Can a player be snookered on a touching ball?

[davis_greatest]

moglet, yes, your diagram looks bang on.

The minimum value on your graph occurs at (√7/2 - 1)-balls' width, which (based on a ball's width of 52.5mm) occurs at x = c.17mm.

[moglet]

d_g, yes the minimum value for y (exactly half a ball diameter) occurs when x = 16.95mm. Quite elegant!

[davis_greatest]

Thinking about it more, I think that when all three balls are touching, it would not be a free ball. It is true that striking the extreme edge of the pink would mean touching the black at the same time, and ordinarily simultaneous contact with pink and black would be a foul; however, if the white is touching pink and black and one plays away from both after a Touching Ball call, that would not be a foul. Therefore, no free ball would be awarded in this case.

However, if white, pink and black are equidistant at anything up to and including one ball's width apart, it would be a free ball. That includes the case where they are 1mm apart!

At exactly one ball's width apart, the white would strike the extreme edge of the pink and the extreme edge of the black simultaneously, which would be a foul.

Anything more than one ball's width apart, and it would not be a free ball.

I have edited post 13 above a little to reflect this.

[The Statman]

I still agree with you, Davis Greatest.

However, when cue-ball and ball-on are touching, one could interpret the 'both extreme edges' as playing 90° in one direction and 90° in the other, in which case there are grounds for a free ball.

(The other object ball need not be also touching the ball on, of course; it could be touching any part of the cue-ball excluding only directly opposite the ball on.)

However, I think the only logical conclusion to draw is that the finest edge of the ball on is already hit and, by playing away in any direction, you are deemed to have hit both finest edges and everything (which is nothing) in between!

The further awkward situation is where the white is touching the ball on and two or more other colours, so that no stroke in any direction is possible. However, a free ball here would be just as useless as having no free ball, and any stroke would be the same whichever ball was nominated!