Sainsbury's hopes the Reward scheme will be taken up by 6-7 million of the 9 million shoppers who pass through its stores every week. That figure would still be less than the 8.5 million customers who hold a Tesco ClubCard, which was launched more than a year ago.
With Safeway claiming that more than 3 million customers hold its ABC card and with Asda testing a scheme in 18 of its stores, it could mean that almost 20 million supermarket cards would be in circulation. Many customers would hold more than one.
The high numbers add weight to the argument that as the number of cards in circulation increases they become less effective. The supermarket groups are under growing pressure to add more and more services and promotions to their schemes to differentiate them.
Sainsbury's launched its Reward scheme on 17 June after chairman David Sainsbury had initially dismissed rivals' versions as nothing more than "electronic Green Shield stamps".
Asda chief executive Archie Norman last week described the mass launch of cards as part of the "culture of sameness" afflicting the industry. He said Asda preferred to offer lower prices on the shelves now.