Through The Ages - Part XVIII - Military: Aggression and Wars

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Sorry for the late post.  Writing this article took much longer than anticipated as analyzing the various Military statistics and required more in-depth study than it initially seemed.  Enjoy!
Aggression and Wars
Military options in Through The Ages are very limited.  At the start of every player's turn that player has the option to perform a single political action: either a Pact/Treaty or an Aggression/War.  Pact cards are few and from our analysis account for little in way of culture.  Aggression/Wars do generate significant culture, being the third largest source of culture after buildings and Wonders.

A Popular War:
War over Culture

Aggression and Wars differ significantly.  Aggression cards resolve immediately and only the defender is at risk.  Furthermore, the defender of the Aggression may play Defense Cards to try to meet or beat the attacker.  Wars resolve the turn after they are announced, Defense cards may not be played by neither attacker nor defender, and both players are at risk to lose.

Aggression and Wars also differ in timing.  Prior to Age II, only Aggression are available.  During Age II only 3 Wars exist, and during Age III 7 Wars exist.  Given that Age III is the shortest Age, there are fewer Wars than Aggression cards.  One thing both have in common is a Military Action "cost" to play.  This is critical only when one realizes by playing an Aggression/War, the player will have fewer Military Actions with which to build units/replacements.  In a 4-player game this can become critical as a player who has current military domination may see an opponent overtake them if they continue to use their military actions to declare War or Aggression cards.
Popularity of Aggressions & Wars
The chart below shows the overall breakdown of Aggression and Wars.
Overall, through the 100 games played, there were a total of 808 Aggression or Wars played.  This implies players should expect to see 8 military conflicts in a typical game.  The largest number of conflicts recorded was 16, and the smallest was 2.

The other item the chart above tells us is when the conflicts take place.  During Age I most players focus on their economy, and so military conflicts are rarer in Age I.  As time goes on, military conflicts become increasingly common.  In general, the breakdown of military attacks in a typical game for each Age are as follows:



Our first chart also shows the "popularity" of the different conflict cards.  More Raids and Plunders exist than other cards, so seeing them high in the play list is not surprising.  Next on the high list are the two "Culture Stealing" cards: Armed Intervention and War over Culture.  Although War Over Culture exceeds Armed Intervention in number of cards in the deck, War Over Culture suffers in number of plays because it may not be played on the last round, whereas Armed Intervention is playable on the last round.
Success of Aggression
Declaring an Aggression or War is one thing, being successful at it is something else.  Since Wars and Aggression cards have different outcomes we will look at the two differently.   As long as the attacking player doesn't sacrifices troops to increase the attack, there is very little risk in initiating an Aggression.  At most, the Aggression costs some Military Actions, but that is essentially it.  Looking at the following chart we determine the ability of an Aggression or War of succeeding.

From the diagram we can see the odds of a military action succeeding is just under 60%.  The odds of success do differ depending on the Age of the attack, however.  All Age I attacks have less than 50% odds of success.  During Age II and Age III the odds of success increase to just above 55%.  However, during Age IV the success rate increases to 70%

A Popular Aggression:
Raid

These discrepancies are easily explainable.  During Age I the players' military strengths are all relatively close together, being within 1 or 2 points.  Spending a Defense card, or even sacrificing a military unit to make up the difference is not to terrible a loss.  By Age II the player's begin to differentiate themselves both economically and militarily.  Tactics come into play which greatly influence strength.  Similarly, more advance units are researched and built which increase the military strength further.  Lastly, the cost of replacing units puts a tax on the player's economy, so player's are less likely to sacrifice military units in defense if replacing the unit will cost more than the player would lose from letting the attack succeed.

