Mathematical odds of winning in a lottery syndicate? Would my new system work?

On average you must lose because the house takes a (large?) cut. The winning numbers are selected at random regardless of whether you select your numbers deliberately. Playing the same three numbers each time may result in winning more, but less often. Playing the same three numbers may prevent a big winner when those three number are not drawn. However, selecting three 'lucky' numbers (or more?) may add fun to the game. Remember that the losers make the winners possible (and enjoy).