I thought this might be a "Three Pipe Problem", which
for me translates to 2 mugs of coffee and a Monster drink.
However, it turns out the playoffs are about 1000 times easier
than in Spectacular scoring - almost Free Parking - so that speeds
things up a lot.
Because the playoffs are exactly 3 points, you can just generate
a set of 3 results, eg {1, 1, 0 }, which can represent { server
wins, server wins, receiver wins }. If the 3 teams that qualified
for the playoff are A, B, C, then the 3 results can map directly
to:
1,1,1 = binary 111 = SSS = decimal 7 = case 7 = A-B-C
1,1,0 - binary 110 = SSR = decimal 6 = case 6 = A-C-B
case 5 = C-A-B
case 4 = A-C-B
case 3 = B-A-C
case 2 = B-C-A
case 1 = C-B-A
case 0 = B-C-A
So it's a simple map where you can also generate just one random
number in the range of 0 to 7 to tell you how the A-B-C teams
finished.
That is a incomparably simpler than having to keep track of
scores and rotation positions while watching out for 'Possible
Place Point' which has different point values depending on
the circumstances.
Now, on further review, it looks like the impossible numbers
are not just PAIRS, as dejada said, but sets of 3 consecutive
numbers, namely 4-5-6, 5-6-7, and 6-7-8. As I stated to Tiger,
once the 3 teams reach the playoffs, any sequence is possible.
Therefore, it follows that if any A-B-C tri is impossible, then
so is the whole A-B-C tri-box.
In case anyone is interested, the bottom 6 possible numbers
are:
435 = 1 in 9832
534 = 1 in 10010
345 = 1 in 12674
543 = 1 in 13422
453 = 1 in 15698
354 = 1 in 16207
so we see the next group of consecutive numbers struggling to
just make it in.
One more thing, while I'm at it. I would hate this scoring
system for singles because if post 1 serves his way to the playoffs
with 3 quick ones, he would then also be first up to serve in
the playoffs. That is radically different from the way it is now
where if the 1 comes back on the court receiving against Solo
or Arriaga, he is facing a real challenge to get the serve back.
As far as the supers go, maybe next time.