Saturday, November 19, 2011

Surface Area III...Defensive Options

First, I have added a poll question to the right bar which I'd like to collect everyone's response.  Please let me know what you think.
The Player's Positions
Yellow: On the Defensive
It may seem Yellow has no actions when on the defensive, but there are things Yellow can do to adjust the mental state of their opponents.  This allows Yellow to control their opponent's actions to a degree.  However, first Yellow must come to terms with a given fact:
Yellow Will Lose Territory.

Inevitable Loss of Territory
Unless Yellow has an unusually large number of units compared to their opponents, it is not possible for Yellow to defend every space.  The following chart lists each color, their number of units, and their 'Army Density': how many troops may be spread evenly along each location adjacent to an enemy.

Player Spaces Surface Area Army Density
Blue 15 5 3
Green 12 7 1 (5 Leftover)
Red 9 4 2 (1 Leftover)
Yellow 14 10 1 (4 Leftover)

Looking at the chart, Yellow has the lowest Army Density of all players.  At best, against green, it is a 1 to 1 match.  Against Blue the odds are 3 to 1.  From this, it is Yellow needs to come to the realization loss of territory is inevitable.  With that in mind, Yellow can take steps to control where the opponent attacks and potentially whom the opponent attacks.

The first option is to negotiate with the players, if allowed.  This would permit a 'Peace Treaty' with a neighbor.  An agreement with another player would permit both players to reduce their Surface Area and thereby increase their Army Density.  For this to have an effective impact, both players need to have something significant to gain.

From the Player's Positions, Green is the most eligible candidate for a peace treaty.  Red is "locked" behind Yellow with no other player to fight, so peace with Red is least likely.  Yellow and Blue share only a single location, so a peace treaty between them will provide little gain to either.  However, a non-aggression pact between Yellow and Green would greatly benefit both players.  Green's Surface Area reduces to 5 and Yellow's Surface Area reduces to 6.  This leads to an army distribution as indicated below:

Surface Area
Army Density
Green1252 (2 Leftover)
Red942 (1 Leftover)
Yellow1462 (2 Leftover)
By negotiating a cease fire with Green, both player's benefit greatly.  Yellow now exceeds Red's density.  Similarly, Green is much better off in comparison to Blue.
Bait Your Enemy
The charts above assume Yellow attempts to defend each location evenly.  However, there is no reason Yellow must add new armies to the locations evenly.  Instead, Yellow could choose to not reinforce a given location.  This increases the Army Density without changing the surface area.  It does leave Yellow open to attack at these weak points in an attempt to lure the enemy in attacking at the 'weak point'.  The trick is to choose the correct 'weak point'.

For example in the diagram below, Yellow reinforces all the states next to Red except for Nebraska:
Reinforcing all but Nebraska
Yellow is attempting to make it easy for Red to take Nebraska.  If Red takes the space, then Red's surface area increases to 5, while Yellow's remains unchanged.  Ideally, Yellow's Surface area would decrease while Red's would increase, but no such situation exists to take advantage.  However, it does illustrate the point that Red and yellow are reaching a closer parity in army density, despite the fact Red gains 1 extra army while Yellow loses 1 army.
Surface Area
Army Density
Yellow13101 (3 Leftover)
There is always the danger your enemy will not take the bait.  In many cases they will, but it remains their choice.  Usually player's like to 'play the odds' and will usually choose the easiest method of attack.  It is not guaranteed.  The best Yellow can hope for is to make the other options too expensive for consideration.
Use Bait to Open Up New Fronts--For The Enemy
Baiting 2 Enemies
Red takes South Dakota, Green takes Iowa
In our example, Yellow is fighting against three enemies.  One of them, Red, has no other focus than to crush Yellow.  In this case, it may be best for Yellow to Bait Red and Blue into opening up territory adjacent to one of the other player's.  This means giving up territory, but territory loss for Yellow is already determined to be inevitable.  In the example, yellow an achieve this in one turn by baiting Red to take South Dakota and Green to take Iowa.  The impact of such a move is indicated below:

PlayerSpacesSurface AreaArmy Density
Green1381 (5 Leftover)
Yellow1291 (3 Leftover)
This has several effects.  First, Yellow's Surface area decreases so the army density goes up.  Both Green and Red have increased surface area, so their Army density decreases.  Most importantly, Green and Red are now in conflict with each other.  Unfortunately, Red and Green may reach negotiations and decide to not attack each other.  This would be the worst situation for Yellow, but gambles must sometimes be made.
In Summary
To sum it up, the goal of irregularly shaped boards is to reduce surface area and increase army density.  Many of these same principles apply to hex-based war games, but with irregularly shaped boards the configurations are easier to see.  In short, it focuses on the principle of Concentration of Force: bringing the most equipment to bear at the correct time.

What I find amazing is even young children can understand the principles behind this concept.  It would seem the focus would be on 'getting the most armies', but those of us playing Risk quickly learn having a long line of territories with a few troops in each is not nearly as effective as a smaller clump territories with many troops in just a few territories.  These games represent an odd case where productivity, the ability to generate more troops than the enemy, may not lead to eventual victory.
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