Jesse Cardiff racks the pool balls before the type of game is even decided upon and before the breaker is determined by coin toss. Typically the breaker will rack the balls. Not only that, Cardiff racks the balls with the 8-ball in the bottom right corner, which is incongruous with both typical eight-ball pool and in 14.1 straight pool, which they decide to play.
How would Jesse be able to claim he is 'best in the world'? First - there were no witnesses to their games, and second - Fats has been dead for several years. No one will believe Jesse.
When Jesse(Jack Kaufman) flips the coin "Fats"(Jonathan Winters) calls tails. It's revealed it was heads yet "Fats" says it's his break. He lost the flip so Jesse had the choice to break or not.