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Subject: Maximize Hits with Flanking rss

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Nick Graan
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EDIT: This was a misinterpretation of the rules. Flanking bonuses are not cumulative.


Basic Strategy: Always make sure buildings with the largest number of units get the largest flanking bonus.

I’ve long been a fan of all the statistical analysis of Heroscape units. The Ares Project is currently lacking those statistics, so I thought I’d start. I’ve only played the basic game so far; feedback on how the advanced game changes this strategy is encouraged.

Here’s a scenario that wasn’t obvious to me at first, but seems fairly elementary. When you’ve got the advantage over your opponent in number of buildings participating in the battle, you get to reorganize your unengaged forces. You have two options here (straight from the rulebook):
1) In Flanking position
2) Unopposed (no Frontline enemy force in the same column)

Defensively, it makes sense to reorganize your most fragile units far away from enemy fire (option #2). What happens, however, when you want to maximize your number of hits? For example, your opponent has a particular nasty enemy, and you don’t want them firing back. Which unit should you pick to be your frontline force, and which should go into flanking position in the same column?

To set up the scenario, let’s say you are playing Terran in the basic game, and your opponent is playing the Kahoum. Your opponent has a single building, the Firestorm, with two armor.
Kahoum Inferno (3 cost, 1 shield, tough, initiative 1)
It’ll take 5 hits to eliminate the units on that building before the respond with their powerful 5 attack against your infantry. (1 hit for the shield, and then 2 hits per armor due to “though”)

In your Battle Line, you have 2 Heavy Barracks Stealth (armor attack value 1), 3 Airport Strike Fighters (armor attack value 2), 1 Heavy Barracks Rocket (armor attack value 3). The percentage chance of scoring a hit is below:

Attack Value Hit Chance (Rounded)
1 17%
2 33%
3 50%
4 67%
5 83%
6+ 83% (a roll of a 6 is always a miss)

Without any flanking bonuses, we can expect 1.83 hits against the Inferno (0.17*2 + 0.33*3 + 0.5*1). Let’s see what happens as we reorganize our buildings.

If we reorganize based off increasing attack strength, we can expect 2.67 hits against the inferno. That’s a 0.83 hit increase over the no flanking expectation. This is because the flanking bonus increases our hit chance by 17% per unit. Our Stealth receives no bonus attack value, our Fighters receive one bonus attack value, and our Rocket receives two bonus attack value. (0.17*2 + 0.5*3 + 0.83*1).

If we inverted the order, and gave our Stealth the two bonus, and Rocket being positioned on the Frontline, the expected hits jumps to 3 (0.5*6), but it’s not immediately obvious why it went up by 0.33 hits.

To maximize hits, the buildings should be assigned based on number of units on the building. Since there’s only 1 Rocket, place it on the Frontline. The two Stealth should go next (they receive one bonus attack value). Finally, the three Fighters go last (they receive two bonus attack value). We end up with an expected number of hits of 3.17. (0.33*2 + 0.67*3 + 0.5*1).

Exceptions to the rule:
It doesn’t make sense to push a unit beyond attack value “5” in this example. Even if there are four units on a building, you no longer receive any bonus in expected hits beyond the 5, instead, you should give the bonus to the building with the second most units.
*I’m curious as to how combinations of Flanking and Position Modifiers work into a strategy. There are strategic reasons for Flanking to get an attack bonus greater than the Position Modifier penalty.
*It may make sense to go beyond a value “5” if you think the Frontline unit will be eliminated prior to your attack. If that were to happen, the Flanking bonus changes mid round.

An attack value “0” unit follows slightly more complicated rules. The first Flanking bonus adds one or two dice to the pool depending on how many units are on the building. This means you only get a 0.17 – 0.33 expected hit value increase. Instead of simply counting the number of units on the card, you have to first divide the number of units by 2 (round up). The 2nd or 3rd Flanking bonus is treated like normal, so it may still make sense to have a “0” attack building with 4 units receive more Flanking that a bunch of 2 unit and 3 unit buildings. If you pretend your “0” attack buildings have ½ a unit less, you’ll do ok without having to worry about the math (treat a 4 unit building as having 3.5 units; a 3 unit building as having 2.5 units, etc).
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Lee Fisher
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Nice write up.

However I didn't quite follow what is the "two bonus attack value" you are referring to?
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Edward Longbottom
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I believe that each force that is flanking only gets +1, it is not cumulative. Everywhere in the rules it only specifies that "they each gain the +1 modifier" and from the blue box on p9 "+1 if in flanking position".
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Clinton Paris
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MadWookiee wrote:

Attack Value Hit Chance (Rounded)
1 17%
2 33%
3 50%
4 67%
5 83%
6 Automatic Miss

Just to clarify, bumping up a unit's attack value to 6 doesn't cause them to automatically miss, rather they are statistically the same as if they had an attack value of 5 in that they only miss when a 6 is rolled.

meeple

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Nick Graan
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gumstabber wrote:
I believe that each force that is flanking only gets +1, it is not cumulative. Everywhere in the rules it only specifies that "they each gain the +1 modifier" and from the blue box on p9 "+1 if in flanking position".


I think you're correct. I guess this is a strategy article for a rule that doesn't exist.
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