It is fun to have jam sessions. Playing music together has also has the balance of how much planning vs. improvisation, – and it also depends on the different levels of the participants.
The blues is a wonderful and simple form to improvise upon, especially for beginners like me.
It has a well defined chord progression, and scale where you can improvise, so for a blues in C, the simple version of the 12 bar blues would be like:
| C | C | C | C |
| F | F | C | C |
| G | F | C | G |
And the basic scale that you improvise on is:
C Eb F F# G A Bb
With practise you can vary the scale more, depending on where you are in the chord progression, – and the chord progression, has 7s, can have diminished variations etc. – but the thing mentioned above is the core structure.
Now comes a nifty trick, if you are playing with a complete beginner on the piano: you play the chords and the bassline in Eb, instead of C, and thus the scale to improvise on just becomes:
Eb Gb Ab A Bb Db
which is just the black keys plus A. So just encourage the piano novice to play on/with the black keys, (and later mention that he/she can also focus around Eb, and also might include A sometimes). With a good rhythm, you can now play an awesome blues-jam, with somebody who has never touched a piano before.