Early bird or last minute

A 15 % discount does not need 15 % more nights. It needs 17.6 %. The cut comes off every night sold at it, while the extra nights arrive at the reduced price too, so the uplift required is d/(1-d) and not d. At 30 % off it is 42.9 %. Because discounts get sized against the first number, a season that looked busier than the last so often ends level with it or below. The second half is what makes last-minute work at all: a discount only costs you something on nights that would have sold anyway. An early-bird rate is taken by guests who were going to book — the cut is margin given away. A last-minute rate sits on nights about to expire worthless. How much of it you take from yourself is the one number that decides this, and nobody measures it — so we ask, and show where the answer turns.