You have three green slots, three gray slots, and three blue slots. You put three counters each on each of the green and gray slots, and one counter each on each of the blue slots. The frequencies of counters per slot is [3, 3, 3, 3, 3, 3, 1, 1, 1]. The total number of counters you put down is 3*6 + 3 = 18 + 3 = 21. To turn the frequencies into a probability distribution, you divide everything by 21, to get [1/7, 1⁄7, 1⁄7, 1⁄7, 1⁄7, 1⁄7, 1⁄21, 1⁄21, 1⁄21]. Then the entropy is 6⋅−17log217+3⋅−121log2121, which is 67log27+321log221. Right? (Thanks for checking—it would be really embarrassing if I got this wrong. I might edit the post later to include more steps.)
You have three green slots, three gray slots, and three blue slots. You put three counters each on each of the green and gray slots, and one counter each on each of the blue slots. The frequencies of counters per slot is [3, 3, 3, 3, 3, 3, 1, 1, 1]. The total number of counters you put down is 3*6 + 3 = 18 + 3 = 21. To turn the frequencies into a probability distribution, you divide everything by 21, to get [1/7, 1⁄7, 1⁄7, 1⁄7, 1⁄7, 1⁄7, 1⁄21, 1⁄21, 1⁄21]. Then the entropy is 6⋅−17log217+3⋅−121log2121, which is 67log27+321log221. Right? (Thanks for checking—it would be really embarrassing if I got this wrong. I might edit the post later to include more steps.)
Ahhh! Yes, that helps a great deal. Thank you!