The Potter's Permit

One two-stage decision, solved backward, shows why the right to decide later can be worth paying for.

A potter can buy tomorrow's fair permit today for 20, or wait for tomorrow's reliable morning forecast — but fair-day permits cost 35. Sun, at even odds, makes the fair worth 100 gross; rain makes it 30; skipping the fair for the neighborhood market yields a safe 40. Solve tomorrow first, each weather separately. Bought-today, sun: go — 100 minus 20, 80. Bought-today, rain: going nets 10; bailing to the market nets 40 minus the sunk 20 — 20. Take 20. Waited, sun: buy at 35 and go — 65 — against the market's 40: buy. Waited, rain: buying nets minus 5; take the market's 40. Now roll back to today. Buying now averages 0.5 × 80 plus 0.5 × 20 — 50. Waiting averages 0.5 × 65 plus 0.5 × 40 — 52.5. The potter waits — despite the 15-unit price penalty — because waiting buys the right to decide after the world shows its hand: the value of information, wearing a schedule. And state the answer properly, as a policy: wait; if sun, buy and go; if rain, take the market. Three clauses, every branch covered, solved in exactly the backward order the striped trees taught. One more reading closes the case: compare the two plans world by world. In sun, waiting loses 15 to the price rise — 65 against 80. In rain, waiting gains 20 — 40 against 20. The forecast converts a coin-flip exposure into a chosen response, and the gain in the bad world outweighs the toll in the good one: 52.5 against 50, the whole story in one subtraction.