The question you opened
Second shirt half off, or 25 percent off both
Two shirts at 40 dollars each. Deal A: the second shirt half off. Deal B: 25 percent off both.
Which deal costs less at the register?
They cost the same
Deal A charges 40 plus 20, so 60. Deal B charges 30 plus 30, so 60. Half off one item out of two is a quarter off the pair.
Deal A pays full price for one shirt and half for the other, so 40 plus 20 is 60. Deal B takes a quarter off each, so 30 plus 30 is 60. The two are identical, and the store has chosen the wording that sounds better. The reason is arithmetic about averages.
Half off applies to one of two items, so the discount averaged over the basket is half of a half, which is a quarter. Buy one get one free is a 50 percent average discount for the same reason: a full discount on one of two items. Buy two get one free is a third off across three items, which is 33 percent, and it reads much larger than that on a sign.
The general rule is easy to carry. A discount of d applied to k items out of n is worth d times k over n across the basket. Half off one of three items is a sixth off, about 17 percent, which is a weak offer dressed as a strong one. The catch to watch for is the condition attached. Deal A only pays if you actually want two shirts.
If one would have done, Deal A costs 40 and Deal B costs 30, and the deal that looked equal is now a third more expensive. Multi buy offers move volume precisely because the discount is conditional on buying more than you came for. The habit is to compute the price of the basket you actually want, under each offer, and compare those two numbers. Percentages printed on signs describe the offer rather than the purchase, and the purchase is what leaves your account.
Technique: Half off one of two is a quarter off both