9-ball pool game

9 balls are racked in a diamond formation:
__5__
_4_6_
3_9_7
_2_8_
__1__
The 1 and 9 never change position except in some European variations where the 9 ball is at the apex instead of the 1 ball. Many official rules state the rest of the balls are to be placed randomly. The lowest numbered ball on the table must always be struck first (possibly after a bank), what happens after this does not matter unless call shot have been implemented (this is extremely rare, official rules of 9-ball do not use call shot). Obviously, the 9-ball can be struck first on the break in 9-apex variations, otherwise the break must start with the 1 ball. If no balls are pocketed nor strike a rail on the break, then it is an invalid break. The opponent has the decision to play the table as a foul by the breaker, or re-rack and become the breaker (some tournament rules impose one of these choices). The game is won by sinking the 9-ball without fouling. This can be done at any time, including the break, provided that the player has struck the lowest ball on the table first (failure to do so is a foul). Having developed somewhat recently in billiard history, their are many variations to a rule called "The push-out". Whoever gets the turn after a break (regardless of how, see above choices) can call a push-out and hit the cue ball wherever they want, no foul, an their turn is over. The opponent can play it, or pass it back. In some variations, one push-out per game is allowed at any time, in others one push-out per player is allowed at any time. Still in other variations, their are unlimited push-outs, though this is uncommon, except in Texas where they simply must overdo everything. The goal of a push-out is to put the ball in a place where the opponent thinks they can make a shot, but can't. OR, the pusher places the ball in where they think they can make a shot but it will be too intimidating for the pushed opponent so they will pass it back. Some variations say that a push-out shot must strike a ball, a rail, or both, or a struck ball must strike a rail. During play, a player keeps their turn as they sink a ball and do not commit a foul. A skilled player can run the whole table from break every time. This is why it is common for the loser to break in tournaments with very skilled players. In some tournament rule variations, a skilled player may want to lose a round preceding a tie breaker so that they get the break and can run the table. Fouls in 9-ball are penalized by "ball in hand" for the fouler's opponent. "ball in hand" means the player can place the cue ball anywhere to strike the lowest ball on the table regardless of where the lowest ball is. The player can place the cue ball to setup a combo shot to sink the 9 and win. Even if a 9 combo cannot be setup, a run of the table can be planed. Hence, fouls are not merely a setback like in 8-ball, they will likely result in a loss.