A Chess Tournament: Middle Secondary Mathematics Competition Question

A speed chess tournament is organised according to the following rules. Each round consists of all one-game matches played between two players. A player is eliminated from the tournament once that player has lost 2 games. No games are drawn. The draw for each round is done by randomly drawing names from those players still in the tournament. If there are an odd number of players in a round, a bye* is given to one player randomly drawn from the set of players with the smallest number of losses and the least number of byes already received; this takes place before the draw for that round.

Given that 33 players start the tournament, what is the minimum number of games needed to guarantee reaching one outright winner?

*Note that a bye means the player does not play in that round but still passes onto the next round.

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