Saturday, October 22, 2011

Surface Area

Map of Red Storm Rising -
Thin black lines indicates the various spaces
In past articles we discussed hex based war games.  Not all war games are hex based, some have irregularly shaped spaces which create an interesting mosaic for players to work around.  Although many of the same advice can apply to these types of games, there is one concept particular to these games to discuss: Surface Area.

Irregular Board
The following board comes from Red Storm Rising(RSR).  The spaces are all polygons, mostly four sided, but put together like a mosaic.  This type of board can require some time to decipher.   Unlike hexagonal grids, where distance become easy to determine by simply counting from one hex to another, irregularly shaped boards do not always have a "clear shortest path" from one location to another.  Adding in terrain effects (Rivers in RSR are more difficult to cross), and the calculations become more challenging.

The first question which comes to mind is "Who would come up with such a crazy map scheme".  Probably the same group which tried to break states up by natural border lines, waterways, and political boundaries.  An example of such a map is provided below:
Look familiar?
Surface Area
The "Surface Area' of any given location is equal to the number of adjacent spaces.  Color coding our Map of the United States, we get the following:
Individual Surface Areas of the States

Maine, the state in the uppermost right, is the only state adjacent to a single other state.  This means any attacks must come from New Hampshire.  Compare this to Texas, the large state in the south, which may be attacked by any of its four neighbors: Lousiana, Arkansas, Oklahoma, and New Mexico.  As expected, the states at the edge of the map have fewer neighbors than in the middle.  Still, one state, Kansas, is dead center in the map but only has four neighbors.

Objective of Surface Area Games
Normally, in games with irregular maps, players try to create 'fronts'.  A front consists of a group of units strung out along a contiguous line which faces the enemy.  Since most games limit the number of units a player receives each turn, it is best if the player's front is smaller than their opponents.

This becomes basic mathematics and a war of attrition.  If players received 12 units a turn, the player who occupies 4 locations will have 3 units added to each territory.  If their opponent occupies 6 locations, then the opponent will have only 2 units per territory.  Furthermore, the player has the option of attacking any 6 of their opponent's locations.

Kansas: Breadbasket, Corn fields, Stronghold
Missouri: watch your back, front, top, bottom...
Stronghold of Kansas
Some games permit units from surrounding territories to combine their units in attacks.  Even with this rule, Kansas stands out as a 'stronghold' in the center of the map. At most, 4 states could attack Kansas.

Compared to the state to its left, Missouri, where 8 states could combine efforts.  In this case, the smaller surface area again provides advantages in defense.

Oddities like the "Stronghold of Kansas" exist in many such games.  Identifying these oddball locations can create situations where players' "run to Kansas" just to force their opponents to thin their lines.  In the Kansas situation, it is odd because it rests in the middle of the board.  Thus, it differs from "Fortress Australia" from Risk.

Siam: Gateway to Fortress Australia

Fortress Australia

"Fortress Australia" is another common configuration found in games with irregular boards.  Made famous by Risk, the Fortress Australia configuration is more easily identifiable than "Stronghold Kansas".  The primary feature is a section of the map with an obvious choke point.

In the game of Risk, the continent of Australia can only be attacked through Siam.  Furthermore, if a player controls all of Australia's territories, the player gains bonus armies.  While the bonus armies are few compared to North America, Europe, Africa or Asia, Australia has an advantage in that it is easy to defend.  Furthermore, Australia is isolated next to the largest bonus continent: Asia.  Defending Australia consists of Occupying Siam and building a massive force.  While holding Siam, Australia provides 2 bonus armies and denies a player Asia's benefit of 7 armies.

The "Fortress Australia" is usually fairly obvious and the strategy around it is fairly simple.  Railroad Tycoon has a similar "Fortress Australia" in the Northeastern States, where there is a greater concentration of cities with relatively easy terrain.  If left alone, a single player can quickly dominate the game.

Next Article
The next article will discuss more about Surface Area as it applies to the players positioning.  We will cover Tips for Attacking and Defending, setup the ground rules for a sample game, and discuss how irregularly shaped boards need to affect the overall strategy.

