Old Catapult Rules

Newly released Conquest of the Empire by Eagle Games.
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Krieghund
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Post by Krieghund » Sat Sep 22, 2007 10:57 am

I don't think that anyone advocates buying all catapults, to the exclusion of buying other units. Cannon fodder is always necessary, but the fact remains that he who has the most catapults wins.

Let's look at a more realistic example. Player A's army consists of 3 catapults and 6 infantry. Player B's army consists of 18 infantry. Both armies cost 180 talents. In order to win a battle, player B must roll six infantry hits (4 or higher) and three catapult hits (6) before player A rolls eighteen infantry hits (varies with combat advantage). Player B can approach this in one of two ways. He can either go for A's infantry first, then the catapults, or the other way round.

Assuming B goes for the infantry first, it will take him twelve rounds on average to kill off A's infantry. During this time, player A will kill 12 of his infantry, receiving automatic hits (with +3 combat advantage) . On round 13 he starts on the catapults. Player B now has to roll a 6 before player A even has to start rolling for hits, and he only has 6 infantry left. It doesn't look too good for player B. Not only is he going to lose the battle, but he's going to lose his full 140 talent investement, while player A will keep 80 to 120 talents of his.

If player B goes for the catapults first, it will take him six rounds on average to kill the first one. During that time, A will kill 6 of his infantry. But now A's combat advantage is only +2. In the 6 rounds it takes B to kill another catapult, A will kill 5 more infantry (rolling 2 or higher). In the 6 rounds it takes B to kill the last catapult, A will kill 4 more infantry (rolling 3 or higher). Now player A still has 6 infantry, but player B only has 3. This is a closer fight, but the advantage still clearly goes to A.

As you can see, the player with the least catapults is far better off targeting the other player's catapults in an attempt to reduce his combat advantage, for both strategic and economic reasons. However, while he is trying to roll a 6 in order to do so, he will probably still take staggering losses. The larger the armies involved, the more pronounced the advantage of the player with more catapults. This leads to a catapult "arms race", since neither side can afford to let the other gain the advantage.

With two large armies in which one has a number of catapults, both sides are obliged to target each other's catapults increase their own advantage or decrease the enemy's. In a case where one army has a one-catapult advantage, that army has twice as much chance of success as the other army, having to roll a 5 rather than a 6. In addition, the more catapults the army with the advantage hits the greater its advantage becomes. The number it needs to roll to eliminate a catapult becomes smaller with each success, while the other army continues to have to roll a 6.

Once all the catapults are gone, the disadvantaged army will be decimated while trying to roll multiple 6s to even get to the point where the army with the advantage has to roll higher than 2 to hit. By then, it will be severely outnumbered, if it even ever gets to that point.

For example, player A's army has 6 catapults and 25 other units, while player B's army has 5 catapults and 25 other units. Odds are player A is going to roll a 5 or higher before B can roll a 6. Player A now has a +2 advantage and a 50% chance of hitting a catapult. After three more rounds, on average player B will have hit a catapult with a 6, but player A has also hit another one. Now A has five and B has three. On average, this will continue until A has three or four catapults left and B has none. From here on, it will look pretty much like the first example, except B will be at even more of a disadvantage here since the number of non-catapult units in both armies is the same.

Of course, these examples assume average dice rolls. Your mileage may vary, since luck is always a factor. I hope this helps!
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xxstefanx
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Post by xxstefanx » Sat Sep 22, 2007 2:16 pm

Hello Krieghund!

Thx for the answer!
It answers some aspects but the main question still remains (I think!)

Clear is, the player who has the most catapults in his army wins if BOTH players have catapults in their army!

Clear is also that your 18 Inf-player WILL target the enemies catapults first to reduce combat advantage. But to my opinion it is not perfectly clear that the fact that the inf.-player must always roll 6s automatically leads to defeat due to the cannon fodder effect of "4 inf=1 cat".

The inf.-player fairs beter if he manages to roll a hit in one of the first 3 rolls against the army with the catapults which has the following probability:

For k successes in n rolls it is:
P(k I n,p) = (n above k) p'(k) x q'(n-1) ; p=1/6; q=5/6
(don'T know how to note the formula in a better way).

Besides that for k=1,2, 3 in sum it is:
P(k=1,2,3) = P(1) + P(2) + P(3)

p=0,42

If you include n=4 which includes the outcome in which the inf.-player fairs equally compared to the catapult owner the probability for k=1,2,3,4 is:

p=0,52

which is marginally better than the "bad side".

Comments?
Last edited by xxstefanx on Sat Sep 22, 2007 7:01 pm, edited 3 times in total.

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Krieghund
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Post by Krieghund » Sat Sep 22, 2007 6:33 pm

As I said, "luck is always a factor". While the disadvantaged player may roll an early hit, that won't stop him from rolling a late hit in subsequent rounds to make up for it. There are an awful lot of die rolls in a combat like this, which allows plenty of time for the probabilities to move back to the center of the curve. While there will always be exceptions, most of the time things are going to go badly for the player with less catapults.
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"War is much more fun when you're winning!" - General Martok

xxstefanx
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Post by xxstefanx » Sat Sep 22, 2007 6:47 pm

Hello Krieghund!
Plz refer DIRECTLY to my elaboration of probability maths! It was your own example with player A and B so lets go on with it. I already agreed to the situation that the player is on the advantage who has more catapults but the point is that this is not valid if the other player has NONE! (right?)

Comment plz!

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Krieghund
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Post by Krieghund » Sat Sep 22, 2007 8:14 pm

I agree that using your formula yields better results for the non-catapult army in smaller battles. However, I don't believe not buying catapults at all will help you in the long run. That will simply lead to a larger catapult deficit as the game progresses, which will in turn lead to worse results as more and more catapults need to be hit before automatic hits are eliminated. Unless, of course, you buy up all the infantry, leaving the catapult player with no fodder at all!
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"War is much more fun when you're winning!" - General Martok

xxstefanx
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Post by xxstefanx » Sat Sep 22, 2007 8:58 pm

The problem is that there is no fodder aspect in this game in the true sense of words as the rolling player is allowed to determine the target! So even if a player has catapults and Infantry in his army the rolling player will always asign the hit to the catapult no matter if there is 1 or 10 infantry fodder!

It simply does not matter if there is:
Player A: 4 Inf.
Player B: 1 cat.
or
Player A: 6 Inf.
Player B: 2 Inf, 1 cat.

In the end it all boils down to the 4 Inf./1 Cat.-aspect of the combat.

xxstefanx
Posts: 155
Joined: Thu Sep 16, 2004 1:46 am
Location: Hamburg

Post by xxstefanx » Sat Sep 22, 2007 9:41 pm

The interesting question might be to determine the number of catapults from where the "hit always"-combat advantage will take too much of an effect as it is too far to reach the combat reduction if a catapult is hit.

This comes from p=0,48 for the catapult player to fair better if the always hit advantage is still valid which equals 0,58 not to outcome worse.

To my understanding it is out of question - and you already agreed - that the all infantry is better till 3 catapults. 4? Likely! But after that?

Strategically as 5 catapults for example is already 200 talents the interesting gameplay question might be: How early can you start building catapults to reach that "more catapults"-advantage when you are on an (slight) disadvantage in early game combat strenght and numbers to conquer territory?

Tbh, I am not sure!
But I am sure, it is a great game!
:wink:

Nice discussion, Krieghund! :D

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