BOGO, spelled out
BOGO stands for buy one, get one. The classic version is buy one, get one free: you pay full price for the first item and pay nothing for the second. Retailers also run buy one, get one 50% off, buy two get one free, and buy one get one for a fixed low price like $1. Each version has different math, and the headline rarely tells you which one you are getting.
BOGO free: the math
Two shirts at $40 each, buy one get one free. You pay $40 total for two shirts, so each shirt effectively costs $20. That is 50% off per item. The key detail: the discount only exists if you wanted two. If you only needed one shirt, you did not save $40, you spent $40 on one shirt and got a second one you may not wear.
BOGO 50% off the second item
Two $40 shirts, second one half price. You pay $40 + $20 = $60 total. Your total discount is $20 on an $80 pair, which is 25% off overall, or $30 per shirt. Compare that with a straight 25% off sale on the same two shirts: $80 x 0.75 = $60. Identical. BOGO 50% off the second item is exactly a 25% discount when both items cost the same, which is why stores love the BOGO framing: it sounds bigger than "25% off."
Buy two, get one free
Three items at $30 each, the cheapest free. You pay $60 for three items, so each costs $20 effective, a 33.3% discount overall. The pattern: buy X get Y free on equal-priced items equals Y / (X + Y) off. Buy one get one free is 1/2 = 50% off. Buy two get one free is 1/3 = 33.3% off. Buy three get one free is 1/4 = 25% off.
When BOGO beats a percent-off sale
Put BOGO free head to head with 30% off on two $40 items. BOGO free: $40 total. Thirty percent off: $80 x 0.70 = $56 total. BOGO wins by $16. Now try BOGO 50% off the second item against a 30% off sale on the same pair. BOGO: $60. Thirty percent off: $56. The percent-off sale wins. The lesson: BOGO free is usually the strongest deal in the store, while BOGO 50% off the second item is just a 25% discount wearing a costume.
Grocery BOGO: mix and match
Grocery stores run BOGO on mix-and-match items constantly: buy 6 yogurts, get 6 free. At $1 each, you pay $6 for 12, which is $0.50 each, or 50% off. The catch is the same as always: the deal assumes you can use 12 yogurts before they expire. With perishables, calculate the per-unit price and then ask whether you will actually consume the doubled quantity. A 50% discount on food you throw away is a 100% loss on the wasted half.
Why BOGO outsells an identical percent-off sale
Retailers have tested "buy one, get one free" against "50% off when you buy two" for decades. The deals are mathematically identical, but BOGO consistently sells more. The word "free" short-circuits the comparison part of the brain: shoppers stop calculating and start grabbing. A 50% off sign invites the question "50% off what price?", while "free" invites no questions at all. Knowing this does not make you immune, but it does let you pause and run the per-unit math before the second item lands in your cart.
Three BOGO traps to watch
First, the forced second item. BOGO math assumes you buy the pair. Stores count on you buying something you would not have bought alone. Second, exclusions. Fine print often excludes sale items, new arrivals, or premium brands from the free item, and the "free" item is usually the lower-priced one. Third, the inflated base price. A BOGO on a $40 shirt that is always $40 somewhere else is a 50% discount; a BOGO on a $40 shirt that was quietly raised from $28 is barely a deal. Check the single-item price history before you celebrate.