lancehoch wrote:e_i_pi wrote:Joodoo wrote:e_i_pi wrote:The chances of having a mixed is the same as the chances of having a coloured set you know

then we should make all of the sets worth 10 armies / 8 armies

That's what I mean.

RRR: 6 armies

GGG: 6 armies

BBB: 6 armies

RGB: 10 armies

is exactly the same as

RRR: 10 armies

GGG: 6 armies

BBB: 6 armies

RGB: 6 armies

statistically

pi, that is not true.

Subject: 10 army sets... are these common to turn in repeatedly?lancehoch wrote:To answer the question from the thread title, actually mixed sets are more common than any single instance of a single colored set:

3 cards: 27 possibilities- 1/27 red, 1/27 green, 1/27 blue, 6/27 mixed, 18/27 no set

4 cards: 81 possibilities- 9/81 red, 9/81 green, 9/81 blue, 36/81 mixed, 18/81 no set

5 cards (note you can have a mixed set and a plain color set, I am counting these as mixed): 243 possibilities- 31/243 red, 31/243 green, 31/243 blue, 150/243 mixed, 0/243 no set

in percentages (mixed only):

3 cards: 22.22%

4 cards: 44.44%

5 cards: 61.73%

So to answer your question, yes it is very common to get a mixed set.

More in depth analysis for the 5 card situations:

only red: 31/243

only green: 31/243

only blue: 31/243

only mixed: 90/243

red and mixed: 20/243

green and mixed: 20/243

blue and mixed: 20/243

totals:

red: 51/243

green: 51/243

blue: 51/243

mixed: 150/243

What I would suggest is (if there is to be a change) actually changing the values to mixed = 4 and red/green/blue = 10.

Given the probabilities I would agree that there should be a game type to compensate for this. Possibly a true flat rate, 6 or 8 or 10 whatever, but all sets given equal compensation.

However relatively speaking the cumulative probability of turning in all of one color, red is = green is = blue.

With 5 cards, that is to say P(RRR, GGG, BBB) = 153/243 or about 63% vs. any combination of P(RGB) at about = 62%

At 4 cards, P(RRR, GGG, BBB) = 33% vs any combination of P(RGB) = 44%

At only 3 cards P(RRR, GGG, BBB) = 11% vs. any combination of P(RGB) = 22%

If we were going to be "Fair" about compensation for cards we would have to figure out a percentage based measurement which would be separate for each number of cards such as:

With 5 cards compensation for RRR, GGG, BBB = RGB since percentages are relatively the same.

With 4 cards possibly one extra troop.

With 3 cards perhaps a set of RRR, GGG, BBB should be 2xRGB that of RGB or maybe two additional troops since the likelihood is half.

The problem is figuring out how large a percentage advantage is needed for each additional troop. It all seems fairly extreme, it would be much easier to just make another variation of game with a true flat and equal rate for any card set.