This last item is particularly true when it comes to Armed Intervention.  Armed Intervention takes 7 points from the defending player and gives it to the attacking player.  However, by the time Armed Intervention comes into player most players are making more than 7 culture per turn.  Looked at over an entire game, the loss of 7 culture is roughly equivalent to losing a single game turn.  Most players are willing to accept this loss if it means their economy remains untouched and can be increased on following turn.
Success of War
Wars carry significantly greater risk.  First, the outcome takes a turn to determine and greatly impacts the uncertainty of the outcome.  First, the attacker must have a clear numerical majority in units as the act of declaring war will decrease the number of available actions to build more units for the attacker the War.  Second, the defender has a turn to play a combat changing Tactic, research an improved unit, or build more military units.  Third, although defense cards may not be played, the defender has a clear advantage in deciding if sacrificing units is a feasible option or not to reduce the Wars effects.  Lastly, Wars go "both ways", the attacker loses something if the Defender succeeds.
For our discussion of "success" in wars, we will consider wars which were Won by the player that initiated the War.  This yields the following chart:
The high success rate of Wars follows from the above discussion: there is so much at risk for the attacker Wars are only initiated when the player believes victory is certain.  Still, roughly 1 out of every 5 Wars will not succeed for the two most popular Wars: War over Culture and Holy War.  The losses of these Wars come from three primary sources: Defender Military Jump/Leader Loss, Acquisitions, and Scavenging.

Gandhi is a leader which doesn't
cause a Military Jump, but
ends Wars immediately and
protects from them in the future.

Defender Military Jump/Leader Loss
This scenario occurred in roughly half of the losses.  Basically, the defender managed to play a tactic, build a unit, or place a leader which greatly increased the military of the defender of the war to the point the War.  In 4% of the cases the defender achieved parity with the attacker rather than exceeding the attacker's strength, counting as a 'loss' for the attacker, although neither side gained nor lost any resources.

A similar situation occurs if an Age ends after a War is declared but before it resolves.  Usually the attacking player's leader was Napoleon Bonaparte and his loss resulted in a dramatic loss of military strength, making the construction of military units capable of overcoming the attacking forces.
Acquisitions
Acquisitions involve a territory coming up for bid after a player has declared a War.  The scenario may seem relatively rare, but accounts for a little under one-third of War losses:

1. The War Initiator declares a War,
2. During some other players turn a Territory appears as an event,
3. The War Initiator wins the bid for the Territory and must sacrifice military units,
4. The lost military units cost the War Initiator the war!

It is hard to determine if the War Initiator forgot a War was going on at the time the Territory bid came up, but the fact this accounted for a third of losses means the player made a decision which said the Territory was worth more than the war.
Scavenging
The last scenario where player's lost wars I refer to as "scavenging".  This scenario takes account of the multi-player aspect of Through The Ages.  This scenario is complex and seems difficult to pull of, but it goes as follows:

1. Player A declares War on Player B.  Player B has a smaller military than Player A.
2. Player C then declares an Aggression against Player A.
3. To defend from Player C, Player A must sacrifice units to defend from the Aggression.
4. This weakens A to the point where Player B then wins the War.

"Scavenging" involves attacking
a player just after they declare a war.
Consider the Tactic above, the loss of even
a single 3-point unit results in a loss
of 16 points of Military Strength!

In this circumstance usually Player C and Player A are close militarily, although often times Player C was not as strong as Player A and may sacrifice units to boost the attack.  Interestingly, the lead player rarely had a Defense card in hand to defend from this, usually because being in the lead means the Defense card is taking up space another, more useful card would occupy.  The only other last note was many times the Aggression card played was a card which attacked Player A in a significant economic or military way, such as the following:

• Annex,
• Assassinate,
• Sabotage,
• Raid.

Rarely did the second player attack with Armed Intervention, which directly steals culture, or Plunder which reduces resources.  The point here is the second player is forcing the War player to either lose critical infrastructure or weaken themselves to the point where they may lose the War.  Depending on the War played and the potential infrastructure lost, the War player is placed in a Lose-Lose situation.

Observations
Aggression, Wars and Military Strength form a major component of Through the Ages.  Overall, Aggression cards form the majority of military attacks.  Part of this is there are more Aggression cards than War cards.  Timing is critical for both, however.  Wars are more likely to succeed than Aggression cards, but both are more likely to succeed in the later Ages the card is played.  An Aggression will fail just a little over half the time, but Wars will succeed upwards of 80% of the time.  However, the attacker in Wars needs to be careful of timing to avoid end of Ages, how close the second player is to them in military strength, and be aware of the military cost of bidding for territory cards if a card is drawn.

This concludes the Military section of Through the Ages.  There are a few Odds and Ends to wrap up, but now we will begin to discuss various Strategies to improving the play.  Yes, many of these articles touched on various aspects of Strategy, but now it is come time to put them all together into a cohesive whole!

