Most people are under the impression that the maximum break in snooker is 147 - a "one-four-seven".
There are 15 reds - so potting all 15 reds (value 1) and a black (value 7) would give 120 - i.e. 15 x(1+7). Potting all six colours gives another 27 points (2+3+4+5+6+7), giving a grand total of 147.
However, don't forget the free-ball rule. If the player 1 visits the table and fouls - player 2 gets 4 to 7 points depending upon the foul. Although added to Player 2's frame score, this in itself would not add to the break total for player 2's next visit. The free-ball rule states if after a foul the player can not hit both sides of a target ball then the player may nominate any other ball to count as the target ball.
Imagine player 1 tries to clip a red during the initial post break-off safety play, misses and ends up behind the brown. Player 2 could nominate the brown as the free-ball, pot it, and would receive 1 point for the break. If he then goes on to pot the black they would score another 7 points, i.e. have a break of 8 and still have 15 reds on the table.
Adding 8 points to 147 means the true maximum break in a frame of snooker is 155.
So has it ever been done?
The record in the Guiness Book Of Records is 149 - achieved in 1998 by Tony Trago. The true maximum of 155 has been achieved in a 2005 practice frame (with witnesses) by Jamie "Shotgun" Cope (pictured below).