Another mathematical conundrum

A street fair is offering six Fairbucks coupons for $5. Or you can opt for 5-for-$4 – a better deal, the bonus is 25% instead of 20%’ You give him a fiver, get a dollar change and 5 Fairbuck.

Across the street a bank, to get foot traffic, offers $6 cash for $5 if you ask about an account. You give the hostess a five, and as she reaches for an envelope with $6 in it, you tell her there’s a better deal out in the street. She takes a dollar out of the envelope , hands it to you and says “I’ll match that – Here’s your change, and $5, for your four”.

Wait a minute. What happened to my 25%? I still gave her my five and got $6. That’s only 20%

In both cases, you get a return of 6 dollars for an investment of 5. If the street exchanger actually insists on getting a five-dollar-bill, there is no difference. If you can buy for exactly four, the street exchanger’s offer is actually a little better, since at the end of the day you might have exactly four dollars left, which will buy you his offer one more time but not the bank’s.

It’s a variation of the “missing dollar riddle”

5 for 4 vs. 6 for 5 is only a better deal if you can repeat it. If you can only do it once it’s 1 free dollar for anyone with at least 4 (or 5) dollars.

Here’s a realistic way of repeating the deal:
If you give the street fair guy 20 dollars, you get $25 in coupons. If you instead gave each of three friends a fiver and you each walked in to ask about an account, you would only get a total of $24.

No you didn’t - after getting $1 in change, you gave her $4 and got $5, just like on the street. Alternatively; if on the street you gave the fair $5, but ask for $1 in change, you will get 5 Fairbucks. Same deal.

I don’t believe this is the right comparison - instead you need to give 4 friends $4 each, tell them to go to the bank and ask for the same deal as the fair, just like you did. If the bank won’t do it, insisting on $5 down, than as pointed out in the first reply to the thread, it’s not actually the same deal as the fair.

The bank deal doesn’t really resemble the first. It’s really “prove that you carry $5 cash on you and we’ll give you a free dollar”. Altering exactly how the exchange of money happens doesn’t change that. You would have had to negotiate a different deal in advance (“I only have $4 on me; is that enough?”) to change that.

What are Fairbucks coupons worth? If they can be exchanged 1-for-1 with dollars at local businesses, then they’re worth less than dollars, since you can’t spend them at Amazon. So it’s really a worse deal, since at best matches the bank offer (a free dollar), but in practice you may not be able to spend it.

If the banker wanted to give you a really killer deal, she would have given you $4 change, and then given you $2 for your remaining $1. That’s a 100% bonus!