from discrete to continuous and more charges

i have a theory about bookings and i can't help it, i have to share. most people eat out a given number of times per month, year, whatever and these discrete events, when summed over the population, gives the (approximately) continuous distribution of available bookings over a given period of time. sometimes the discrete events intersect, valentine's day is the best example, and we see a peak in the wave function and at other times they mostly don't and bookings are hard to come by. for us, last saturday was one of those events, the latter, whilst last night was the former. we could have seated another eight tables and this presents us with a problem.

we are not going down the two sitting route, book a table with us and it's yours as long as you want it, but we may have to ask for deposits on large tables. the problem that we had last evening was that we had a booking for 14, only ten of whom turned up. one person had rung to let us know and 13 versus 14 makes no difference anyway, however the other three meant that we had a table of 4 which we could not sell because we did not know about it. in the future for large tables we will book in principle but ask for a deposit one week before, the need for this is precipitated by the reduction in spend per head that we've noticed since the beginning of the year. our margins are such that small differences can have significant effects, especially as we are only open 3 evenings a week.