Sunday, October 16, 2011

Hex War Games - Right Unit for the Job

Generally speaking, when attacking or defending, the smartest action involves using the best unit type against the enemy unit.  These are not always clear cut, but the following recommendations make good generalization.

vs. Infantry
Unlike most of the other units, the power of infantry lies on the terrain it occupies.  If in the enemy is in the open, hit infantry with armor, artillery or air units.  In any other terrain, it requires a combination of units to bring infantry down.  This is due to the fact nearly every other terrain allows infantry to sneak behind and get close to the attacking unit, except in Open terrain where there is no cover.  In jungle terrain, infantry are the best unit to use against other infantry units, although mobility becomes difficult.

vs. Armor
When combating armor in open terrain, use artillery, anti-tank guns, and other armor to bring them down.    In the case of anti-tank guns, attempt to provide them concealment to ambush the tanks.  If given notice of where the AT guns are located, armor can either engage the enemy AT guns from a distance or stay out of reach and bypass them.  Even Self-Propelled AT Guns are only good in ambush as they must rotate the entire vehicle to engage the tank.

If armor is in a city or any other terrain type, infantry are by far the best unit.  When in enclosed terrain, such as cities or forests, tanks suffer from many blind spots.  Additionally, infantry can rise up from beneath the belly of the tank (think sewers or mines), or they can fire down from the tops of tall buildings. 

vs. Artillery
Best use against artillery is to get in close and hit it with anything.  Even during the Civil War, when artillery was armed with canister rounds which would shred infantry to pieces, the long reload time of artillery meant if the infantry held together they could usually take the pieces, if the artillery was unsupported.

Otherwise, the best unit to hit Artillery is probably air units or other artillery units.  If there is insufficient Air Defense units, artillery are a sitting duck for aircraft.  Artillery should be at the top of the list of units to destroy.  Without artillery, attacks will eventually falter and defenses will eventually fall.

Artillery does have one very weak spot that, if the game allows for it, should be exploited: the baggage train.  Armor can carry jerrycans of fuel and attacks generally have enough fuel to attack in and, if it falters, flee back.  Infantry can carry days or weeks worth of supplies, plus small infantry units can always "live off the land" if there is sufficient livestock nearby.  And in close in fighting a person with a pitchfork can be as deadly as a man with a pistol.

Artillery, however, must have a constant supply of ammunition to be effective.  Furthermore, the munitions themselves are explosives.  Destroying this "baggage train" of explosives, or even disrupting the supply line for a turn or two, can remove artillery's effectiveness and leaves the artillery canon unscathed for capture.

vs. Air Units
The effectiveness of Air Units will differ depending on the era.  WWI aircraft were effective at spotting for Artillery, tracking enemy movements and possibly attacking ammunition depots.  The ability to track enemy movements was, by itself, enough of a threat to make taking down aircraft an important goal.  One important development in WWI aircraft was the creation of specialized "roles": Fighters, Bombers, Spotters, and Recon.

By WWII aircraft came into their own.  American aircraft were the primary means by which they defeated the Imperial Japanese Navy (IJN).  Strategic Bombing changed the face of warfare, bringing the concept of "total war" to fruition, making every person a subject to the pains of war.

There are two primary defenses against Aircraft: Air Defense Guns (AD, includes Surface to Air Missiles for purposes of this discussion) and other fighter aircraft.  Of the two, fighter aircraft are the most effective at shooting down other fighters in interception-based engagements.  However, AD can be extremely effective in defense of a given point.

This sounds confusing, but basically AD guns are static and can only defend a given area around the gun.  Aircraft have the ability of engaging the incoming enemy at any point in the enemy flight path, as long as the enemy can be identified.  Thus, if defending a given point or unit, such as a supply depot, large numbers of AA units surrounding the area will provide adequate defense.  If the need is to attack high flying bombers out of the range of AD units, other aircraft become a necessity.

vs. Ships
The best units against ships is a submarine.  But against a fleet of ships, I recommend aircraft.  Left to their own devices, the best way to attack a ship is to put a submarine just off the path of the ship.  The submarine simply waits, and then ambushes the ship, remaining silent and hidden the entire time.  The trick becomes predicting what the enemy ship's path will be, as the enemy will zig-zag the course.  Although capable of moving underwater, submarines are to slow to catch even the smallest of ships without surfacing, thereby losing their advantage.

The second best method is with Aircraft, if they are available.  Aircraft can fly high above the target, and attack ships with either bombs or torpedoes.  If in a fleet, aircraft will have to attack en masse, relying on numbers to sink or damage the target.  Once spotted, a single aircraft will have difficulty escaping a fleet of specially armed AA destroyers, and if a carrier is nearby, one can expect a swarm of fighters to flood the area.

