OPs assumption is: “there are infinite guests, so at any point someone will be checking out at that exact moment.”
Under the information given by the problem, making that assumption is wrong. In fact, assuming any of the guests will ever check out is already wrong. The problem never makes any mention if checkout at all. All guests checking out a millisecond after checking is just as likely of a scenario as them never checking out until the death if the universe.












Brothers: a tale of two sons
You play two characters at the same time. The left half of the controler for one brother, the right for the other. Many (not so) special abilities can only be done by one brother and the corresponding button is on that side of the controller. Its a short game that can only truly be experienced once so beware the spoiler!
Tap for spoiler
At some point the older brother dies. You now only use half the controller until the surviving brother overcomes his fear of swimming, which was an ability of the (now) dead brother. Just standing in front of the water and realising that I have to use the dead-brother-controlls to control the alive brother was mind blowing. Its also really emotional to a point that would not be possible without that twist. Using a button that was assigned to the dead brother just elevates the feeling of growth of the alive younger brother