How does the Overkill weapon tag interact with critical hits?

Question

The Overkill weapon tag is defined on page 105 of the Lancer Core Book First Edition PDF as follows:

OVERKILL: When rolling for damage with this weapon, any damage dice that land on a 1 cause the attacker to take 1 [Heat], and are then rerolled. Additional 1s continue to trigger this effect.

The rules on critical hits (p. 64) state:

A 20+ on a melee or ranged attack causes a critical hit. On a critical hit, all damage dice are rolled twice (including bonus damage) and the highest result from each source of damage is used. For example, if a player got a critical hit on an attack that would normally deal 2d6 damage, they would instead roll 4d6 and pick the two highest results.

How does the Overkill weapon tag interact with critical hits?

Does a roll of 1 on any of the weapon's doubled damage dice (from the crit) result in the Overkill tag activating, causing the mech to take 1 heat before the die is rerolled? Or are the "two highest results" chosen for the crit before the Overkill tag is considered/activated?

For instance, license rank 2 of the SSC Death's Head unlocks not only the Death's Head mech frame but also the Vulture DMR main rifle weapon, which does 1d6+1 kinetic damage and has the Overkill tag (among others). If a pilot using the Vulture DMR gets a crit, in what order are the above events resolved?

Answer 1

Others have also thought about this very thing, and the rule-text underwent a revision clarifying that all damage dice are to be rerolled

Here is a link to a discussion about this very thing, and below is an excerpt from it:

Overkill was changed to affect all damage dice rolled as of November release, thus making Critical Hits with Overkill hilarious [...]

Without such clarification, the two possible scenarios would be very different

1. Unused damage dice do not trigger OVERKILL

In this scenario you would roll 4d6, and choose the two highest, completely ignoring the other two dice. This is somewhat supported as the Critical Hits section says

[...] On a critical hit, all damage dice are rolled twice (including bonus damage) and the highest result from each source of damage is used [...]

Though this does not actually say that the two lower dice cannot be used at all it does say that the two higher dice are used. It may very well be the case that this means they are the only dice used for anything but it may be that they are the only dice used for damage.

2. Unused damage dice do trigger OVERKILL

In this scenario you would roll 4d6, and reroll any and all 1's until all four dice read 2-6 (triggering OVERKILL some number of times). Then you would use the two highest dice for your damage roll. This is somewhat supported because OVERKILL occurs "When rolling for damage" and a critical hit's extra dice can certainly be seen as part of the process of "rolling for damage".

The expected amount of gained heat is very different in these scenarios

1. In this scenario you would only trigger OVERKILL if 3 or 4 of the dice rolled a 1. Thus 20/1296 crits would add 1 heat and 1/1296 crits would add 2 heat (plus the odds of even further heat being added by OVERKILL). The average heat gained when rolling only 1d6 is .2 and using this we can see that the expected heat gain is the following:

$$.2\left(\frac{20}{1296}\right) + .2\times 2\left(\frac{1}{1296}\right) = .00339506172$$

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2. In this scenario you would trigger OVERKILL if any of the dice rolled a 1. There are only 625 rolls which will cause no OVERKILL. This is shown in the following calculation, multiplying the odds of rolling no 1's with the total possible number of rolls:

$$\left(\frac{5}{6}\right)^4\times 6^{4} = 625$$

Similarly there are five-hundred cases where exactly one 1 is rolled, one-hundred-fifty in which 2 are rolled, twenty in which 3 are rolled, and one in which 4 are rolled. Just to check, these numbers do add correctly, 625 + 500 + 150 + 20 + 1 = 1296 = 6⁴

This allows us to calculate the expected heat gain as follows:

$$.2\left(\frac{500}{1296}\right) + .2\times 2\left(\frac{150}{1296}\right) + .2\times 3\left(\frac{20}{1296}\right) + .2\times 4\left(\frac{1}{1296}\right) = .1\overline{333}$$

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The second scenario has you gaining 39.27 times more heat than the first scenario.

The expected damage is also different

As pointed out by user nick012000 in a comment, the expected damage will not be the same.

