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Tactical Analysis in
Granada: The Fall of Moslem Spain

A player just starting to learn Granada: The Fall of Moslem Spain might look at the combat system and think, “Oh, just another ‘roll a 10-sided die and kill a unit on a hit mechanism.’” Well, at first blush this seems to be true — but Granada employs several unique features that if not fully understood can seriously hurt a player’s chance to win. This article details the combat system as well as some idiosyncrasies that add great flavor to this game, which covers a little-known but fascinating period in Spanish history.

Once you’ve mastered the combat system, you must now apply the rules to your actual battles. Several questions must be addressed in virtually all battles.

First: To which units do I assign my Leader bonuses, and from which units do I take my losses? A casual player may just assign the bonuses to his stronger units, hoping for a better chance of a hit, and when taking losses he may just start eliminating his weaker units, holding the stronger ones for later battles.

This may seem like a great strategy but in some cases, but sometimes it is completely wrong.


Boabdil Bids Farewell, by Alfred Dehodencq. Boabdil should have done the math.
Applying Leader Bonuses

In most cases, it does not matter where you apply the Leader bonus. However, you would definitely not apply it to a unit whose strength would exceed 7 (such as an unreduced Siege Engine whose strength is already at 7).

But why not make as many units as possible attack at strength 7 to maximize your the chances of hitting your opponent? Before addressing this, we need to talk about “expectation.”

“Expectation” is defined (for our game application) as the amount of hits you would expect to make in one round of combat. A single unit of strength 7 has an expectation of 70%, or 0.7. In ten rounds, he would expect to cause 7 hits. Similarly, a unit of strength 3 has only an expectation of 30%; he can expect to cause 3 hits over ten rounds.

Let’s assume we have a combat force of five 5-strength units and one 1-strength unit. The expectation for an attack from this force (without any modifiers) is (5 * 0.5) + (1 * 0.1) = 2.6. Thus, this force can expect an average of 2.6 hits per each round.

Now let’s assume we have five leader points to assign to this force. In our first case, we will add them to the five 5-strength units, making each of them effectively a 6-strength unit. Our new expectation is 3.1 ([5 * 0.6] + [1 * 0.1]).

If instead we add all five points to the 1-strength unit, we still get the same expectation, 3.1 ([5 *. 0.5] + [6 * 0.1]).

In fact, it doesn’t matter where you add these five points as long as none of them are wasted by adding them to a unit whose strength is already at 7. The leader bonus simply adds a 10% bonus to your expectation for each Leader point you use. Because of the design of the various leaders, the Spanish (assuming they use Ferdinand) will almost always be adding 60% to their expectation when attacking, and 50% when defending. The Moors, assuming they use al-Zagul (and don’t use Boabdil) will be adding 40% to their attack and 50% to their defense. In either case, this translates to about an extra one-half hit per battle.

So it doesn’t really matter where you put those leader points, right? Well, wrong, sort of. You can’t affect the final expectation by reassigning leader points, but you can affect the distribution of how many hits you get.

For example, assume you have 3 units each at 4 strength, and you also have 3 leader points to assign (I’ve picked smaller groups to make the math a bit easier). In Case 1, we will distribute the points such that each unit gets one point. In Case 2 only one unit gets the benefit of all the leader bonuses. Table 1 illustrates the possible results.

Table 1

Case 1
Three units: Each attacks at strength 4.

0 hits
12.5%
1 hit
37.5%
2 hits
37.5%
3 hits
12.5%
Expected number of hits: 1.5
 
Case 2
Three units: One attacks at strength 7, two attack at strength 4.
0 hits
10.8%
1 hit
39.6%
2 hits
38.4%
3 hits
11.2%
Expected number of hits: 1.5

Each case has exactly the same expectation: 1.5 hits. It does not matter where you allocate the Leader Points. But a subtle change has happened in how these hits are distributed. In Case 2 (we concentrated our Leader points in one unit) we have now increased the chance that exactly one unit will be hit at the cost of decreasing the chances of hitting exactly 0, 2, or 3 units.

This shows that you have a better chance of hitting the maximum number of units (in this case, 3) if you spread your Leader points about, but you also increase your chance of killing 0 units. If you concentrate your Leader points on one unit, you increase your chance of hitting exactly one unit but decrease your chances of hitting the maximum number of units.

The difference is small because of the few units involved in the above example, but the trend is important. Generally, I would recommend spreading the Leader points as you give yourself a better chance to kill more units. One exception is if there is only one reduced defender left. Then you are better off assigning the Leader points to one unit to increase your chance of a kill. After all, it doesn’t do any good to get 3 hits if there is only one step left in the defending stack.

In general, assign your Leader Bonus points only to as many units as there are defending units.


Courtyard of Granada. The prize to be won.
Elimination or Reduction

Now that we know how to efficiently assign our Leader bonuses in attacks, how should we allocate losses when attacked? You could easily think that just reducing and then eliminating the weakest units would the best strategy, but again (surprisingly), that is not always the case.

Unit Reduction

Each combat unit shares one interesting feature in common: When reduced, they lose exactly 2 strength points. A Santiago Cavalry when reduced goes from 6 to 4; a lowly Moorish infantry is reduced from 3 to 1.

