Ideal territory counts

[e_i_pi]

Intended to increase the knowledge base for prospective and current mapmakers

I just did a quick analysis of the way territory counts on maps impact on number of neutrals in the initial drop. I used this equation to rank them:

Score = Spare neutrals generated on 2 player, multiplied by number of finished 2 player games
plus neutrals generated on 3 player, multiplied by number of finished 3 player games
plus (same for 4p-7p games)
...
...
plus neutrals generated on 8 player, multiplied by number of finished 8 player games
all divided by 100000 to produce a smaller number (as they end up in the millions)

...where "spare neutrals" is the number of neutrals beyond what each player starts with (eg - 29 territory map is 9 per player, 11 for neutral, therefore 11 - 9 = 2 "spare" neutrals.

The table below shows
(Territory Count) - (Score) - (Perfect Distributions)
so...
40t - 33s - 4, 5
...means 40 territories - scored 33 - 4 and 5 player maps have no neutrals.
The lower the score the better

Top 20 Territory Counts

96t - 1.9s - 2, 3, 4, 6, 8
72t - 2.8s - 2, 3, 4, 6, 8
48t - 4.6s - 2, 3, 4, 6, 8
60t - 5.1s - 2, 3, 4, 5, 6
24t - 5.5s - 2, 3, 4, 6, 8
36t - 6.0s - 2, 3, 4, 6
84t - 9.8s - 2, 3, 4, 6, 7
90t - 11s - 2, 3, 5, 6
66t - 12s - 2, 3, 6
42t - 13s - 2, 3, 6, 7
18t - 15s - 2, 3, 6
30t - 16s - 2, 3, 5, 6
81t - 18s - 2, 3
57t - 19s - 2, 3
78t - 20s - 2, 3, 6
33t - 21s - 2, 3
54t - 21s - 2, 3, 6
45t - 22s - 2, 3, 5
21t - 22s - 2, 3, 7
93t - 25s - 2, 3

Keep in mind the scoring is based on the popularity of player-number games multiplied by the number of neutrals generated. So a territory count like 31 scores very poorly, as it generates 7 neutrals on 8 player maps (which are quite popular).

[Ditocoaf]

Sorry, but I don't think I know what a "Perfect Distribution" is... at first I thought that it meant that the numbers were perfectly divisible (with no remainder), but you have 2 listed as a perfect distribution on maps with odd numbers of territs...

[e_i_pi]

Sorry, but I don't think I know what a "Perfect Distribution" is... at first I thought that it meant that the numbers were perfectly divisible (with no remainder), but you have 2 listed as a perfect distribution on maps with odd numbers of territs...

Yep thats' right. When 2 is in there it means that neutral has the same amount of territories as the players. That's as perfectly divisible as 2 gets. Essentially, if it's divisible by 3, then it will be perfectly divisible in a 2 player game too

[MrBenn]

The number of neutrals on the map isn;t necessarily as important as the number of territories...

I've added 4 neutrals to Europa to help balance the drop... I didn;t need to add them , but wanted to take away the advantage of starting with 18, 15 or 12 territories (and an extra army to the player who goes first, assuming they'd be able to knock an opponent down by one army).

Personally I think there is more merit in this 'golden number' line-of-thought. I'll have a rummage around and see if I can find the other thread...

edit: and here it is viewtopic.php?f=127&t=34210&hilit=golden+number

[e_i_pi]

I've added golden number technology, and given it double weighting to the neutral count. This seems a reasonable weighting, though I can easily change it for updated rankings. The results are below:

Format:
Territories -
(2 player starting provinces.2 player extra neutrals /
3 player starting provinces.3 player neutrals /
4 player starting provinces.4 player neutrals /
5 player starting provinces.5 player neutrals /
6 player starting provinces.6 player neutrals /
7 player starting provinces.7 player neutrals /
8 player starting provinces.8 player neutrals)

