In snooker, push shots and double contacts are not allowed. This particular double contact was performed in a recent 2024 WSC semi-final. The referee Marcel Eckhardt was unaware that a foul had been committed. There is a very simple formula that all referees can use to identify a double contact foul in a live situation: Quite simply if (A) the distance the cue travels through the white is greater than (B) the distance between the two balls then it has to be a double contact. This is because the cue-ball will always slow down when it meets the object ball and this allows the cue to catch up for a second contact. (This all happens in a split second of course.) In this video, we can clearly see that A is much greater than B. This is a double contact foul. The second contact is a push (cue contacts white exactly when white contacts object ball). It has to be otherwise the ball would not go in the hole. The timing would be off. So the referee could call a foul for either a double contact or a push (two separate fouls (RB2022), take your pick. We can also see that the player withdraws his cue quite quickly immediately after the shot. This is usually done to disguise the push. The player did not profit from this unfouled push shot as his break broke down shortly afterwards and he lost the match anyway. *The 'Very fine edge' loophole* From the rule book: "Where the cue-ball and the object ball are almost touching, it shall not be deemed a push stroke if the cue-ball hits a very fine edge of the object ball.” Loophole: As there is no definition in the rule book for a 'very fine edge' the player can define it himself/herself in any way that suits them. So, technically speaking, it's only a foul if the referee says it is (but in this case he wasn't even aware that anything was amiss, lol). This video is for educational purposes only.

Well your formula is obviously true but hardly very useful as referees can't measure these distances with a ruler!