As a non-USian who does not know this system, can somebody please explain what "gas rewards" are and why they would prevent the kind of card shuffling explained by ChuckMcM?
The size of the discount is tied to the amount of purchases made with that card present. So if you make a lot of purchases you get a bigger discount per gallon at the gas station.
If you share the card or exchange it with others, the first one to use the discount gets that savings, the next person does not. The discount resets on use, and it can be re-established by the next set of purchases on the card.
What that does is creates an economic incentive for someone to use the same card (maximize purchases to maximize discount) and not share it (discount is one time only, and to the current holder of the card.)
you could still pool all the cards and split the reward between you, couldn't you?
In the US, most large grocery store offer a card that you can use which gives you various rewards, and in turn allows them to perform analytics on their customer base.
Historically, these rewards were related to coupons for products in the store. However, this means that there is no benefit to using your particular card instead of someone else's.
More recently, the grocery stores have added other bonuses. The one that I'm most familiar with is for fuel / petrol. They team up with some fuel brand, say exxon, and when you've purchased enough on your loyalty card, you get something like $0.05 of your per gallon fuel costs.
The scheme with the poster above breaks down, because you need the physical loyalty card to use the fuel discount, and it's unlikely that everyone is refueling their car an equal amount each week, and that everyone is purchasing an equivalent amount of product at the store each week.