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Old 01-23-2024, 05:20 PM   #1
HeatDeath
 
Join Date: May 2012
Default Digging infantry out of towns: a worked overrun example

Can someone check my math on this?

A town hex contains a 3-strength platoon of infantry. They get triple defense in a town, so their effective stats are A3, R1, D9, M2.

A heavy tank rolls up to range two from the town. His attack is 4. 4 attacking 9 is less than 1:2, so he cannot even damage the infantry from afar.

He has to get the infantry out of that town, or die trying. [His commissar is very insistent on that point.] If he rolls into the town, and the town is intact when he does this, the infantry will get tripled defense. So he rolls into the town and initiates an overrun,

The infantry splits into 3 1-squad pieces. They get doubled attack strength, because they’re in an overrun. They still get tripled defense, but their defense goes down to 1 each because they’re split up. So we now have three infantry squad units, each of which has the following effective stats: A2 D3. [Range and movement are irrelevant, because this is an overrun.]

The tank does not get additional defense from the town, so his effective stats are still A4 D3.

Note also that D results count as Xs.

So the infantry get the first fire round. At first glance, they can do this one of three ways.

First, each squad can attack individually. Attacking with A2 against D3 is 1:2. The first squad gets a 33% odds of destroying the tank. If they fail at this, the second squad will get another, independent, 33% chance. Then the third. The odds of the tank surviving this is ⅔ * ⅔ * ⅔ = 29.6%, so the infantry has 70.4% odds of destroying the tank.

Second, two squads can combine fire, with the remaining squad there to try again if the first attack fails. Attacking with A4 against D3 (1:1) with D’s counting as X’s, the first attack has 66% to destroy the tank. If the tank survives, the second attack, A2 against D3, is a 1:2 attack, as above, with 33% odds of destroying the tank. Taken together, the tank has 22% odds of being surviving, or 77.77% odds of being destroyed.

Third, all three squads can combine fire. This is mathematically the simplest case, and by far the best. A6 attacking D3 is a 2:1 attack. With Ds counting as Xs, they have 83% odds of destroying the tank.

If the tank survives this attack. It gets to attack one of the infantry squads at 4:3 -> 1:1. 66% odds of destroying one squad.

Assuming it destroys the squad, The remaining two squads get to counter attack. Per the calculations above, their only real option is to combine fire, and that gives them a 66% chance of destroying the tank.

If they fail at those odds, the tank gets another fire round, where it has 66% odds of destroying another squad. If it succeeds at this, The remaining infantry squad can attack the tank at 1:2 odds, with 33% odds of destroying the tank. The two sides will continue exchanging fire at these rates, the tank destroying the last squad at odds of 66%, and the squad destroying the tank at 33% odds. The remaining infantry can still technically win, but is at a significant disadvantage.

All of this sounds like a bad plan for the tank. His odds of survival are well under 22%. Let's consider the case where he rubbles the town. Rubbling the town will require sustained attacks at D4, which is to say 1:1. Damaging the town won’t change anything, but an X result (or a D result if the town is already damaged) will rubble it. The infantry will survive this process, since they only take spillover fire with a defense of 9.

Once the town is rubbled, the infantry will still have doubled defense. The tank should not enter the town - he will have no defensive bonus. Moreover, he may very well get permanently stuck. However, the effective defense of the infantry is now only 6. Attacks at 4:6 reduce to 1:2. The tank can now bombard the infantry with 1:2 attack from beyond the infantry’s range. This will take a while to destroy them, but the end is inevitable, unless the infantry leave the town to engage the tank directly, or can evacuate in such a way that the tank cannot catch up to them and re-engage in open countryside (i.e. if the town is a chokepoint and any pursuit must pass through the rubble hex).

Concluding, an infantry platoon’s defense is sufficiently enhanced by a town that heavy tank is significantly incentivized to wreck the town rather than rolling in after them. It is also worth noting that a heavy tank can rubble 1500m x 1500m of town in four minutes of bombardment, one third of the time. This places a very high lower bound on the yield of a heavy tank’s munitions and/or its volume of fire.

Last edited by HeatDeath; 01-24-2024 at 10:30 AM.
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