Ultramarine suddenly comes face to face with N PL 5 goons who are armed with shotguns.

The relevant portion of Ultramarine’s statline: Dodge 10, Toughness 10, +10 to-hit, Damage 10.

The goon statline: Dodge 5, Toughness 5, +5 to-hit, Damage 5.

Ultramarine’s tactics are to fire as a routine check every turn, increasing her Power Attack by one each time until she misses, then use the highest value she hit with for the rest of the fight. The goons just shoot.

Assumptions: No relevant terrain, Ultramarine’s turn is after half (round down) the goons and before the rest. Ultramarine does not kite. Nobody uses Extra Effort. Goons do not provide cover.

(In a more detailed analysis, Takedown-Ultramarine's ability to deal with large goon-groups is ENTIRELY dependent on her initiative roll.)

The question: For what value of N is Ultramarine roughly 50% likely to win?

Ultramarine’s goon-busting: 100% chance to hit, even at full Power Attack. 95% chance to incapacitate a goon on turn 1, 100% thereafter. One attack per turn. So, effectively N turns until victory.

Question therefore becomes how many attacks Ultramarine can take.

The goon’s Ultramarine-busting: 30% chance to hit. One attack per remaining goon per turn. Since N goons means N turns for Ultramarine, (N*(N-1)/2+Floor(N/2)) attacks. So 0.3*(N*(N-1)/2+Floor(N/2)) hits.

Question therefore becomes how many hits Ultramarine can take.

I ran a simulation a hundred-thousand times, and the median number of Damage 5 hits required to incapacitate Ultramarine was 17.

The smallest integer for which 0.3*(N*(N-1)/2+Floor(N/2)) is greater than or equal to 17 is 11.

So Ultramarine has a >50% chance of beating 10 or fewer goons, and a <50% chance of beating 11 or more goons. So Ultramarine is a roughly even match for 10-11 goons.

But wait, what if Ultramarine had Takedown 2?

In that case, Ultramarine can expect to defeat 20 goons on the first turn, and the rest on the second.

So the goons will get Floor(N/2)+(N-20) attacks. The smallest integer for which 0.3*(Floor(N/2)+(N-20)) is greater than or equal to 17 is 52.

So a Ultramarine with Takedown 2 has a >50% chance of beating 51 or fewer goons, and a <50% chance of beating 52 or more goons. So Ultramarine with Takedown 2 is a roughly even match for 51-52 goons.

That’s a two power-point difference, but about five times as many goons. A 2 PP difference is as good has having four allies. This indicates a major systemic issue, which echoes my in-game experiences. A hero with Takedown 2 is capable of comparatively insane minion-fighting stunts. This would be fine if everyone, or noone, had Takedown 2. But is that usually the case? Not in my experience.

How have the GMs and players here dealt with this?

The relevant portion of Ultramarine’s statline: Dodge 10, Toughness 10, +10 to-hit, Damage 10.

The goon statline: Dodge 5, Toughness 5, +5 to-hit, Damage 5.

Ultramarine’s tactics are to fire as a routine check every turn, increasing her Power Attack by one each time until she misses, then use the highest value she hit with for the rest of the fight. The goons just shoot.

Assumptions: No relevant terrain, Ultramarine’s turn is after half (round down) the goons and before the rest. Ultramarine does not kite. Nobody uses Extra Effort. Goons do not provide cover.

(In a more detailed analysis, Takedown-Ultramarine's ability to deal with large goon-groups is ENTIRELY dependent on her initiative roll.)

The question: For what value of N is Ultramarine roughly 50% likely to win?

Ultramarine’s goon-busting: 100% chance to hit, even at full Power Attack. 95% chance to incapacitate a goon on turn 1, 100% thereafter. One attack per turn. So, effectively N turns until victory.

Question therefore becomes how many attacks Ultramarine can take.

The goon’s Ultramarine-busting: 30% chance to hit. One attack per remaining goon per turn. Since N goons means N turns for Ultramarine, (N*(N-1)/2+Floor(N/2)) attacks. So 0.3*(N*(N-1)/2+Floor(N/2)) hits.

Question therefore becomes how many hits Ultramarine can take.

I ran a simulation a hundred-thousand times, and the median number of Damage 5 hits required to incapacitate Ultramarine was 17.

The smallest integer for which 0.3*(N*(N-1)/2+Floor(N/2)) is greater than or equal to 17 is 11.

So Ultramarine has a >50% chance of beating 10 or fewer goons, and a <50% chance of beating 11 or more goons. So Ultramarine is a roughly even match for 10-11 goons.

But wait, what if Ultramarine had Takedown 2?

In that case, Ultramarine can expect to defeat 20 goons on the first turn, and the rest on the second.

So the goons will get Floor(N/2)+(N-20) attacks. The smallest integer for which 0.3*(Floor(N/2)+(N-20)) is greater than or equal to 17 is 52.

So a Ultramarine with Takedown 2 has a >50% chance of beating 51 or fewer goons, and a <50% chance of beating 52 or more goons. So Ultramarine with Takedown 2 is a roughly even match for 51-52 goons.

That’s a two power-point difference, but about five times as many goons. A 2 PP difference is as good has having four allies. This indicates a major systemic issue, which echoes my in-game experiences. A hero with Takedown 2 is capable of comparatively insane minion-fighting stunts. This would be fine if everyone, or noone, had Takedown 2. But is that usually the case? Not in my experience.

How have the GMs and players here dealt with this?

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