In fact, it is possible to attain a break of 155 in snooker. Here's how.
Before any of the balls is potted, one of the players
commits a foul and leaves the other player snookered. This player then exercises the right to choose a
free ball, which he pots for one point. Then he pots the
black for seven points. At this point he has run up a break of 8 and
still has 15 reds on the table. He then pots 15 reds and 15 blacks (15*(1+7) =
120) and
all the colours (2+3+4+5+6+7=
27) to conclude his break of 155.
By the way, a break of 155 has never (to my knowledge) been done before in
professional snooker, primarily because it is
highly unlikely that a player would
commit a foul near the start of the game that leaves his
opponent snookered, especially as the full
complement of reds is on the table, and professional players would be skillful enough not to foul so badly so early in the
frame.