Card Distribution

Card
Value
Total #
of Cards
4 1 1    
5 4 3 1  
6 10 6 3 1
7 16 7 6 3
8 19 6 7 6
9 16 3 6 7
10 10 1 3 6
11 4   1 3
12 1     1
total 81 27 27 27
Card
Value
Total #
of Cards
4 1 1    
5 4 3 1  
6 10 6 3 1
7 16 7 6 3
8 19 6 7 6
9 16 3 6 7
10 10 1 3 6
11 4   1 3
12 1     1
total 81 27 27 27
Card
Value
Total #
of Cards
4 1 1    
5 4 3 1  
6 10 6 3 1
7 16 7 6 3
8 19 6 7 6
9 16 3 6 7
10 10 1 3 6
11 4   1 3
12 1     1
total 81 27 27 27
Card
Value
Total #
of Cards
4 1 1    
5 4 3 1  
6 10 6 3 1
7 16 7 6 3
8 19 6 7 6
9 16 3 6 7
10 10 1 3 6
11 4   1 3
12 1     1
total 81 27 27 27
The above tables show how many total cards there are for each value, and for each value and combination. For example, there are 6 '8' cards with a 1 star.
Of course, if you want to win, you need to add all the cards above it too.
  6   '8' cards with 1 star 
  3   '9' cards with 1 star 
  1   '10' cards with 1 star 
  0   '11' cards with 1 star 
+ 0   '12' cards with 1 star

10 cards with 1 star of value 8 or greater


Constructing the table
Although this table is included with the cards, it is simple to reproduce.

First, note that it doesn't matter which shape you are looking at; they are all the same table.
Second, note the columns for 1, 2, or 3 shapes are all the same, just offset by 1 each.
1    
3 1  
6 3 1
Third, note the distribution mirrors itself. In other words there are as many cards with 1 cube on the high end as the low end.
1
3
6
7
6
3
1
Fourth, of course the total number of cards for a given value is the sum of the number with 1 star + 2 stars + 3 stars.
16 = 3 + 6 + 7

Fifth, remember the sequence 1 - 3 - 6 - 7.

Now, start at the top for 1 shape, and follow the sequence (remember to mirror it) 1,3,6,7,6,3,1
Then start 1 down for 2 shapes, 1,3,6,7,6,3,1
And start 2 down for 2 shapes, 1,3,6,7,6,3,1
Sum them up, and there you have it.