Buy one get one free, 3 for 2, second half price: what discount is it really?

Multi-buy offers are discounts on the whole bundle, not on each item. Buy one get one free is 50% off two items, 3 for 2 is 33.3% off three, and second item half price is only 25% off two. Each is a saving only if you would have bought that many anyway; otherwise it is extra spending.

The real percentages

Divide what you save by what the items would normally cost together. With items priced at 10 each:

• Buy one get one free: pay 10 for 20 of goods. Saving 10 ÷ 20 = 50%.
• 3 for 2: pay 20 for 30. Saving 10 ÷ 30 = 33.3%.
• Second item half price: pay 15 for 20. Saving 5 ÷ 20 = 25%.
• Buy 2, get a third half price: pay 25 for 30. Saving 5 ÷ 30 = 16.7%.
• 4 for the price of 3: pay 30 for 40. Saving 25%.

The general rule: the discount is the number of free (or cut-price) items’ worth divided by the total number of items. “Half price” on one of two items is half of one item’s worth out of two.

When items have different prices

Most mix-and-match deals give the cheapest item free. Buy a 12.00 item and a 7.00 item on 3 for 2, add a 5.00 item, and the 5.00 one is free: you save 5 ÷ 24 = 20.8%, not 33.3%. To get the full percentage, pick items with similar prices. To check a mixed basket, use the Percentage Calculator’s “X is what percent of Y” with your saving and the full price.

Comparing a multi-buy with a straight discount

Turn both into a price per item. If one shop sells something at 10 with buy one get one free, and another sells it at 6.50 with no offer, the first works out at 5 each — but only if you take two. If you want one, the second shop is cheaper. The Discount Calculator handles straight and stacked percentage discounts, and its reverse mode finds an original price from a sale price.

Things that quietly reduce the saving

• A raised “normal” price. A deal is measured against the usual price. Compare with the price per item, kg or litre elsewhere, not just the shelf label.
• Waste. Free food that goes off before you eat it saved nothing. If you use only one of the two items, you paid full price for it and the deal was no saving at all.
• Bigger pack sizes. Sometimes the multi-buy price per kg is still higher than the large single pack.
• Stacking. A multi-buy plus a percentage voucher does not add up: 3 for 2 then 10% off is 1 − (0.667 × 0.9) = 40% off, not 43.3%. Discounts multiply; see how stacked discounts work.

Quick mental shortcuts

• “Buy N, get 1 free” = 1 ÷ (N + 1) off. Buy 2 get 1 free: 33%. Buy 3 get 1 free: 25%.
• “Buy N, get 1 half price” = 0.5 ÷ (N + 1) off. Buy 1 get 1 half price: 25%.
• “N for the price of M” = (N − M) ÷ N off. 5 for 4: 20%.

Offers worded as “free”

“Free gift with purchase” and “free delivery over 40” are discounts too. If you add a 9.00 item you did not want to reach free delivery that would have cost 4.00, you paid 5.00 more. Measure every offer by what you would have paid without it for the things you actually wanted.

Mistakes to avoid

• Reading “second item half price” as 50% off.
• Mixing expensive and cheap items in a deal that frees the cheapest.
• Adding a multi-buy saving and a voucher percentage together.

Checklist

• Would you buy this many without the offer?
• Price per item (or per kg/litre) compared with other options?
• Items in a mix-and-match deal similarly priced?