You would think that by reducing all your weaker units first, you would retain better attacking chances. But this is not the case. Each hit effectively reduces your attack capability by 20%. It doesn’t matter if the hit is against an elite cavalry or a weak infantry; your expectation for the next round will be exactly the same whether you reduce a unit of strength 7 or a unit of strength 3.

Why not then reduce the weakest units first if it doesn’t matter? In most cases that would be the recommendation. But other factors should be considered, such as Unit Reduction, Replacement and Rally.

Who Gets Reduced?

Let’s now assume you have two units defending, a 6-strength cavalry and a reduced 3-strength cavalry. Your opponent rolls one hit; should you reduce your 6-strength unit, or your 3-strength unit?

In this case you should reduce your 6-strength unit as this only lowers your expectation by 20%. If you eliminate the 3-strength, you have lowered your expectation for the next round by 30%.

An unreduced unit that takes a hit will lower your expectation 20%. Therefore you should almost always take reductions instead of eliminations unless the unit to be reduced is 1-strength infantry. A loss of this unit only reduces your expectation by 10%.

Another reason to reduce instead of eliminate units is because it keeps more units on the board, and thus more dice, and thus a chance to kill more units. Even though the expectation might be the same, you can still affect the distribution of results.

For example, assume you have a full 4-strength unit and a reduced 2-strength unit, and must apply one hit. Do you reduce your 4-strength unit or eliminate the 2-strength unit?

In either case, your expectation for the next round will be 40%. However, if you do the rather simple math, you will see that with one 4-strength unit, you have a 40% chance of killing one enemy unit and a 60% chance of missing. However, if you have two 2-strength units, you now have 4% chance of killing two units, a 32% chance of killing exactly one unit, and a 64% chance of missing. So you have increased the chance of missing by a bit, but also given yourself a small chance of killing two units. Table 2 illustrates this a bit more clearly:

Table 2

Chance to kill
  0 units 1 unit 2 units
One 4-strength unit 60% 40% 0%
Two 2-strength units 64% 32% 4%

If there was only one reduced unit attacking you, you might choose to eliminate one unit and keep a non-reduced unit as this now gives you a better chance to kill the one attacking unit; the extra hit would be worthless if attacking only one reduced unit.

In general, you should first reduce and then kill your 3-strength infantry units, but there are two exceptions to this rule. The first is not to eliminate more 3-strength infantry units than you would expect to get back during you Winter Lull.

The second is a rather unusual case where you have an awkward mix of units. Suppose after several combat rounds you are left with 6 Leader Points, 1 full-strength cavalry worth 6, and 1 reduced infantry worth 1. The “rule” tells us to eliminate the 1-strength infantry — but this would then waste 5 of the Leader Points. If instead you reduce the 6-strength cavalry, you can now utilize all five points. You have raised your expectation of hits for the next round from 0.7 to 1.2, which is not insignificant, especially when are you now dealing with few units.

 

The Reinforcement Pool

Another very important part of unit reduction is the composition of your reinforcement pool. If you are the Moorish player and have 8 dead infantry units, and no dead cavalry, you should seriously consider reducing and eliminating a cavalry unit before adding any more infantry to the dead pool. At most, you can only get seven infantry units back through reinforcement, but you are guaranteed to get at least one cavalry unit back. However, the ability to rally troops (return a reduced unit to full strength during the Winter Lull) complicates this issue a bit more.

Is it better to eliminate a unit completely or reduce two units and hope that you can rally (return them to full strength) during the Winter Lull?

The key to this dilemma is the player’s average reinforcements, which can vary hugely as a result of how many castles are controlled (or not controlled). For example, the Spanish infantry reinforcement can average as low as 1.7 to as high as 3.3.

After a significant amount of analysis, I found that a player should strive to keep only a number of units in the dead pool equal to the average he will get back during the Reinforcement phase. This will allow the highest rate of return when combining the Reinforcements with Rallies.

Table 3 should help players decide how many units players would ideally have in their dead pool when Winter rolls around:

Table 3

Average number of reinforcement units based on Die Roll Modifier.

  –2 –1 0 +1 +2 +3
Spanish            
Infantry
2.2 2.5 2.8 3.1 3.3
Artillery
1.0 1.0 1.0 3.0 5.0
Cavalry
1.0 1.0 1.0 3.0 5.0
Naval
1.0 1.0 1.0 3.0 4.0
Alcantara
2.0 2.0 2.0 4.0 5.0
Santiago
3.0 3.0 3.0 5.0 6.0
Calatrava
2.0 2.0 2.0 4.0 5.0
Moors            
Jund Cav.
1.6 1.9 2.3 2.7 3.1
Jund Inf.
2.1 2.4 2.7 3.0 3.3
Vol. Inf.
0.7 0.9 1.2 1.5 1.8
Otto. Inf.
0.3 0.6 1.0 1.4 1.8
Otto. Nav.
0.3 0.6 1.0 1.4 1.8

Summary

Leaders Combat Modifiers: In general, assign your Leader Bonus points only to as many units as there are defending units.

Elimination versus Reduction:
• First, reduce and then eliminate as many 3-strength infantry units as you would expect to receive back during the Winter Lull (see Table 3). Note exceptions discussed above.
• Then reduce all units before eliminating any units.
• After all units have been reduced, start eliminating the weakest units first (again, only to the number you would expect to receive back as reinforcements).
• Finally, start eliminating the weakest units as you take losses.

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