Having said that, it really depends on the type of spud, earlies you wait for the flowers drop off, main crops you leave them until the whole plant has died off.
I usually have a gentle little dig with a trowl around the first plant to see what I can find. I did this at the weekend and found a perfectly sized new potato so carried on digging and harvested a couple of meals worth.
If what you find is smaller than a hens egg, leave them another week then try again.