If playing prior to the introduction of aircraft or submarines, the best way to engage a ship is with a larger ship.  In the age of sail, positioning or "crossing the T" may make up the difference.  In this case, it is not the larger ship which makes the difference, but the number of canons which can be brought to bear on the enemy ship/fleet at one time.  This is much harder to calculate, and where one must use judgement.

vs. Submarines
Post-WWII, the best anti-submarine weapons is another submarine, preferably an attack submarine.  In a pinch: aircraft, destroyers, and even some cruisers have anti-submarine weaponry.  During diesel age of submarines, the best weapon was the aircraft.  A submarine was force to charge its batteries and much of its "strategic" movement was performed on the surface.  Aircraft were best at ambushing these machines while they were on the surface.  In all those cases, however, their effectiveness depends on number of units, quality of units, and luck.

Oddly, submarines are the best way to sink an enemy submarine, but a fleet of anti-submarine ships is the best way to suppress a submarines.  Place enough anti-submarine ships between the submarine and its desired target, and the submarine may give up.    Once detected, submarines must go defensive, their ability to attack diminishes greatly.    While a single ship attempts to engage the submarine, the fleet slips away.  Aircraft cannot maintain the constant contact and attack runs against submarines like specialized Anti-sub destroyers.

It is necessary to therefore determine the objective when dealing with submarines: is it to sink the submarine, or to protect the fleet.  If the former, it may require multiple ships, at the expense of leaving the fleet insufficiently guarded, and the submarine may still escape.  In the latter, it may take one or two fast destroyers and the fleet or convoy is perfectly safe.  Destroying a submarine may "feel good" to a player, but if it prevents the fleet from arriving on time to save the land troops, consider the victory a defeat.

vs. Cavalry
Cavalry represent a special case.  Cavalry combine elements of submarines and armor.  The best counter against cavalry in a straight up fight is infantry.  A solid infantry square of poorly led troops still  has good odds of defeating a cavalry charge.  This is because cavalry, once removed from their horses, are weak infantry.  Like armor, cavalry units need to engage units in the open, as the forest terrain breaks up the formation too much, while swamps, jungles and mountains will damage the mounts.  Unlike Armor, cavalry can rarely perform true 'breakthrough' attacks independently and wait for infantry reinforcements. Cavalry historically are used to either pin the enemy down until reinforcements arrive, harass the enemy baggage train, or finish off retreating units after they have already been routed.

However, Cavalry can provide fast support where needed.  This requires another quick unit to intercept and engage them before they can provide that support.  In this case, the best unit is another cavalry unit.  However, Cavalry on Cavalry exchanges will result in heavy losses from either other, and it is not always easy to determine which side will suffer.  Often times, simply engaging the cavalry to slow them down is enough to counteract their effects.  Thus, Cavalry can be a 'situation' unit, one which may be incredibly useful if in play, or completely ineffective.

Thursday, October 13, 2011

FMA Argument for Dominion

William, a friend of mine, recently left a comment on the FMA article found here:  I then received some emails arguing if FMA exists in dominion.  Rather than become embroiled in an discussion, I'm going to answer this with simple example to prove FMA exists.

Dominion Basics
I won't go into too many specifics of Dominion except as it is relevant to this example:

Dominion "estate" card,
completely useless during the
game, but worth 1 VP
at the end

  1. Dominion is a game where player's use cards to purchase other cards (namely: 'Treasure' cards are used to purchase other cards,
  2. Players may do the following on their turn: Play one card for an 'Action', then 'Buy' one card, Discard, and then draw.
  3. Discard phase: All just purchased cards and cards in the player's hand are discarded
  4. Player draws up to 5 cards.
  5. If a player cannot draw up to 5 cards, the discard is then shuffled and cards are drawn until the player has 5 cards in hand.
Yes, there is more to the game than this, but to test for FMA, the above is all we need.

For this example we will make the following assumptions:
  1. It is a 2 player game,
  2. All players will draw the same set of cards,
  3. All player's are attempting to get the same card, 'Militia'
Treasure card: vital for
buying new cards
Assumption 1: Keeps the example small, in reality, more could be added, but the example takes longer.
Assumption 2: I expect the most comment from this example.  We will discuss the 'randomness' later in the article
Assumption 3: Others could say there are better cards out there, but bear with me on this as it is necessary to the example.

First Hand
Each player will have the following cards available in their hand:
1 Estate - effectively useless card for the first hand
4 Coppers - enough to purchase the Militia card.

