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3 added 33 characters in body
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There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

  • In the same way that the chances of hitting all 3 are increased. As, so are the chances of missing all 3.
  • Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit. And, though the reduced damage per hit halves the impact of getting a critical hit.
  • Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not always better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit 

$$ \begin{align} 20 \cdot 3 \cdot 0.5 = 30 &\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.5 = 30 \\[5pt] 20 \cdot 3 \cdot 0.15 = 9&\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.15 = 9 \end{align} $$ The damage per round is exactly the same for the same AC (chance to hit)

There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

  • In the same way that the chances of hitting all 3 are increased. As are the chances of missing all 3.
  • Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit. And halves the impact of getting a critical hit.
  • Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit

$$ \begin{align} 20 \cdot 3 \cdot 0.5 = 30 &\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.5 = 30 \\[5pt] 20 \cdot 3 \cdot 0.15 = 9&\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.15 = 9 \end{align} $$ The damage per round is exactly the same for the same AC (chance to hit)

There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

  • In the same way that the chances of hitting all 3 are increased, so are the chances of missing all 3.
  • Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit, though the reduced damage per hit halves the impact of getting a critical hit.
  • Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not always better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit 

$$ \begin{align} 20 \cdot 3 \cdot 0.5 = 30 &\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.5 = 30 \\[5pt] 20 \cdot 3 \cdot 0.15 = 9&\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.15 = 9 \end{align} $$ The damage per round is the same for the same AC (chance to hit)

2 mathjax for calculations
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There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

  • In the same way that the chances of hitting all 3 are increased. As are the chances of missing all 3.
  • Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit. And halves the impact of getting a critical hit.
  • Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit
20 x 3 x 0.5 = 30 vs. 10 x 6 x 0.5 = 30
20 x 3 x 0.15 = 9 vs. 10 x 6 x 0.15 = 9

$$ \begin{align} 20 \cdot 3 \cdot 0.5 = 30 &\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.5 = 30 \\[5pt] 20 \cdot 3 \cdot 0.15 = 9&\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.15 = 9 \end{align} $$ The damage per round is exactly the same for the same AC (chance to hit)

There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

  • In the same way that the chances of hitting all 3 are increased. As are the chances of missing all 3.
  • Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit. And halves the impact of getting a critical hit.
  • Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit
20 x 3 x 0.5 = 30 vs. 10 x 6 x 0.5 = 30
20 x 3 x 0.15 = 9 vs. 10 x 6 x 0.15 = 9
The damage per round is exactly the same for the same AC (chance to hit)

There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

  • In the same way that the chances of hitting all 3 are increased. As are the chances of missing all 3.
  • Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit. And halves the impact of getting a critical hit.
  • Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit

$$ \begin{align} 20 \cdot 3 \cdot 0.5 = 30 &\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.5 = 30 \\[5pt] 20 \cdot 3 \cdot 0.15 = 9&\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.15 = 9 \end{align} $$ The damage per round is exactly the same for the same AC (chance to hit)

1
source | link

There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

  • In the same way that the chances of hitting all 3 are increased. As are the chances of missing all 3.
  • Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit. And halves the impact of getting a critical hit.
  • Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit
20 x 3 x 0.5 = 30 vs. 10 x 6 x 0.5 = 30
20 x 3 x 0.15 = 9 vs. 10 x 6 x 0.15 = 9
The damage per round is exactly the same for the same AC (chance to hit)