Artificial intelligence (AI) is expected to bring to the physical retail environment the kind of mass personalisation that is already common in online commerce, delivering offers that are targeted to each customer, and that adapt to changes in the customer's context. However, factors related to the in-store environment, the small screen where the offer is delivered, and privacy concerns, create uncertainty regarding how customers might react to highly personalised offers that are delivered to their smartphones while they are in a store. To investigate how customers exposed to this type of AI-enabled, personalised offer, perceive it and respond to it, we use the personalisation-privacy paradox lens. Case study data focused on UK based, female, fashion retail shoppers exposed to such offers reveal that they seek discounts on desired items and improvement of the in-store experience; they resent interruptions and generic offers; express a strong desire for autonomy; and attempt to control access to private information and to improve the recommendations that they receive. Our analysis also exposes contradictions in customers' expectations of personalisation that requires location tracking. We conclude by drawing an analogy to the popular Snakes and Ladders game, to illustrate the delicate balance between drivers and barriers to acceptance of AI-enabled, highly personalised offers delivered to customers' smartphones while they are in-store.