From 0% to 50%. There are many factors that determine the chance of sinking the 8 on the break.
First, table size. A 7 foot table has more pocket opening space to rail space as a ratio than an 8 foot, and 8 foot more than 9 foot. So, the smaller the table, the higher percentage of succes, all else being equal.
Second, player skill. A break has to be fast and accurate to get the necessary ball action on all the balls to even give the 8 ball a chance of making it to a pocket.
Third, hitting the "pocket" in the rack that has the highest percentage of getting the 8 ball in good play, and use of cue ball control in that shot.
Fourth, is just plain luck.
On a 7 foot table, experienced amateur players will typically pocket the eight ball on the break once every 50 games. So, 2% of the time. Professional and highly skilled players can do better even on a 9 foot table.
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In the Pocket Billiards game of 8 Ball it may be a foul or may end the game depending upon the rules being played. If the 8 ball goes in on the break, under APA Rules and some house rules, this is a win if not also a scratch. Under all other rules, play will continue. If the 8 ball goes in as a result of other than a shot, it is spotted.
Don't know if exact odds could be calculated. Depends on the skill level of the shooter, and some luck. I have seen it happen plenty of times though.