[RPG] How does the Overkill weapon tag interact with critical hits

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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?

Best Answer

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.

  1. 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:

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

  1. 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:

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

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.

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