whatifbench

Energy

Energy questions get argued about in the wrong unit. Someone says a bath uses more than a shower, someone else says it depends how long you stand there, and neither says whether they mean the water or the heat. Those are two different quantities that happen to arrive on the same bill, and they do not cross at the same moment.

That is the shape of almost everything in this section. A 9.5 litre per minute shower passes an 80 litre bath at about the eight-minute mark on water — but the energy curve has its own crossing, at its own minute, because the two are computed from different things: one from flow rate alone, the other from flow rate and the temperature the water has to be lifted through. Drawing them on one chart with two separate crossings marked is the honest version of the answer. Quoting one number is not.

The arithmetic itself is undramatic — a flow rate times minutes, a specific heat times a temperature rise. What makes these worth a dial is that the inputs are personal and the published averages are not. A household's real shower head, real bath, real inlet temperature and real habits move the crossing point around enough that the general claim cannot survive it. You have the numbers for your own house; the model does not.

So these pages are built to be argued with. Every coefficient is sourced, every assumption is named, and where a figure depends on a tariff or a climate or an appliance that varies by country, the page says so rather than quietly picking one. Where the answer would need a judgement call about how somebody actually lives, the tool draws the range and stops there.

Finished elsewhere on the site

The writing above is this section. Below are the tools running on the site today, from wherever they sit.

Monty Hall with N doors

Move the door count and the number of doors the host opens. The model puts the advantage of switching at (N−1)/R — it tracks the reveals, not the door count.

0.667the model's switch win rate at three doors

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