Through The Ages-Part XVII - Military: Tactics Progression

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Military
Military forces in Through The Ages require units, which come from the population.  At first, only warriors are allowed but through civil actions and science, players may increase the strength and type of military units available.  The strength of military units is entirely based upon their Age, as show in the table below:

What makes the different types of military units important are the Tactics, which are found in the Military/Events deck.
Tactics
Tactics represent how the player's nation organizes is military.  Unlike civil cards, where the player has some control on choosing if a military technology can be learned, Tactics cards are drawn at random (see The Numbers Game).  Still, players can make plans around these tactics cards and determine which ones they wish to keep/upgrade, and which to discard.  Given the requirement in science resources, military actions, civil actions and population requirements, players prefer an "efficient" progression of tactics.  The following chart displays the units, the cost to build, and the strength (for those tactics with antiquated strengths this is displayed in parenthesis).

Drawbacks of Advanced Tactics - Flexibility
Overall, the more advanced tactics provide a greater increase, but there is a drawback to them beyond their cost.  Since a tactic has no effect if a single unit is missing, attempting to control territories can become "more expensive" for those with tactics requiring more units, especially if forced to sacrifice a unit.  This is a common occurrence when bidding for territories.

Consider this as an example: Two players, Alicia and Brutus have four military units each of the same type and strength - 2 Infantry and 2 Cavalry (both minimal Age for maximum gain).  Alicia has Medieval Army giving a total strength of 10 ( (2[infantry x2] + 4 [knights x2] +4 [Tactics: 2 sets of Medieval Army] = 10) ).  Brutus has Conquistadors giving a total strength of 14 ( (3[infantry x2: One is Age I for maximum Tactic effect] + 4 [knights x2] + 5 [Tactics] = 12) ).

The next political phase a Territory appears which both players want to bid on.  In this scenario, Alicia can bid an Infantry and Knight for a combined strength bid of 5.  Alicia's final strength is reduced to 5 if she wins ( (1[infantry x1] + 2 [knights x1] +2 [Tactics: 1 set of Medieval Army] = 5) ).

Brutus' best bid would be 3 (both infantry) or 4 (Age II infantry and a Cavalry).  If using the Age 3 unit, Brutus' strength drops from 14 to 4( (0[infantry] +  4 [knights x2] = 4) ). If using Age 2 Units for a bid of 4, his strength drops to 3 ( (1[infantry:Age A] +  2 [knights x1] = 3) .  In the latter case, Brutus could simply build a Knight to gain partial us of the tactic, but this only yields 8 ( (1[infantry x1: Age A ] + 4 [knights x2] + 3 [Tactics] = 8) ).

The difference seems minor, but to restore their armies to their original strength will require more resources for Brutus than for Alicia.  Alicia's smaller unit requirements on her Tactics card gives her a small advantage in Bidding wars for territory.  Although a single bid doesn't seem to make much difference, two or three territories over the course of two rounds can cripple a player with larger unit requirement tactics as they consistently spend additional resources to restore their military.  This is a topic I hope to return to later as it is a strategy I have used effectively in several games to keep "military suppressed" by simply seeding territory cards when in a weak position.
Tactic Popularity
The final discussion for this article will be the "popularity" of the various tactics.
The results really don't come as much of a surprise.  The earlier Age techs are more popular, with the exception of Heavy Cavalry and Light Cavalry.  Most of this is due to the effects of Age I Events, and the fact Cavalry technologies are not available immediately.  Except for Conquistadors, which is a natural progression from both Medieval Army and Light Cavalry, there is a significant drop in the popularity of the various Tactics.  They still remain popular, but not overwhelmingly so.

I attempted to draw results on the final position of  a player and their chosen tactics, but the results were all the tactics were evenly spread out among the various Tactics.  Out of 100 games (400 players), only 4 chose not to play any Tactics cards.  Although not conclusive, it is interesting to note their final results were also evenly spread out.

In short, it is not "which tactic you choose", but "how you choose to use it" which makes a difference in Through The Ages.

The next article will cover the various forms of Military Aggression and Wars, bringing the Military portion of the blog to a conclusion.