In the first scenario you are selecting the two highest dice; however, if either of those are a 1, then you reroll them until they are no longer a one. This gives an average damage of 9.4

In the second scenario, since all 1s are being rerolled, you're effectively rolling dice with sides 2-6 and then selecting the two highest. This gives an average damage of 9.93

You can compare these damage calculations in this AnyDice program made by user Carcer. The difference in damage is 0.53 - nothing major, but certainly not nothing either.

Answer 2

Rolls of 1 on all damage dice you roll are considered for Overkill, before the highest are kept

This is actually an intentional change from the prerelease version of the rules, which becomes more obvious if you compare the wording of the two.

The description of the Overkill tag in Prerelease Beta v2 (aka PR2) of the core rulebook reads (p. 131; emphasis mine):

When attacking with this weapon, if any of the final damage dice come up as ‘1’, take 1 heat, pick them up, and re-roll them. This process can repeat if you keep rolling ‘1’s.

However, this was changed in the official release of the core book to read as quoted in the question (p. 105; emphasis mine):

When rolling for damage with this weapon, any damage dice that land on a 1 cause the attacker to take 1 [Heat], and are then rerolled. Additional 1s continue to trigger this effect.

This is a clear change that affects how the Overkill tag is resolved; it refers to not only "final" damage dice, but "any" damage dice that show that result. This seems to indicate that all damage dice you roll are checked for 1s (triggering the Overkill weapon tag's effect and resolving it) before keeping only the highest results of the final dice rolls.

This especially matters for the IPS-N Vlad's Combat Drill

As noted in this issue report for PR2 about Overkill's interaction with critical hits and the discussion below it, this change does actually matter quite a bit for at least one weapon: the IPS-N Vlad's Combat Drill (p. 155), unlocked at license rank III of the Vlad.

The Combat Drill is a Superheavy Melee weapon with the Overkill tag that does 3d6 kinetic + 1d6 energy damage normally, and has this additional effect:

When attacking a character that is PRONE, IMMOBILIZED, or STUNNED, this weapon’s OVERKILL tag does an extra +1d6 bonus damage each time it activates. This can activate indefinitely if the new bonus die result is a 1, triggering OVERKILL again.

The apparent intent of Overkill is to effectively institute a minimum damage total (since you can't end up with any 1s), at the cost of taking heat. The Combat Drill adds an extra damage die on top of that, when the Overkill tag activates in the specified circumstances.

However, the PR2 version of the Overkill tag actually resulted on doing less damage on a crit than on a regular hit, according to an analysis by the user liq3, initially referenced by the poster of that issue report and then shared by liq3 themselves:

Someone else also noted that due to the way Overkill interacts with critical hits, it is harder for the Combat Drill to activate it's overpenetration on a critical hit, which seems counterintuitive. Whether this is a big enough deal to warrant a rules change is a developer decision.

I'm the one who ran numbers for it. The results always came out to something like this. The damage and heat are average, 1,000,000 damage rolls for each one.

Non-final Dice Crit - Damage: 29.174002 Heat:2.000419
Non-crit roll Damage: 19.99817 Heat:0.998748
Final dice crit Damage: 19.267168 Heat:0.007653

So, ironically, if you only explode the top 4 dice out of 8, it does less damage than a normal roll of 4 dice with exploding. Here's the python code I used to calculate that if anyone wants to check it. https://pastebin.com/he3j17pA

In essence, before accounting for Overkill, you'd roll 4d6 on a regular hit with this weapon, or 8d6 (keep highest 4) on a crit. Each time Overkill activates against a Prone, Immobilized, or Stunned target, you also add 1d6 bonus damage (in addition to adding 1 Heat and rerolling the damage die).

As can be seen from the analysis above, taking only the highest damage dice results first and then checking for results of 1 would cause Overkill to activate less often than checking for results of 1 and resolving Overkill first before keeping only the highest dice. As a result, in PR2, crits with the Combat Drill did less damage on average against qualifying targets than even regular hits, because the bonus damage had much less chance to apply.

The more damage dice you roll, the less likely there is to be a result of 1 in the damage dice kept on a crit. This effect is less noticeable for a weapon like the SSC Death's Head's Vulture DMR (which only does one die of damage and has no additional effect on Overkill), as seen in Medix2's answer - but it's very noticeable for a weapon like the IPS-N Vlad's Combat Drill. This may have partly motivated the change to Overkill between PR2 and the final release.