Brute force approximation of average luck on best strategy.

25% 18 + 25% 27 + 16% 45 + 16% 89 + 16% 80 = 46.92 SK / beacon

Working with the mythical 6,000 SK to start, you could open about 127 beacons in first round.

32 18s, 32 27s, 21 45s, 21 80s, 21 89s, 127 beacons total, 5,934 SK total, 66 SK remains.

10% of 32 = 3 bonus, 240 SK.

7% of 21 = 1 bonus, 80 SK

5% of 21 = 1 bonus, 300 SK

12% of 21 = 2 bonus, 200 SK

Total = 820 SK.

886 SK -> about 18 beacons in the second round, 5 18s and 27s, 3 45s, 80s and 89s, 19 beacons total.

No bonus, 19 remains.

And let's say you get an 18 in the third round, no bonus.

So, we opened 127+19+1 = 147 beacons.

38 18s, 37 27s, so 75 staffs from singletons. 24 45s, so 48 staffs from duples. 48 80s and 89s, so 144 staffs from triples. Total of 267 staffs. 14 Grand Prizes. Winner winner, Complete Set Dinner.

If we start with the more realistic Average-effort average luck 5,600 SK...

... you could open about 119 beacons in first round.

30 18s, 30 27s, 19 (had to round down someone) 45s, 20 80s, 20 89s, 119 beacons total, 5,585 SK total, 15 SK remains.

10% of 30 = 3 bonus, 240 SK.

7% of 19 = 1 bonus, 80 SK

5% of 20 = 1 bonus, 300 SK

12% of 20 = 2 bonus, 200 SK

Total = 820 SK.

835 SK -> about 18 beacons in the second round, 4 18s and 27s, 3 45s, 80s and 89s, 17 beacons total.

No bonus, 13 remains.

So, we opened 119+17= 136 beacons.

34 18s, 34 27s, so 68 staffs from singletons. 22 45s, so 44 staffs from duples. 46 80s and 89s, so 138 staffs from triples. Total of 250 staffsl. 12 Grand Prizes. And, only 6/7 Set Buildings.

So, that's my effort. Average luck and average effort collecting SK, average luck and best strategy, and you're likely-ish to get half-way to completing the last map for the last piece of the set.