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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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[Update 2-14-09] I’m on vacation; articles will resume in a week or two, or as soon as I recover 🙂

I usually find cheap gas based on experience. In my vicinity, I am aware of gas stations that sell for good prices. A few pennies here or there does not bother me as it is the average that matters. When I travel, I often ask a friend or I just suck it up since it’s a one-time expense.

But that is going to change. I learned of an ingenious solution from William Spaniel, who makes great instructional game theory videos.

Here is William’s story:

I ran into an interesting problem today, and I thought you might enjoy what I realized the solution was.

My friends and I were driving back from Las Vegas to San Diego. About half way through the trip, we needed gas. We weren’t worried about suddenly running out, but we definitely couldn’t make it to two towns ahead of us–we absolutely had to get gas in the town we were about to pass through. There were five exits to the freeway in this city. The goal was to get gas for as cheap as possible.The problem was that we knew virtually nothing about what the price of gas should be in this town, and we weren’t keen on going around in circles until we found the best one around.

Then, I realized that you had covered a similar problem about a year ago. Instead of cheap gas, the problem was to find true love.

The solution to maximize your probability of success was to reject the first few suitors and pick the first of the remainder who is better than those you had gone out with previously. I suggested we try a similar strategy with the gas stations, as it has the same property. We breezed by the first two (which were selling for almost $3.50 each) before stopping at one with a much more reasonable price of $2.95. As it turned out, $2.95 was the best station available.

I then explained to the other people in the car that we just solved a math problem. They may or may not think I am full of you-know-what. 🙂

I am definitely going to try this strategy! It is amazing that in statistics you can sample to find the best and save much time on your search.

Here is a quick cheat sheet on the rule (full details in how to find true love):

Number of gas stations in vicinity (N) Number of gas stations to reject (k) 4 1 5 2 10 3

Note that the strategy works even better because, as game theory predicts, gas stations locate in clusters.

What about you guys? How do you find cheap gas at home or while traveling?

(And remember to subscribe to William’s game theory videos to show your thanks)