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Number of 'board' possibilities on Med Earth?: 2/8/2013 16:26:57

ChrisCMU
Level 60
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Anyone have any idea the number of possible 'maps' on medium earth (1v1 strategic settings)?

It of course varies based on warlord locations and wasteland locations.

Just curious, I'm sure some math expert on here can figure it out, or has.
Number of 'board' possibilities on Med Earth?: 2/8/2013 18:07:37

Wenyun
Level 59
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First, we'll have to consider wastelands, since they can overwrite normal maps.

Wastelands cannot be placed in the same place, but order does not matter. Medium Earth has 131 territories.

Thus we get...

131!/(7!(131-7!)) = 11,600,996,000 possible combinations of wastelands.

Now, while the next step would be to place Warlords down, we would normally just multiply that number by the number of choices per warlord. If a warlord is behind a wasteland, it is still a different choice, as the bonus with the wasteland won't have a warlord.

But now we run into a problem. If there are two wastelands or more in the same bonus, then the map is the same if the warlord ends up behind either wasteland.
Number of 'board' possibilities on Med Earth?: 2/8/2013 18:18:45

Wenyun
Level 59
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(Whoops, pressed post a bit early.)

If we ignore that little problem for now, all we have to do is multiply by the number of territories in each bonus.

There are 4 bonuses with 4 territories.
There are 9 bonuses with 5 territories.
There are 4 bonuses with 6 territories.
There are 6 bonuses with 7 territories.

If I counted right it's 8.8441993x10^26 without considering the problem I put in my previous post. As for how to deal with that, though, I'm too lazy :P
Number of 'board' possibilities on Med Earth?: 2/8/2013 18:21:09

ChrisCMU
Level 60
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So basically you might never have the same map in two games you play, ever.

That is good.
Number of 'board' possibilities on Med Earth?: 2/8/2013 18:28:55

Ironheart
Level 53
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The odds of that happening is very low however it's a tiny possibility.
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