Sale Maths Card
What the signs mean once you do the arithmetic. Small enough for a wallet, which is where it is useful.
BFCBrilliance · bfcbrilliance.com/tools/discount-calculator
Stacked discounts never add up
- 20% then 10%
- = 28% off, not 30
- 30% then 20%
- = 44% off, not 50
- 50% then 20%
- = 60% off, not 70
- 50% then 50%
- = 75% off, not 100
- 50% three times
- = 87.5% off — never reaches free
- The rule
- multiply what is LEFT: (1-d1) x (1-d2)
What the common offers really are
- Buy one get one free
- 50% off
- Buy one get one half price
- 25% off
- Three for two
- 33.3% off
- Buy two get one half price
- 16.7% off
- 'Up to 70% off'
- one item is 70% off; most are not
Before deciding it is a bargain
- Final price worked out - not the percentage
- Stacked discounts multiplied, not added
- Compared against the price somewhere else, not against the ticket price
- Was the 'original price' ever the actual selling price?
- Delivery costed in - it can erase the whole discount
- Return policy checked, especially on clearance
- Would you buy it at this price if it were not on sale?
The second discount only cuts what is left
Every surprising thing about stacked offers follows from this one line. The second sign is not applied to the price on the tag — it is applied to the money you were still going to spend after the first one. That is why two discounts are always worth less than their sum, and why the gap grows as the discounts get bigger.
A percentage is not a price
A discount is a percentage off a number the seller chose. Seventy percent off an inflated price can easily be worse than ten percent off a fair one, and no arithmetic on this card can tell the difference. The only honest comparison between two shops is the final amount you hand over.