This puzzle is very much inspired by a recent, excellent, one, posted here. If anyone, in particular the author of the other puzzle, prefers this one to disappear, I will immediately do so and I apologize already beforehand for plagiarism (as I am rather new here on this nice exchange but perhaps not yet fully aquainted with its etiquette).
I refer to excellent @WhatsUp 'The "Loop of rope" dilemma' puzzle #112422. That puzzle is about continuous values, this similar one is about discrete values. And attempts to add a twist.
Every evening, Alice and Bob serve their employer's guests. Those guests are seated at a round table. All seats are always occupied. In order to each time work slightly different, and, doing so, to break out of the daily routine, Bob came up with following work-plan: every day Alice may choose seat A of a guest which she would like to serve that evening, and, Bob chooses two different seats B and B'. They choose independent of one another, without knowing each other's choice. All choices have equal probability. Bob's seats B and B' could be any (but different) and Alice's favorite guest could occupy any seat A (potentially same as B or B'),
Bob's work-plan further states: either starting from seat B to seat B' (not including B'), or, in same rotation sense, starting from seat B' to seat B (not including B), Alice serves those guests to whom her choice seat A belongs, and, Bob serves the other guests. The number of guests that are being served by Alice or Bob, and the location of their seats, can vary every day, and, therefore, one working day is not always like another one, ... sometimes more, sometimes less work, and, ... sometimes more, sometimes less time to spend time on the (favorite) guest(s).
Some questions are: on average, do Alice and Bob serve the same number of guests?, or, does one serve, either on average more, or on average less guests than the other, and, if so, exactly how much more or less?
Bob had explained to Alice: B and B' are random seats whose location cuts, on average, the number of guests in half. Your (i.e. Alice's) independently chosen seat A belongs to one of both parts determined by B and B', and, on average, we both serve half of the number of guests.
But Alice, who is sensitive to work and injustice, got, after some time, the impression to have to work harder than Bob.
Alice and Bob are both paid 240 euro per working day. Their employer agreed with the variations of the work-plan and assumes that, on average, both serve an equal number of guests. But Alice calculates that, if their employer wants to pay same total 480, she (Alice), should be paid 310 euro per working day, and, he (Bob), should be paid 170 euro per working day.
More questions are: does Alice calculate and reason correctly? And, if so, how many seats are there around the table?