Top 20 Territory Counts

24 - (8.0 / 8.0 / 6.0 / 4.4 / 4.0 / 3.3 / 3.0)
42 - (14.0 / 14.0 / 10.2 / 8.2 / 7.0 / 6.0 / 5.2)
18 - (6.0 / 6.0 / 4.2 / 3.3 / 3.0 / 2.4 / 2.2)
30 - (10.0 / 10.0 / 7.2 / 6.0 / 5.0 / 4.2 / 3.6)
33 - (11.0 / 11.0 / 8.1 / 6.3 / 5.3 / 4.5 / 4.1)
21 - (7.0 / 7.0 / 5.1 / 4.1 / 3.3 / 3.0 / 2.5)
60 - (20.0 / 20.0 / 15.0 / 12.0 / 10.0 / 8.4 / 7.4)
25 - (8.1 / 8.1 / 6.1 / 5.0 / 4.1 / 3.4 / 3.1)
69 - (23.0 / 23.0 / 17.1 / 13.4 / 11.3 / 9.6 / 8.5)
27 - (9.0 / 9.0 / 6.3 / 5.2 / 4.3 / 3.6 / 3.3)
96 - (32.0 / 32.0 / 24.0 / 19.1 / 16.0 / 13.5 / 12.0)
16 - (5.1 / 5.1 / 4.0 / 3.1 / 2.4 / 2.2 / 2.0)
78 - (26.0 / 26.0 / 19.2 / 15.3 / 13.0 / 11.1 / 9.6)
28 - (9.1 / 9.1 / 7.0 / 5.3 / 4.4 / 4.0 / 3.4)
43 - (14.1 / 14.1 / 10.3 / 8.3 / 7.1 / 6.1 / 5.3)
19 - (6.1 / 6.1 / 4.3 / 3.4 / 3.1 / 2.5 / 2.3)
31 - (10.1 / 10.1 / 7.3 / 6.1 / 5.1 / 4.3 / 3.7)
88 - (29.1 / 29.1 / 22.0 / 17.3 / 14.4 / 12.4 / 11.0)
51 - (17.0 / 17.0 / 12.3 / 10.1 / 8.3 / 7.2 / 6.3)
32 - (10.2 / 10.2 / 8.0 / 6.2 / 5.2 / 4.4 / 4.0)

[BENJIKAT IS DEAD]

The number of neutrals on the map isn;t necessarily as important as the number of territories...

I've added 4 neutrals to Europa to help balance the drop... I didn;t need to add them , but wanted to take away the advantage of starting with 18, 15 or 12 territories (and an extra army to the player who goes first, assuming they'd be able to knock an opponent down by one army).

Personally I think there is more merit in this 'golden number' line-of-thought. I'll have a rummage around and see if I can find the other thread...

edit: and here it is viewtopic.php?f=127&t=34210&hilit=golden+number

Indeed as I argued a year ago, I strongly think that territory count is more important than neutral count.

However there is another very important factor - connectivity. I think BaldAdonis gave this a definition somewhere, but for me I have always thought of it as the average (not necessarily the mean) number of attack routes per territory, however this could only tell part of the story if the map's connections are uneven (think Oceania).

The lower the connectivity, the greater the impact of neutrals... and vice versa.

So a true list of "golden numbers" needs to map against connectivity values.

I personally prefer larger maps with lots of connectivity, as (especially in 1v1s) they provide the greatest opportunities to outplay your opponent, and discovering this intuitively caused me to want to figure out why.. hence my previous thread.

There is a big final "however" though - homogeneity is NOT something we should be aiming for - the fact that different maps play in different ways means that adaptability is also tested, and therefore increases the amount of fun (Pearl Harbor is not a "fair" map, but it is one heck of a lot of fun).

e_i_pi - I suggested the rudiments of a method of calculating the golden numbers in a more comprhensive way in my thread and it seems you may be the first who could be up to that challenge! (I'll help any way I can)

Your current method of factoring in the number of games may be flawed? - To my mind, the number of players affected is more important... i.e. 4 1vs1 are equivalnent to a standard 8 player. A further extension of this is to count "teams" - i.e. units of points loss & gain - quads=2, 1v1=2 etc