This is for a class project but I think you will enjoy it. nwpsych.qualtrics.com/SE/?SID=SV_899DmJcjeN5o9mc (copy and paste this URL - as a new member I can't post a link) Please don't read the replies to this thread until after you've finished. Thanks
I stopped at the first gas station. I don't care about the price of gas. It's more important to me not to run out (assuming I have to drive a stinker in the first place, which I never do except for extended road trips.) I don't think there's any way to play this game. No matter what you do you're guessing. I ended up paying less than the most, but more than the least. I voted "meh" in the "How did you like this?" at the end of the survey. In real life I fill up when it's convenient or when I'm down to a couple of bars. I don't even look at the prices.
I got the lowest price in the test but in reality I search for brands where I get a discount from credit cards, groceries, etc.
If you follow the link at the end to the explanation of the "Stopping Rule" you'll see that there IS an optimum way to play. But since there's no exposure to this principle until the end, for anyone not familiar with it it's just arbitrary guessing. As presented I have no idea what could be inferred from the results, as there's no unamibiguous way to ascertain whether a player applied the principle knowingly. I've only seen this before in the context of choosing whom to marry. The principle works out to seriously dating a dozen prospective spouses then marrying the first prospect who appeals to you strongly enough to marry at least as well as the best of the dozen. The likelihood of encountering someone better than the best of the dozen isn't worth waiting for. And I believe a study of long-lived marriages found most such couples had dated about a dozen or so prospects before meeting for the first time. Obviously not every successful marriage is achieved this way, but holding out for that shining knight or Mrs. Right probably makes more than a few people look in the mirror one day and cry out in surprised despair the trip to the altar is a trip they'll never make.
I looked at the link to the "secretary problem" and realized that since they imposed an arbitrary rule, i.e. "once rejected, you can never, ever, ever go back and select that person ever, ever again" (my interpretation), the exercise is pretty much useless. As for not turning back to a previous gas station, I agree with Daniel, I fill up when I need gas, not because it's cheaper today. The way things are heading, it will always be cheaper today...
On my recent extended ski trip, this was not at all true. Going online to see the prices ahead, I could see that filling up in Golden BC was going to be $10 more expensive than waiting until Banff. Getting a partial fill in Revelstoke permitted skipping Golden's high prices completely. Similarly, when returning to the U.S., making the last BC refueling stop just big enough to comfortably get back across the border saved $12. For some of us, these sorts of puzzles and optimizations are easy and actually fun. For others, such as a relative who can't even do jigsaw puzzles and used to count cows by cutting notches in wood fence rails, these puzzles are simply too hard to address.
Gas prices change daily, in case you haven't noticed. They're indexed to the oil futures price on the stock market the previous day. So are electric utilities, which are now indexed quarterly to oil prices. My electrical rates in SE PA have gone up about 25% vs last year. Seems we are all prisoners to the speculative price of oil. It started with Bush, and hasn't changed with Obama.
There is no such pattern here. Prices can be steady for weeks, then change three times in a single day. But relative price differences between stations and areas have considerable persistence. That depends on location, and does not apply here. My electric rates change at most once per year. But for my electric energy, oil is one of six sources lumped together as 'Other', collectively supplying 1% of our total.
I looked up Secretary Problem on Wiki and the math is interesting. Basically if you pass up the first ~1/3 (1/e) of the stations and then commit to the first one you see that is better than those, you will have the exact answer ~1/3 (1/e) of the time....if I understand.
Sorry, but the prices in my area have changed almost daily for years. And my power company confirmed their electricity cost is now indexed to the price of oil.