[set fair (OP)]

Although the pros break off wth the "same" shot every time, the balls come to rest differently each time, sometimes very differently.

This might be due to the shot not being identical or the balls not being identically racked. But I remember reading somewhere that taking account the number of collisions and uncertainty :- identical breaks wouldn't result even with identical shots and identically placed balls - even if these two "identicals" were possible.

Is this true?

It sugests an experiment. Mechanically set up the red balls and mechanically cue the break shot and photograph the results of dong this multiple times, under different conditions -
a) with obsevers
b)  with a video camera
c) with neither
then see if a pattern emerges so that repeating the experiment and presenting the three groups of photographs one could identify which of the three groups were a,b and c.

[evan_au]

the balls come to rest differently each time

A snooker break is extremely sensitive to the initial conditions. Even small variations in the position and speed of the balls affects which other balls they run into, the amount of spin, and the angle they impact the sides of the table. Even the path that previous balls took could compress the felt slightly, and deflect the balls on the next break. This produces a different final location for the balls.

Similar things happen for chaotic systems like weather. In weather systems, any deviations in the initial conditions grow exponentially over time, until these tiny deviations overwhelm the state of the system.

One difference between a snooker break and the weather is that the snooker balls soon slow down and stop, limiting the exponential growth of the deviations. However, weather is continually driven by energy from the Sun, so these deviations continue to grow indefinitely.

with observers

The suggestion here seems to be that the final location of snooker balls might driven by quantum properties of the snooker balls, which is affected by observers(?)
Bear in mind that any quantum mechanical uncertainty will be removed as soon as photons strike the balls, revealing their position and velocity.

Its true that even tiny variations in temperature, air pressure or air currents could affect the balls, if they continued rolling for long enough.

One thing that affects temperature and air currents is bright lighting of the table; these air currents would have a greater impact than the tiny momentum imparted by the photons reflecting off the balls (especially since overhead lighting reflects off all sides of the ball fairly evenly).

If you left the lighting on, the air currents would be fairly similar regardless of whether you had observers, just a video camera, or neither. But convection currents are a small weather system, which has chaotic behavior. So turning off bright lights might affect the outcome slightly....

[Bored chemist]

Has anyone ever measured the number of collisions that happen during a break in snooker?
It would be interesting to analyse a good sound recording to see how many times the balls bounce off eachother as they separate.

[alancalverd]

The break shot may look the same to an amateur, but that is very far from the truth. In my misspent youth I played against a guy whose opener just  kissed the pack and left me with a brown snooker and no loose reds! Years later, I have given up trying to replicate it.