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How can I determine which stores are regarded as supermarkets for a rewards credit card?
Credit card companies organize types of businesses into different categories. (They charge different types of businesses different fees.) When a business first sets up their credit card processing merchant account, they need to specify the category.  Here is a list of categories that Visa uses. Grocery stores and supermarkets are category number 5411. Other types of businesses, such as the examples you provided in your question, have a different category number. American Express simply looks at the merchant category code for each of your transactions and only gives you rewards for the ones in the grocery store category. It's all automated. They likely don't have a list of every grocery store in the US, and even if they did, they would probably not provide it to the public, for proprietary reasons. If you are in doubt about whether or not a particular store is in the grocery category, you'll just have to charge it to your card and see what happens. Often, the category of transaction will be shown for each transaction on your credit card's website.