This is an old thread, but I'd like to chime in. The gift availability is designed through methods of ABA (applied behavior analysis) which is actually common for games. The 'schedules of reinforcement' (i.e., availability of the gift) are selected to create specific patterns in YOUR (and MY 😊) behavior. The time pattern mentioned above is a Fixed Interval (FI:4hours) and the percentage of the gifts given us a Variable Ratio (VR:5responses(?)). The two are used together to ⚽ limit the amount of reinforcement (i.e., the gift) that is given AND encourage high rates of responding (i.e., when we check the other cities) during that availability window.
All that to say, from your observations and my own, I think the gifts are available every four hours for an unknown duration at an average rate of every 5 cities visited.
This seemed to be true regardless of if purchases were made it not. I'm unsure about whether or not the TYPE of gift was random or dependent on your needs or behaviors.
Hope this was helpful! #gamer #behavioralscientist