smallest impregnable force

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smallest impregnable force

Postby NJLonghorn » 11 Oct 2017, 22:29

I was thinking about the DIAS option, and my initial impression was that it would be fairly easy for some powers (especially Turkey) to carve out a quiet, impregnable corner and wait for the rest of the game to (hopefully) deadlock.

This led me to a thought question -- what is the smallest number of units one power can have and reliably control a section of the board? This would require enough units to protect an impregnable front, and enough supply centers along or behind the front to support those units.

Turns out, it isn't nearly so easy as I was thinking. I've spent some time trying to come up with a 10-unit solution, with no luck so far.

Have any of you thought through this before, or care to try?
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Re: smallest impregnable force

Postby Captainmeme » 11 Oct 2017, 22:41

Depends on who is eliminated.

I believe the award goes to an 8-center England with France & Germany eliminated and no enemy fleets in the north. England can hold Por, Lon, Edi, Lvp, Den, Swe, Nwy, StP with Por & NAO S MAO, Den H, Nwy S StP.
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Re: smallest impregnable force

Postby Malachite » 11 Oct 2017, 22:42

F Mid H
F Por S Mid
F NAt S Mid.
This was first noted by John McCallum in 1966. It uses three units to blockade the exit from the Mediterranean. It holds four centers (England & Portugal). F NAt could be Iri or Eng.
England (or a Power that holds England) can maintain this position indefinitely under certain circumstances. The enemy must be a Southern Power (Austria, Italy, or Turkey). The Atlantic Powers (France, Germany, Russia) have been eliminated or are allied. It is not impossible to see a game stalemated like this: Assume, for instance, two Southern Powers have overrun the board. Their armies occupy all of Europe. However, their fleets are bottled inside the Mediterranean and they can't get out. They hold 30 centers (15 each or perhaps 14-16 or 13-17). Neither can win without stabbing the other. This is a powerful negotiating weapon in England's hands.

Stalemate positions might be boring, but I think this one is the smallest one I've seen.
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Re: smallest impregnable force

Postby FloridaMan » 13 Oct 2017, 03:44

This is the part of the game where being a strategy nerd comes in more handy than being persuasive, I'd imagine. That has never been my real strength, but it's interesting to see other people examine it. I had also often wondered what the smallest position was that you could hold and survive. It makes sense that a position like that hypothetical English one would depend to some degree on who your enemies were.
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Re: smallest impregnable force

Postby jay65536 » 17 Oct 2017, 18:16

In addition to what has already been mentioned, there's another cool position that can be assumed by, let's say, Italy, assuming that France, Austria, and Turkey have been eliminated:

F Por S Spa, F Wes S Spa, U Spa H, U NAf H, U Con H, U Arm H

This holds Por/Spa, Tun, and the Turkish home centers--6 centers held indefinitely by 6 units.
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