The maths behind a ten-stamp card

Every stamp card is a discount with extra steps. That is not a criticism — it is the whole point. The question is whether the discount buys you enough extra visits to pay for itself, and that is arithmetic you can do in ten minutes.

The numbers below are an illustration, not a benchmark. Swap in your own.

Start with the give-away, not the gimmick

Say a flat white sells for £3.60 and costs you £1.05 in beans, milk, cup and lid. On a ten-stamp card, the eleventh drink is free, so you are giving away £1.05 of goods after £36.00 of sales. That is a 2.9% discount on the cohort of customers who finish a card — cheaper than almost any voucher platform, and it only pays out to people who already came back ten times.

The trap is measuring it against everyone. If only a third of your members ever complete a card, your real cost is lower again — but so is the behaviour change you bought. Both halves matter.

Then ask what one extra visit is worth

The card is not supposed to reward loyalty you already had. It is supposed to move the customer who would have gone somewhere else on Thursday.

• Average spend per visit: £4.80
• Gross margin: roughly 70%, so £3.36 per visit
• Cost of the reward: £1.05

One extra visit per completed card more than covers the free drink. Two extra visits and the programme is comfortably profitable. If you cannot imagine the card producing even one additional visit, the problem is the reward, not the maths.

Choosing the number of stamps

RayPass defaults to ten because it is what people expect from paper. It is not the only sensible choice:

| Purchase frequency | Suggested card length | Why | | --- | --- | --- | | Daily (coffee, lunch) | 8–12 | Fills in two to three weeks — fast enough to feel live | | Weekly (bakery, groceries) | 6–8 | Two months to complete is already a long horizon | | Monthly (salon, barber) | 4–6 | Ten visits would take a year and the card dies |

The rule of thumb: a card should complete within about six weeks of normal behaviour. Longer than that and it stops being a goal and becomes a receipt.

Give the last stamp a nudge

The steepest part of any loyalty curve is the gap between "almost" and "done". That is why the app tells a member when they are one stamp away, and why a two-times multiplier on a quiet Tuesday works so well: it collapses two visits into one and moves people over the line while their intent is still warm.

What to watch after launch

Three numbers tell you almost everything:

1. Completion rate — how many members reach the reward at all.
2. Days to complete — if it is drifting up, your card is too long.
3. Redemption gap — the time between unlocking a reward and using it. A long gap means the reward is not exciting enough.

All three are in the business dashboard from day one. If the first two look healthy and the third does not, change the reward before you change the card.