points from flips:
average = 2+3+5+10/4 = 5
x5 flips = 25

from 2-3-5-10
chance of a not getting a 2 = 9/12 * 8/11 * 7/10 * 6/9 * 5/8 = ~16%
chance of getting a 2 = ~84%

chance of not getting a 3 assuming one flip was 2 = 8/11 * 7/10 * 6/9 * 5/8 = ~21%
chance of getting a 3 assuming one flip was 2 = ~79%

chance of not getting a 5 assuming one flip was 2 and one was 3 = 7/10 * 6/9 * 5/8 = ~29%
chance of getting a 5 assuming one flip was 2 and one was 3 = ~71%

chance of not getting a 10 assuming 2 3 and 5 were also gotten = 6/9 * 5/8 = ~42%
chance of getting a 10 assuming 2 3 and 5 were also gotten = ~58%

chance of getting 2, 3, 5, 10 = 84% * 79% * 71% * 58% = ~27%

average score from 2-3-5-10 option = .27 * 20 = ~5.5


from 10-10-10

chance of not getting a 10 = 9/12 * 8/11 * 7/10 * 6/9 * 5/8 = ~16%
chance of getting a 10 = ~84%

chance of not getting a 10 assuming 1 10 already gotten = 9/11 * 8/10 * 7/9 * 6/8 = ~38%
chance of getting a 10 assuming 1 10 already gotten = ~62%

chance of not getting a 10 assuming 2 10 already gotten = 8/9 * 7/8 * 6/7 = ~67%
chance of getting a 10 assuming 2 10 already gotten = ~33%

chance of getting 3 tens = 84% * 62% * 33% = ~17%

average score from 10-10-10 = .17 * 60 = 10.2

from 5-5-5

by symmetry, chance is .17
average score from 5-5-5 = .17 * 70 = ~12

from 3-3-3

by symmetry, chance is .17
average score from 3-3-3 = .17 * 75 = ~12.8

from 2-2-2

by symmetry, chance is .17
average score from 2-2-2 = .17 * 80 = ~13.6


from RRBBGG

with 5 flips cannot happen

from GGGG

chance of a not getting a G = 8/12 * 7/11 * 6/10 * 5/9 * 4/8 = ~7%
chance of getting a G = ~93%

chance of not getting a 2nd G after getting a first = 8/11 * 7/10 * 6/9 * 5/8 = ~21%
chance of getting a 2nd G after getting a first = ~79%

chance of not getting a 3rd G after getting a first 2 = 8/10 * 7/9 * 6/8 = ~47%
chance of getting a 3rd G after getting a first 2 = ~53%

chance of not getting a 4th G after getting a first 3 = 8/9 * 7/8 = ~78%
chance of getting a 4th G after getting a first 3 = ~22%

chance of getting 4 G in one pass = 93% * 79% * 53% * 22% = ~9%

average score from GGGG option = .09 * 120 = 10.8

from BBBB

by symmetry, chance is .09
average score from BBBB = .09 * 200 = 18


from RRRR

by symmetry, chance is .09
average score from BBBB = .09 * 325 = 29


Sum of averages = 25 + 5.5 + 10.2 + 12 + 12.8 + 13.6 + 10.8 + 18 + 29 = 137 armory points per green core on average