Per our Assumption above, each player purchases the 'Militia' card.  This card, when played as an action, forces other player's to discard down to 3 cards.  It costs 4 gold to buy, but that is not a problem the first turn.

Second Hand

Militia: Armed and Dangerous? 

The second hand will have 2 Estates and 3 Coppers.  We know this because the game starts with every player having the same 10 cards: 3 Estates and 7 Coppers.  With this card every player purchases some other card, irrelevant to this discussion.

Just an interesting point here about dominion.  Both of the two hands above could have been drawn in ANY ORDER and it would not change the discussion.  In other words, the first player could have drawn 2 Estates and 3 copper for their first hand, but would have then had 4 copper and 1 estate to purchase the Militia.  This is due to the shuffling mechanic: No player reshuffles cards in their deck until after the they must draw a card and cannot.

Given probability and statistics, the two above hands are the 'expected' outcome for most player's on the first turn.  Players may have 5 treasures in their first hand (and 2 in their second), but we can safely assume the above two hands will occur on the first turn with reasonable expectation.

Put simply, we aren't doing something crazy about the above.

Third Turn
At this point every player will have shuffled their deck and drawn five new cards.  Thus, it is the first player's turn.  The first player draws their Militia card and plays it as an Action.  This card gives the first player 2 coins for purchases and every other player must discard 2 cards.

In this case, FMA raises its head.  No player can stop the play of this card (we will get to counters, such as Moat, later).  This first player is the first player to even have this option.  So, if the First player draws an "average" draw he will have:

  1. 1xMiltia
  2. 3xCopper
  3. 1xEstate
Dominion 'Mine' card.
The first player, upon playing the Militia, therefore has 5 coins to purchase a card.  Every other player must discard 2 of the above cards upon the first player playing Militia.  The second player will discard an Estate (as it is useless during the game) and 1 copper.  This leaves the second player with just 4 coins to purchase a card.

FMA Confirmed
From the above example we can see the first player has an option other player's do not.  From this, the first player has a First Mover Advantage.

Does it Detract from the Game?
FMA does not detract from my playing Dominion.  I enjoy Dominion.  It is a great game and I recommend everyone play it.  I know FMA exists in dominion, but I don't believe it is significantly large, especially not in a 2-player game.  However, the majority of statistics I've seen gathered on plays of Dominion indicate the odds of winning decrease as the player order increases (First and Second player win majority of games, then third player, then last player).

Arguments Against FMA
'But wait!' I hear people say.  It seems the more I hear about discussion for FMA in Dominion, the more I hear a "but wait" argument.  So, I'll discuss some basic arguments against my conclusion of FMA and my counter to them.  Many players take Dominion as a game of "skill", and they argue vehemently against anything to the contrary.  However, the below are common arguments.  If you have an argument I don't have covered here, leave it in the comments or send me an email: I welcome the discussion!

Moat: Counter to FMA?
The above only happens less than 50% of the time
True.  The above scenario (when the first player draws the Militia), will only happen 41.66% of the time.  Still, that is 46% of the games in which the start player is guaranteed a 1 coin advantage.  Not much of an advantage to be sure, but still an advantage.

There are better cards to buy than Militia
Absolutely agree with you.  However, Militia is simply an example to show the first player will have an option the other player's do not, and they will have the option to use that card first.  Militia is simply used as an example to amplify the results and show an 'extreme' version of what can happen.

The Moat would Counter Militia
Again, absolutely true.  However, there are two arguments against this as a counter for FMA.

First, there are usually better cards than Moat to purchase.  So what was the decision behind purchasing Moat?  If it was to counter Militia, then the player is making a purchase based on a move by the First player.  This is effectively 'breaking symmetry', a classic definition of FMA.

Second, particularly with games with more than two players, the "earlier player mover advantage" becomes more pronounced.  Consider, in a three player game, if the first player choose Militia and the second player also chooses Militia, both of these players have the option of playing militia before the third player.  Even if the first player does not draw the card, the second player might and will play it, affecting the third player.

Neither a Borrower nor Lender Be
- William Shakespeare
Working out the odds, if Militia is the 'card of attack', there is a slightly better than 65% odds the Third player will be hit by Militia.  In a Four player game, the fourth player has over an 80% odds of seeing the Militia card played against them if the first three player purchase a Militia.  This should clearly display the odds of being attacked by a specific card increase the later one goes in turn order.

