Ok options for scoring.
Simple doubling S(n + 1) = 2 * S(n)
0: 3 - 1
1: 4 - 2
2: 5 - 4
3: 6 - 8
4: 7 - 16
5: 8 - 32
6: 9 - 64
7: 10 - 128
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22: 25 - 4194304
Advantage increment. S(n+1) = 2 * S(n) + (n + 1) - S(n-1)
0: 3 - 1
1: 4 - 3
2: 5 - 7
3: 6 - 14
4: 7 - 25
5: 8 - 41
6: 9 - 63
7: 10 - 92
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22: 25 - 2047
The second method basically ensures that it is always better to get a longer word plus a shorter word than two middle words. For instance there is a 4 point benefit to getting a 7-letter word and a 5-letter word over 2 6-letter words. In the old system the benefit was always 1 in this system it is n+1
