Started to think about the bagatelle and it seems to be that you are always playing the odds.
After the initial 4 colors that is.
On later balls, there will always be a color or colors that you have better odds of hitting.
This is why this a skill based part of the game.
If you don't know the odds and what you need, you are more likely to end the bagatelle by scoring a number already obtained.
And there is a big risk/reward element.
If you have 3 colors, do you go for the 4th, even though the odds of hitting it are much lower, if say you have a color with only 1 obtained?
Getting 4 colors, lights 2x bonus, so it may be worth gambling and going for it.
Of course, all this happens super, super quickly, so you need cat like reflexes and thinking to even make the right choice.
It is complicated and I get why people have said the bagatelle is a random, luck based part of the game. It is if you really don't understand how it works.