D&D 5E Rule of Three 4/4

[Iosue]

No, he has 2 guys with 15% success TOTAL (he said that's their actual crit chance, not the crit chance of each attack). It's 5% each attack, and he multiplied 5% x the three attacks (which is not how that actually works by the way).

No, he's got two 7th level fighters with Two-Weapon Fighting + Extra Attack (3 attacks/round) and Level 7 Combat Superiority (crit on 18-20). So each round, both fighters get three chances to crit on an 18-20. That's six total chances to hit a 15% target, or 90% chance of a crit being rolled by one of these guys on any given round.

 

[Echohawk]

No, he's got two 7th level fighters with Two-Weapon Fighting + Extra Attack (3 attacks/round) and Level 7 Combat Superiority (crit on 18-20). So each round, both fighters get three chances to crit on an 18-20. That's six total chances to hit a 15% target, or 90% chance of a crit being rolled by one of these guys on any given round.

Hmmm... if there are six attacks each with a 15% chance of being a critical, then I think the odds are...

Chance of 0/6 criticals: ±37.71%
Chance of 1/6 criticals: ±39.93%
Chance of 2/6 criticals: ±17.62%
Chance of 3/6 criticals: ±4.15%
Chance of 4/6 criticals: ±0.55%
Chance of 5/6 criticals: ±0.04%
Chance of 6/6 criticals: ±0.00%

So the chance of at least one out of six being a critical is just 62%, not 90%. The other 38% of the time there are no criticals.

 

[Mistwell]

No, he's got two 7th level fighters with Two-Weapon Fighting + Extra Attack (3 attacks/round) and Level 7 Combat Superiority (crit on 18-20). So each round, both fighters get three chances to crit on an 18-20. That's six total chances to hit a 15% target, or 90% chance of a crit being rolled by one of these guys on any given round.

Oh, you meant Superior Critical (not Combat Superiority, which is something different). Gotcha. Yeah, two fighters with both that ability and three attacks will do that, but the damage is much lower for some of those. The second attack (dual weapon) has no modifier attached to it, and isn't a big weapon, so we're not talking about much damage for that attack even with a crit.

 

[Nagol]

Hmmm... if there are six attacks each with a 15% chance of being a critical, then I think the odds are...

Chance of 0/6 criticals: ±37.71%
Chance of 1/6 criticals: ±39.93%
Chance of 2/6 criticals: ±17.62%
Chance of 3/6 criticals: ±4.15%
Chance of 4/6 criticals: ±0.55%
Chance of 5/6 criticals: ±0.04%
Chance of 6/6 criticals: ±0.00%

So the chance of at least one out of six being a critical is just 62%, not 90%. The other 38% of the time there are no criticals.

Unless advantage or disadvantage occurs, of course. That would really screw the probabilities...

 

[Iosue]

Hmmm... if there are six attacks each with a 15% chance of being a critical, then I think the odds are...

Chance of 0/6 criticals: ±37.71%
Chance of 1/6 criticals: ±39.93%
Chance of 2/6 criticals: ±17.62%
Chance of 3/6 criticals: ±4.15%
Chance of 4/6 criticals: ±0.55%
Chance of 5/6 criticals: ±0.04%
Chance of 6/6 criticals: ±0.00%

So the chance of at least one out of six being a critical is just 62%, not 90%. The other 38% of the time there are no criticals.

Yup, just double-checked on a probability calculator, and that's what it came up to. My mistake.
Just nearly 2/3 does match ambroseji's feeling of almost every round. And advantage for 1 fighter brings the probability up to 77%. Advantage for both fighters brings the probability up to 86%.

I had the math wrong, but the correct math does seem to support ambroseji's impressions of how two-weapon fighters with crit superiority perform in actual play. It would appear that the crit a hell of a lot.

 

[Iosue]

Oh, you meant Superior Critical (not Combat Superiority, which is something different). Gotcha. Yeah, two fighters with both that ability and three attacks will do that, but the damage is much lower for some of those. The second attack (dual weapon) has no modifier attached to it, and isn't a big weapon, so we're not talking about much damage for that attack even with a crit.

Oops, yeah. Superior Critical. I mousewheeled down to page 27, and then I think it popped back up to page 26 when I released it.

But ambroseji is talking about building guys around two-weapon fighting to take the most advantage of the superior critical. The two-weapon fighting style means they can add their ability modifier to damage. That's pretty nice, I think: you figure by level 7 their STR or DEX is maxed out at 20, so 1d6+5/1d6+5/1d6+5. Minimum 6 damage on one regular hit, maximum 51 damage on three crits with full possible damage. On the flip side, a greatsword swinging fellow would do 2d6+5/2d6+5. Minimum 7 damage on one hit, maximum 46 damage on two crits with full possible damage. Hmmm....that's interestingly balanced. TWF has slightly higher ceiling, but THW makes each hit count for more...

Anyone willing to do the damage per round calculation for these two? It's already past 4 am where I am and I have reached my limit for late-night math.

 

[CM]

So, with commander's strike mentioned, lazy warlord confirmed for 5e?

I'm starting to warm up to this iteration.

 

[Blackwarder]

He's got two guys with three shots at a 15% success rate each. That means 0.15 x 6 = 0.9, or just about every round.

You guys need to learn a bit statistics and probability because you are both wrong...
For example if you have a fighter that Frits on 18, 19, and 20 i.e 15% crit chance and you get 6 attacks in a round the chance get one crit is 40% two crits is 18% three crits is 4% and no crit is 38%.

Warder

edit: echohawk has been more through then me.

 

[Falling Icicle]

This is exactly what I was hoping for. Anyone should be able to do things like push, trip or disarm, but fighters have a big advantage in being able to combine those things with their attacks.

 

[Pseudopsyche]

You guys need to learn a bit statistics and probability because you are both wrong...
For example if you have a fighter that Frits on 18, 19, and 20 i.e 15% crit chance and you get 6 attacks in a round the chance get one crit is 40% two crits is 18% three crits is 4% and no crit is 38%.

You are correct if you are talking about the probability of seeing at least one crit. If you are talking about the expected (mean) number of crits, 6 times 0.15 yields the correct value of 0.9 crits per round, on average. (See also http://en.wikipedia.org/wiki/Expected_value#Linearity)

The 38% of rounds with no crits are offset by the 22% of rounds with multiple crits.