8 spaces, empty
8 purchases left to the reward
10 spaces, 2 gifted
Also 8 purchases left
Evidence
Nunes and Drèze (2006) gave car-wash customers stamp cards. One group had a card with eight spaces, the other a card with ten spaces and two stamps already placed. Both had to make eight purchases. The group with the head start redeemed the reward more often: 34 versus 19 percent (χ² = 8.1, p < .01 — a difference that chance alone would produce in fewer than one case in a hundred). Three hundred cards were handed out on two Saturdays in April 2004, and 80 were redeemed.
A second finding is often overstretched. With the head start the interval between visits was on average 2.9 days shorter, and the authors speak of a “more profound” goal gradient. The interplay between head start and progress, however, did not hold up: the interval is consistently shorter, yet the acceleration towards the goal is no steeper.
A second paper supports the illusion of progress. Kivetz et al. (2006) issued a 12-stamp card on which two stamps were gifted: 12.7 instead of 15.6 days for the same ten purchases. They specifically tested whether sunk cost explains it and rejected that.
Limits
The core finding rests on one field study in one context. Independent replications with digital products should be sought. That the head start needs a plausible reason holds only half. In study 3 — 240 people surveyed outside a liquor store about a hypothetical programme — a reason was needed only when progress was counted in purchases; counted in points it worked without any reason at all. And the reason did not have to be sound: “because you are here today” worked as well as “as someone with your purchase record”. The authors qualify their field study themselves: they could measure purchase pace only among those who bought all eight washes.