A past girlfriend and I would occasionally (cheerfully) quibble over the optimal strategy for extracting toothpaste. It occurred to me recently that the disagreement was fundamentally about amortized vs. worst case complexity.

Being lazy, I tend to squeeze the toothpaste out of the front of the tube, optimizing the time spent in the moment and reducing the degree of control required since pressure is exerted near the toothbrush. She would carefully squeeze the tube from the back, maintaining a flat region that would slowly grow as the toothpaste emptied. The main advantage of her strategy is that toothpaste is always at hand, and every iteration is fast. In contrast, squeezing from the front pushes toothpaste both out of the tube and backwards towards the other end. Occasionally, this must be fixed by rolling the back of the tube forwards. Each fix up step takes much longer than a normal toothpaste extraction, but the average time spent might be lower since a normal squeeze is faster. We never did the experiment, so I’m not sure which strategy actually wins on average.