Olympic athletes use a huge amount of sponsor money — not to mention legal and illegal performance aids — to reach gold. Soon we will have genetically engineered physiology to reach even greater records. Schools compete for an annual #1 ranking. They spend more and more money to bid for the best professors and build the best facilities, driving up tuition. Coding theorists run massive simulations to find the best code to compete for the one spot in standards. But is the second place athlete, school, and code that much worse? No, usually they are nearly as good as #1.

I’ve often wondered whether many problems in the world are not variations of attempting “exact optimization” — this being the only way to guarantee success in a winner-take-all reward system.
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t-Mobile has these tiered refill cards for their prepaid mobile phones. The pricing table is here and reproduced below:

$10 for 30 minutes, expires in 90 days
$25 for 130 minutes, expires in 90 days
$40 for 208 minutes, expires in 90 days
$50 for 400 minutes, expires in 90 days
$100 for 1000 minutes, expires in 365 days

So which card should you buy? You could calculate a per minute cost and conclude that $100 for 1000 minutes is the most economical (plus it doesn’t expire for the longest time). Wrong!

It depends on how much you use the phone. The fact that the minutes expire makes the prepaid plan a virtual monthly plan in the regime where you do not use 1000 or more minutes per year, which is highly likely for people who choose prepaid phones to begin with (e.g. temporary visitors, odd occasions, emergencies, etc.). The constraint in that case is the expiration, not the number of minutes. If you blindly purchased $100 refills one after another, you’d have more and more unused minutes piling up. Sure, you could still use them, but even at $0.10/min. it is expensive compared to a straight monthly plan if you really mean to call that much. Of course you don’t, so now what?
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