I am maximally satisfied too.
Well played, my friend, well played!
Note those are just very loose interpretations of popularized mathematical concepts. For further reading, look up the Monty Hall problem and the Nash Equilibrium.
I will probably do so too as I’m not sure I’ve done a good job linking them to my story. Just had some fun doing so.
How to outsmart a smart ass was originally published in The Ascent on Medium, where people are continuing the conversation by highlighting and responding to this story.