A Walk in the Dark A look in to the mind of an RPG designer

David and Goliath

On Twitter somebody - I don't remember who - said that if a lone fighter went up against a lone goblin it would be "impossible" for a goblin to survive. But the mathematician in me has a hard time with the word "impossible", so I figured I'd actually do the math and figure out what a goblin's odds are.

DISCLAIMER: I have not checked all the math here, but it seems about right. If you find errors, please let me know.

FIGHT!!!

Contestant 1:
A 1st level fighter, as presented in the DnD Next playtest materials
published on May 24th, 2012.

Contestant 2:
A common goblin, as presented in the same playtest materials
(DnD Next Bestiary, page 12)

Combat rules: Initiative modifiers are equal (+1), so we're disregarding them for sake of argument. Also assuming that neither party has availability to any sort of healing.

Also not counting the fighter's "Slayer" theme. We'll get to that later.

Round one, straight up fight between the two. No advantage or disadvantage:

Fighter: 65% chance (needs 8 or higher) to hit the goblin with his greataxe. Damage is sufficient to be lethal on any hit (average 14 damage).

Goblin: 40% chance (needs 13 or higher) to hit the fighter with his mace, and 45% chance (needs 12 or higher) to hit with his shortbow. Average damage without advantage is 4 (mace) and 5 (shortbow), which means the goblin would have to hit 4-5 times to kill the fighter. That means the goblin has a 1%-3% chance to kill the fighter in five turns. The fighter has a 98% chance to kill the goblin in five rounds or less.

Not impossible... but highly unlikely.

Round two, fighter has disadvantage:

Goblin: Percentages remain unchanged.

Fighter: Chance to hit drops to 42.25% each round. He still has about an 93% chance to hit the goblin in the next five rounds.

Goblin's chances are improving!

Round three, goblin has advantage:

Fighter: Original values remain unchanged.

Goblin: Now has advantage, which means his hit chance increases to 64% (almost identical to the fighter's) and he deals additional damage (dirty tricks trait), increasing his average damage to 7 (mace) and 8 (shortbow). He now has about a 26% chance to drop the fighter in three turns, but the fighter can drop the goblin in three turns or less 95% of the time.

Round four, goblin has advantage and fighter has disadvantage:

Using all the figures above, the goblin can drop the fighter in three rounds 26% of the time. The fighter has an 81% chance to drop the goblin in the same three rounds. Hardly "impossible"!

The Trump: The fighter's "Slayer" theme.

The fighter does have an ace up his sleeve, though: the "Slayer" theme. As documented, the fighter causes a minimum of 3 damage even on a miss, which means that it's impossible for a single goblin to survive beyond two rounds even if the fighter rolls a natural 1 on every attack. During those two rounds a goblin, assuming he hits twice (16% to 40% chance, depending on advantage), he will score on average between 7 and 13 damage (the latter is with advantage). The fighter will live to see another day... or will he?

But wait! Assume the goblin has advantage... If one of those hits is a critical hit, the goblin causes a flat 12 damage. If his second attack hits, if the damage is above average (average is 7) it *is* enough to drop the fighter! That could happen 2% of the time! And if the goblin scores two critical hits (0.25% chance), the fighter would be CRUSHED and dying at -4 HP!

Conclusion: If the goblin is a lucky bastard, he's hardly a pushover. Also keep in mind that it's one goblin, those are fairly decent odds.

But we're not asking the important question... how often do you come across just one goblin?