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You don't need a loyalty number to track purchases made on the same debit/credit card numbers (though it may improve it slightly).

I generally retire loyalty cards after a few months and ask for a new one next time I checkout. I also never fill in the phone number or other information.

But still I generally pay with cc/debit cards so the banks still know where, not necessarily what, but how much I spent.

What benefit is there in retiring loyalty cards? Creating noise to deflect data collection? Optimizing for returns on some financial aspect?

just use cash for tobacco.