Edit: Corrected the military tree image after Harald Korneliussen recognized I'd left off two arrows.  Good job of keeping me honest, Harald!

Through The Ages-Part XVI - Military: A Numbers Game

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Military Actions and Military Cards
Players have more control over their civil actions than Military cards.  The cards may not appear at opportune times, but through manipulation of the card row, players can choose to pick cards from the card row before other players.  It may cost more civil actions than the player would prefer, but the player has the option to take the card or not.  Military and Event cards differ in that a player's options are limited to what the player draws randomly from the military deck.

A player can pursue a military domination strategy, but there is no guarantee the player will draw the military cards to support the strategy.
Understanding Odds
The possible combination of odds is nearly impossible to figure out in any usable form.  Instead, it is possible to show the different odds of drawing a card(s) under various conditions.  Important to note is that in a 4-player game the deck of event cards will most likely be reshuffled.  In Age I a reshuffle is almost guaranteed.  The turn of the reshuffle will differ depending on the number of military actions the players manage to develop, but it is important to realize any cards which are discarded will become available later in the turn.

A second item to take note of involves when Military cards are viable.  Military cards are not drawn until Turn 2.  Furthermore, any military cards drawn on the last turn of the game (Turn 20 using our example) will not be played, with the possible exception of Defense cards.
The Baseline
The following diagram provides a baseline of drawing a single specific card each turn if no player modifies their original 2 Military actions.  Thus, on the third turn of a game there is only a 4.26% chance of drawing Barbarians by the first player. Using only Age I as our example, we can see a general trend upwards in odds as time goes on.  Overall, this gradually increases for each player, until turn 6 when the odds reach 10%.  After this point, the increase rises dramatically.
We can also see how each player later in the turn has improved odds of drawing the specific copy of the card over the player earlier in the turn order. It doesn't seem greatly significant until turn 7. By turn 8 it is guaranteed that if a card was not drawn, it will be drawn by Player4 as there will be only one card left in the deck to draw. Additionally, in this scenario, Player 4 will reshuffle the discarded cards and draw one of them into their hand.

There are two things which we will deviate for comparison purposes.  First, we will deviate the odds if one player draws an additional military card starting on turn 2.  This is possible with Julius Caesar, a popular leader.  Second we will modify the number of copies of a card available in the deck: such as Medieval Army.
Increasing Military Actions
This next chart involves modifying the military actions of the first player while holding the other three players at 2 actions each, the first player sees a noticeable increase in their odds.
Three things become very clear.  First, the "reshuffle point" moves forward as the number of cards drawn increases.  This impacts decision making only if a player discards a card which they later "want back".
Second, the increase in odds is slightly less than doubled, until the last turn.  From our examination of the baseline, these odds would only be greater for those later in the turn if they increase their military actions. Similarly, the military actions decrease the odds of the other players, but only by a
Increasing Copies of Cards
The second variable to review is the increasing the copies of cards in the Military Deck.  Through the Ages Military cards have four levels of occurrences.  Most cards are singles, like Events and Treaties, with only one copy of the card in the deck.  Aggressions have two to four copies of the cards, based on the Age.  Tactics cards have from 1 to 4 copies, depending on the Age and the card.  Lastly, there are 6 copies of the Defense/Colonization cards in each Age.
From this data, the following graph was formed to represent the odds of drawing at least one (or more) of the cards each turn depending if each player only has 2 Military Actions.
Conclusions

Wars don't appear
until Age II, and even then
they are Rare until Age III

Military cards really are dependent on the "luck of the draw".  Players can still manipulate that luck, to some degree.  First, increasing Military actions greatly improves the odds of drawing a desired military card, although the odds remain relatively low until later turns.  This as the effect of decreasing the time required for a "reshuffle" of the deck.  This may not seem very important, but if a player discards an undesired card early, the card may make a reappearance later in the turn.

Secondly, depending on the number of occurrences of the card, the player's odds increase.  Overall, the increase in occurrences has a greater impact than the increase in Military actions.  Players only have control over their Military Actions.


Although interesting, I'm not sure the information is very useful.  Having more Military Actions provides options, which is one reason Julius Caesar is popular.  But there is little control over what appears and when it will appear.  However, many events depend on Military Strength, so military cannot be ignored.