Robinette wrote:
um, if you do the math you'll see that the odds are the same and that this would not change the game to be "less luck-dependent"...
I did do the math, that's how I know they're not the same.
[the math]
Consider every arrangement of 5 cards. There are 243=3^5. This outline works the same for fewer cards, but 5 gives all the in-game possibilities.
The 5 cards resolve to one of 7 set choices: Red, Green, Blue, Mixed, Red or Mixed (ie RRRGB), Green or Mixed and Blue or Mixed. I'll write these as numbers like this [R G B M R/M G/M B/M]. For example [7 0 0 0 2 0 0] means that there are seven possible sets that end with only a Red set, and 2 that end with either a Red or a Mixed, which is what happens when you start with 3 Reds and draw two more cards (try it!).
Since there's no innate difference between Red and Blue, the number of sets is symmetric with regards to colors. So you can count all the sets that start with red, then flip the red and blue numbers to find the number that start with blue. Using the example above, this means that the sets starting with BBB are [0 0 7 0 0 0 2].
Now we just get counting. There's not that much to do, considering there are 243 sets to look at, because symmetry does almost all of the work.
Since we already know about sets starting RRR, go on to RRG- This can end as a Red set (RRGRR, RRGRG, RRGGR), a Green set (RRGGG), a mixed set (RRGGB, RRGBG, RRGBB) or a choice of Red or Mixed (RRGRB, RRGBR). And that's all, because there are only 9 choices. Since starting RRG is the same as starting RGR, we have
RRG = RGR = [3 1 0 3 2 0 0]
By symmetry around Blue, we get RRB = RBR = [3 0 1 0 2 0 0]
Next, we have RGG =[1 3 0 3 0 2 0] (check it if you want), so RBB = [1 0 3 0 3 0 0 2]
Finally, we have RBG = RGB = [0 0 0 6 1 1 1]. Including the RRR from above, that's all that start with Red, because there are only 9 choices for the second and third cards.
So the sum of all sets beginning with Red is [21 5 5 30 12 4 4]. By symmetry we get the sets starting with Blue and Green, and the total of all three, which is [31 31 31 90 20 20 20].
[/the math]
So there are 90 sets (~37%) which force you to use Mixed, and 60 (~25%) with Mixed or another colour. Since it's worth the most, people will choose it every time, effectively making the set resolution 31 Red, 31 Blue, 31 Green, 150 Mixed. The mixed set comes up ALOT more often than any other.
Making Mixed worth the least makes the sets resolve to 51, 51, 51, 90, still more Mixed than any single other choice, but no longer the outright majority, and now less desirable.