There is too much randomness later on
True.  However, good players can turn a small advantage into a winning strategy.  In fact, that is a goal of many players.  I am not a good Dominion player (I don't play enough), but I fairly good at many other games.  I have a knack of turning a seemingly insignificant disparity into a game winning situation.  The same is true of Dominion.

So Skill doesn't matter in Dominion
Absolutely not.  An unskilled player (such as myself) against a skilled player will get slaughtered.  If I were to play chess with Mr. Kasparov, he could probably let me remove a Pawn of my choosing of his from play and he would still wipe the floor with me.  Skill does matter and skilled players will overcome a FMA of a lesser skilled opponent.  But, this argument does not dispute that FMA does not exist.

What other argument are there?
Let me know if you have another arguments against FMA.  Again, I welcome the debate!

Saturday, October 8, 2011

Games - Tempo

Tempo and initiative are related concepts, but have very different Impacts.  This article discusses Tempo.  We will discuss Initiative in a different article, then combine the two concepts.

Tempo is the "speed at which things develop".  This may seem to be under the control of the players, but only to an extent.  The game system also has a natural rhythm which impacts the speed of play of the game.

Games with fast Tempos are quick, with decisive engagements.  Usually there involves lots of maneuvering, but not always.  Generally speaking, a game with a fast tempo will end quickly, while one with slow tempo takes longer.

Fast Tempo Games
Games with a fast tempo begin at a point where forces are relatively close together or able to engage as early as the first turn.  Fast tempo games may also involve combat which quickly decides whether a unit lives or dies, or where the scale of the board is small enough movement from one edge to the other is relatively rapid.

Memoir 44: a fast tempo game with minimal rules for quick play.
Still loads of fun in a short package 
Fast tempo games tend to be quick and brutal, with heavy losses.  It is not that Fast Tempo games do not have strategic depth, but if a large mistake is made it may be difficult to recover.  The games may be lighter in nature, but that doesn't mean they are no less challenging.  Other fast tempo games may involve territories which change player's control territory.

Memoir'44, or any of the "Command & Colors" games by Richard Borg fall within this category.  Most of these games resolve within an hour, sometimes slightly longer.  Combat is a simple die roll, and the board is large enough to allow maneuvering, but not large enough to allow units to escape combat altogether.  Once damaged a unit remains damaged, and repair or reinforcements may not appear in the entire game
Slow Tempo Games
Other games develop slowly.  Combat may involve partial losses, or damage rather than outright destruction.  This usually mean unit's slowly deteriorate over time rather than completely dissolve.

Slow tempo games may also suffer from a resolution issue.  Some games have a simple quick and dirty combat system: Units hit or miss, and do damage accordingly.  These tend to be quicker combat games.  Games with slower tempos tend to have more complex battle resolutions: such as calculating range effects, determining suppression levels, rolling to determine the power of the attack, then having the target check for morale failure, etc.

Advanced Squad Leader (ASL), and many of the "hex and paper" games of the 1970's/1980's, fall into this category.  ASL focused on tactical level combat at the squad/individual tank level, but other games focus on the operational/theater level.  Slow tempo games usually require greater understanding of strategic placement and the options available to the units to get the most out of them.  Many dice rolls are common in these type of games, meaning luck should even out, and the victory depends more on unit placement, positioning, and mobility.

Changing Tempo Games
VTES(aka Jyhad) is a changing tempo game
where a challenge is to predict when the tempo
will change
*Image provided by Maeglor at
One of my favorite games to play are those with a changing tempo.  Changing tempo games are rare, especially those which change multiple times during the game.  Most games involve a period of setup, during which players construct units, maneuver forces, and explore the area around them.  Then, sometimes unexpectedly, oftentimes planned, there is a flurry of activity as players compete for position or victory.  After this flurry, the game resumes a more leisurely pace as players replenish their forces, repair their units, and prepare for the next assault.

The collectible card game V:TES (previously, Jyhad) is the best example I know of this type of game.  A game with eight players may last 4 or 5 hours, but the tempo tends to accelerate/decelerate every 20 to 30 minutes.  At first players need to build up their forces and get resources into play.  Some little actions occur during these first turns to disrupt the other players, but no major assaults.  Once one player has enough in play to stage an assault, there is a rush of activity as players attempt to defeat one another.  Usually this ends with one or two players removed from the game and everyone weakened.  The process than begins again.