Group Knockout, Progressive [Balanced] strikes (0/1/2/3)
Not sure if this would be a "new" format, or just an option on the existing Progressive strikes format.
The scheme is:
0, 1, 2, 3 strikes for four players (same as Progressive)
0, 1, 3 for three players (between Fair Strike and Progressive)
0, 2 for two players (same as Fair Strike)
In a Fair Strike playing to 6 strikes guarantees players 3 rounds of play, and in this case, we'd play to 7 strikes (or maybe 8).
Reasoning behind this is a scheme where strikes for 1st, 2nd, 3rd, and 4th place are all different. Currently, in Fair Strike there is no reward/punishment to distinguish between 2nd and 3rd place in a 4 player group. This suggestion attempts to combine the fairness and speed gains of these two formats.