There is a small but important number of situations where you want to attack for one round and then withdraw.
The goal is to inflict more damage to your opponent then they inflict on you.
Typically a defender will cause 33%-50% damage (with 33%- 40% being most likely, as infantry and artillery are likely to make up most of the defense force).
As an attacker, you want to cause as much damage as possible, while limiting your probability of taking a country (to 1 in 10, or even 1 in 20 if your stack would be really messed up in a counter-strike if it won the battle). You most likely don’t want to take a country because you cannot hold it, because it would be a move closer to the enemy and they would be able to hit you with more units, and/or if you are able to substantially reinforce the place that you’d retreat to.
So an attacker must balance out the desire to destroy all of the attacker units but one, with the desire to make sure you don’t destroy all the units.
Your best odds of doing this is when you have 10 or more units in the battle (this is a rough figure). As the number of units in the battle increases, the outcome is more predictable (see law of large numbers - statistics).
For instance, I recently attacked French Indo China. The defender had 8 infantry. But they had a massive stack of units on China, so I didn’t want to win because the China stack would crush me. So I attacked the defender with the goal of eliminating 5 units (used a mixture of tanks, and enough infantry to take the expected casualties). The defender would hit 2 2/3 units, so I was hoping to come out 2 1/3 units ahead.
(The fact that the battle was a glorious victory/fluke and I killed 7 of their 8 units, and the defender missed completely is besides the point).
The probability of me completely destroying them was around 8%, so I was taking a greater chance than I should have. Instead I should have downgraded my attack to around 4.5 units of damage.
However, where this strategy becomes even more useful is with greater numbers of units. If you had twice as many units, you could increase your margin of destruction without a serious risk of destroying all the units. For instance, 20 attacking tanks vs 16 defending infantry have less than 1% of destroying them all. 60 attacking infantry vs 16 defending infantry will have only a 3.2% chance of destroying them. Thus with twice the units, the probability of failure decreases by a factor of three or more (depends where you are on the curve). And in that case you can increase the number of attacking units, and increase the ratio of defenders killed per attacker killed.
Note: the more low-power units you use, the greater your chance is of totally eliminating the enemy. For instance in the first round of combat 10 attacking tanks are three times less likely to eliminate 8 infantry (4%), than 30 attacking infantry are (12%). Has to do with a skewed standard deviation curve =)
Ultimately if you are attacking with an infinite number of units (or a very very large one) you can destroy 80-95% of the defense force, whereas they’d only get 33-40% of you - with little to no risk of taking a country.
If anyone plays Civilization 4, there is a similar situation with stacks. You ideally want to fight a one-front war and have all your units in a killer stack. Dividing the stack into two equally-sized adjacent stacks is generally a terrible strategy. Don’t advance unless your stack is big enough to defend itself, or you are prepared to wipe out any attacking force on your next round (because you have a larger stack right behind it - this is more likely to occur in axis and allies where there are greater movement/supply line issues than civilization 4).
Any Comments?
