e_i_pi wrote:4 ways to cash in, each with equal probability (I think) - 4 armies, 6, 8, 10... 4+6+8+10 = 28... 28/4 = 7... therefore a cash-in is worth (on average) 7 armies, and so each card is worth 7/3 = 2.33... armies
The probabilities for each type of set are not the same, mixed is always more likely:
3 cards: mixed 6/27, blue 1/27, green 1/27, red 1/27
4 cards: mixed 36/81, blue 9/81, green 9/81, red 9/81
5 cards: mixed 150/243, blue 31/243, green 31/243, red 31/243
average value:
3 cards: 8.667 if a set is held, 2.889 overall for three cards
4 cards: 8.286 if a set is held, 6.444 overall for four cards
5 cards: 8.469 for five cards