I have long felt limited in the choices of Civs/Civ trait (Mil, Ind, Exp, Sci, Rel, Com) combinations. Tonight I decided to do a little analysis into adding a third trait to each of the standard PTW Civ's.
First, I wanted to make sure I was maximizing the number of trait combinations by using three traits. I suspected I was, but I wanted to make sure.
2 traits per Civ, =
(6 * 5)/2 = 15 where six is the available letters for the first position, 5 is the available letters for the second position, and you divide by 2 since there are two letter slots in the word to remove duplicates.
The Combinations are
MI, ME, MS, MR, MC, IE, IS, IR, IC, ES, ER, EC, SR, SC, and RC
3 traits per Civ, =
((6*5)/2)*4/3 = 20 or rather 15*4/3=20 where we treat this as a two letter word, with 15 choices for the first letter (The double letter solution from above) * the 4 remaining possible letters, then divide by three since there are actually 3 letters used, to remove the duplicates and reversals.
The Combinations are
ERC, ESC, ESR, IEC, IER, IES, IRC, ISC, ISR, MEC, MER, MES, MIC, MIE, MIR, MIS, MRC, MSC, MSR, SRC
4 traits per civ =
(20 * 3) / 4 = 15
At 4 we are back to where we started at with 15 possible combinations.
5 traits per Civ =
(15 * 2) / 5 = 6
At 5, we might as well go back to having only a single trait per Civ. (Actually we have, but instead the single trait picked is the one NOT enabled)
6 traits per Civ =
(6 * 1) / 6 = 1
And this is true because with all Civs having All traits, then there is no diversity and all Civs are alike.
I kind of fumbled my way through this, so to anyone who feels like, please check my math / assumptions. I am always open for correction.
As long as we are limited to 6 traits, the distribution gos like this.
Traits Per Civ / Maximum Different Combinations
1/6
2/15
3/20
4/15
5/6
6/1
Thanks for reading this far... More to Follow.
KP
Edit: Fixed Title
First, I wanted to make sure I was maximizing the number of trait combinations by using three traits. I suspected I was, but I wanted to make sure.
2 traits per Civ, =
(6 * 5)/2 = 15 where six is the available letters for the first position, 5 is the available letters for the second position, and you divide by 2 since there are two letter slots in the word to remove duplicates.
The Combinations are
MI, ME, MS, MR, MC, IE, IS, IR, IC, ES, ER, EC, SR, SC, and RC
3 traits per Civ, =
((6*5)/2)*4/3 = 20 or rather 15*4/3=20 where we treat this as a two letter word, with 15 choices for the first letter (The double letter solution from above) * the 4 remaining possible letters, then divide by three since there are actually 3 letters used, to remove the duplicates and reversals.
The Combinations are
ERC, ESC, ESR, IEC, IER, IES, IRC, ISC, ISR, MEC, MER, MES, MIC, MIE, MIR, MIS, MRC, MSC, MSR, SRC
4 traits per civ =
(20 * 3) / 4 = 15
At 4 we are back to where we started at with 15 possible combinations.
5 traits per Civ =
(15 * 2) / 5 = 6
At 5, we might as well go back to having only a single trait per Civ. (Actually we have, but instead the single trait picked is the one NOT enabled)
6 traits per Civ =
(6 * 1) / 6 = 1
And this is true because with all Civs having All traits, then there is no diversity and all Civs are alike.
I kind of fumbled my way through this, so to anyone who feels like, please check my math / assumptions. I am always open for correction.
As long as we are limited to 6 traits, the distribution gos like this.
Traits Per Civ / Maximum Different Combinations
1/6
2/15
3/20
4/15
5/6
6/1
Thanks for reading this far... More to Follow.
KP
Edit: Fixed Title
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