Spotlight on Games > Analysis
Edison & Co.
Analysis of the Goldsieber board game
Thu May 13 20:35:20 PDT 1999
In the 4-player partnership version of Edison & Co., two pairs of players are seeking to achieve the highest score based on "Ranking Cards" which are known only to them. For their favorite vehicle, they receive points equal to three times its score, for their second favorite, points equal to two times its score, third favorite is 1 times and for the least favorite, zero points regardless. Maximizing this number is actually an exercise in 4-dimensional mathematics, something impossible to visualize in real terms, so let's analyze this in another way.

Suppose we call the vehicles A, B, C and D and suppose we describe the 4 ranking cards in the game as follows:

3A + 2B + 1C + 0D = J
3B + 2C + 1D + 0A = K
3C + 2D + 1A + 0B = L
3D + 2A + 1B + 0C = M

Now suppose that at end of the game the scores for the vehicles are as follows: A = 15, B = 10, C = 5, D = 0.

Then J = 70, K = 40, L = 30, M = 40. Team J has got their favorite vehicle to score highest and as we might expect, have managed to win.

But now suppose D had done somewhat better, in fact, had scored 12 points so that A = 15, B = 10, C = 5, D = 12.

Then J = 70, K = 52, L = 42, M = 76.

Note that Team M has won despite the fact the that their favorite vehicle only came in second place. However, they have managed to score highly on their top two favorites while Team J in second place got nothing at all for the second-place finisher.

In this game, Team M successfully maximized their score while minimizing J's. In fact, we might look at this as (M - J) which translates to

3D + 2A + 1B + 0C - (3A + 2B + 1C + 0D)

which is actually

3D - A - B - C

so in effect, D, their favored vehicle, was the overwhelming vehicle of importance for Team M. Was A similarly important for Team J? Well they sought to maximize (J - M) or

3A + 2B + 1C + 0D - (3D + 2A + 1B + 0C)

which is

A + B + C - 3D

As you expected, this turns out to be the just the same equation used by M with the signs turned around. And lo and behold, no, A was not nearly as important. For both teams, in fact, D was the vehicle of highest importance as only it had a coefficient of 3.

But suppose J were competing against K or L? What would be the vehicle of most importance in that case? Well, at this point we might as well look at the equations for all of the 6 possible pairings. We'll omit the signs of the addends as we know now they are fully-reversible depending on point of view and just study the coefficients:

J : K => 3A B C D
K : L => A 3B C D
L : M => A B 3C D
J : M => A B C 3D
J : L => 2A 2B 2C 2D
K : M => 2A 2B 2C 2D

A very unexpected result has fallen out. Not all races are created equal! While in 4 of them there is a single vehicle which achieves supreme importance, in two less frequently-occurring types of races, J vs. L and K vs. M, every vehicle is just as important as every other.

So what does this all mean for players of Edison & Co.? Well first, it would pay to memorize what the 4 ranking cards are. Then, close attention to your opponents' moves might give you a good idea of which ranking card they have. Once you have deduced this, you are able to determine whether you are playing a balanced race game in which each vehicle has the same importance or whether in fact one vehicle carries three times the weight as any other. If indeed you are in one of the latter games, you should do everything you can to either help or hinder this vital vehicle, depending on the point of view of your card. If not, you should play with a view to maximizing the point swing of a given move or series of moves, in other words, make the play which most significantly raises the score of your favored vehicles or which most significantly lowers the score of your opponents' favorites.

Of course, if you are able to figure out the opposition ranking card, the score is directly determinable anyway, but just keeping the relevant importances of the vehicles in mind may be quite a bit easier than constantly re-calculating all the numbers in your head.

How can you tell what the opposition card is? Well, one clue might be which vehicle they seem to favor most. If this vehicle is one which you have as the second best favorite, you are in the "three times" situation. Also, if the one they seem to favor is your least favored, you are also in the "three times" situation. And in both cases, the vehicle you have used to determine this is also the very one which deserves your extra attention as described above. On the other hand, if the apparently favored vehicle is your 1x vehicle, then all vehicles count equally and you should attempt to maximize the points of your two favored ones and minimize the points of the other two.

What if you are unable to tell, or unable to tell yet? The best thing to do is follow the strategy of our Team J in the very first example. As that example shows, if you ensure that the ratio between your 3x and 2x vehicles is 3:2, that between your 2x and 1x vehicles is 2:1 and your 0x vehicle gets no points, there is no way that you can be beaten.