How many rounds?

 I saw a question on one of Facebook arbiters groups, asking how many rounds for a 16 player tournament. Most arbiters suggested 5 rounds (sqrt(n)+1 rounds, where n is the number of players) while the most imaginative answer was 15. This is technically correct as the original question did not specify a format. A few did suggest 4 rounds would do, factoring the chances that some games would be drawn.

Whether the latter answer is correct will be put to the test at tomorrows NSW Rapid Championship. The event has a field of 142 and is scheduled for 7 rounds. The risk is that if all games are decisive there is a chance that 2 players may score 7/7, without playing each other.  Of course this almost never happens, but it is still dependent on how many games per round are expected to be drawn. Doing a rough, back of the envelope calculation, I estimate around 12 to 15% of games in each round (between players in the leading group) need to be drawn to find a clear winner. So apart from some interesting chess, I will also have one eye on whether my calculations match reality.

(** I am a paid arbiter for this event **)