I recently covered a colleague for the cost of lunch valued at $15
We regularly go out for coffee and we alternate buying both coffees each time (coffees are $5 each)
When it was next my turn to buy coffees they compensated me by paying for my shout (I accept that this only partly compensates for the cost of lunch but I'm fine with that)
Having paid twice in a row, have they already (at least in part) compensated me for the meal regardless of who pays for coffee next?
If this is a question of indebtedness, then it is fairly straightforward.
If $I(t)$ is how much your friend owes you at time $t$, then ignoring the meal, there are two possibilities. If $I(1)=5$ then you bought the first coffee, and $I(t)$ typically alternates between $5$, and $0$. Else, if $I(1)=-5$ then he bought the first coffee, and $I(t)$ alternates between $-5$, and $0$.
Suppose now that at some time $t_i$, $I(t_i)=15+I(t_i -1)$. In the first case, either $I(t_i)=20$ (your friend was to buy the next coffee), or $I(t_i)=15$ (you were to buy the next coffee). In order to return to the previous arrangement where $I(t)$ alternates between $5$ and $0$, if $I(t_i)=20$, then your friend must buy the next $4$ coffees, and if $I(t_i)=15$, he must buy the next $3$ coffees.
In the second case, either $I(t_i)=10$ (you were to buy the next coffee) or $I(t_i)=15$ (he was to buy the next coffee). In order to return to the previous arrangement, if $I(t_i)=10$, then he must buy the next $3$ coffees, and if $I(t_i)=15$, then he must buy the next $4$ coffees.
Now, if we consider either of the two possibilities for $I(1)$ to be fair, then if $I(1)=5$, and $I(t_i)=20$, then your friend may purchase the next $4$ or $5$ coffees, since if he purchases $4$, $I(t)$ continues to alternate between $5$ and $0$ and if he purchases $5$, then $I(t)$ alternates between $-5$ and $0$. Similarly we have
If $I(1)=5$, and $I(t_i)=15$, then he may purchase the next $3$ or $4$ coffees.
If $I(1)=-5$, and $I(t_i)=10$, then he may purchase the next $2$ or $3$ coffees.
If $I(1)=-5$, and $I(t_i)=15$, then he may purchase the next $3$ or $4$ coffees.
Then, in all cases, to guarantee a return to a fair arrangement, your friend must purchase at least the next $3$ coffees, which aligns with our sense that your friend owes you \$$15$ for the meal. However, even if he purchases the next $3$, you might still not return to a fair arrangement. However, you might also return to a fair arrangement if he only buys the next $2$ coffees. It depends on who bought whom the first coffee, and the last coffee before the meal. Also none of this takes into account individual valuations on the meals or the coffees. To do that, we must know how much each individual values these things (which may be different from the price paid).