Most students play with the number pattern

1 2 4 8 16 32 64 128 256

165 is between 128 and 256 so the object is to calculate how many byes are needed so as to get the number somewhere into this list.

If one subtracts 165 from 256 we have 91. Let us give 91 byes. This would leave 74 players in the first round. If they played each other ( 37 matches ) then there would be 37 ready to join the 91 byes for the second round i.e. there would be 37+91 = 128 players left. One can now just follow the above column to reach the winner. This means that there are 37+64+32+16+8+4+2+1 = 164 matches.