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The Three Ball Cascade
This is an asynchronous pattern. In asynchronous patterns one hand throws at a time, with the throws alternating right, left, right, left,.... In the three ball cascade all the throws are cascade throws, which are thrown by one hand and caught by the other.

If you follow the path of one ball in the pattern (for example the red ball) you'll see that it is thrown once every three throws. Throws which allow the same ball to be thrown again three throws later are called 3s. In the three ball cascade every throw is a 3.

So the three ball cascade can be written like this:

Throwing hand: R L R L R L R.....
Throw:         3 3 3 3 3 3 3.....

If you assume that the throws keep repeating, you only need to write:

Throwing hand: R L
Throw:         3 3

If you also assume that the throws alternate right, left, right, left,.... you only need to write: 3.

This is the simplest way to represent the three ball cascade, but you can write 33 or 333 or 3333 or ...