Hey, I was messing around and trying to calculate how GWF effects the expected damage output of a weapon.
So far, after a bit of testing, my method is to take the expected damage of a normal roll / % chance of rolling a 1-2 plus the expected damage of a weapon without adding 1-2.
So for example I calculated a 1d12 as (3 through 12 / 12) + (6.5 / 6) which came out to an expected damage of 7.33
Does this method make sense? Is there anything I am not considering?
I don't quite understand your text explanation but the numbers are correct. You basically want to take the average of all the numbers on the die, but replace 1 and 2 with the average of the dice roll. For a d12, that'd be (6.5 + 6.5 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12)/12 = 7.33, which can be rearranged into the same formula you used.
The other way to look at it (which just takes a little longer to figure out) would be that you have 34 possible outcomes (roll a 1 followed by 1-12 and roll a 2 followed by 1-12 for a total of 24 outcomes and then 3-12 for the other 10). This leaves a 2/34 chance for a 1-2 and a 3/34 chance for 3-12). Add the damage values for each category and multiply by the chance for each category and that should give you the right answer. Incidentally, I'm getting about 6.79. Considering your method is averaging average numbers, being off a half a point isn't bad.
The other way to look at it (which just takes a little longer to figure out) would be that you have 34 possible outcomes (roll a 1 followed by 1-12 and roll a 2 followed by 1-12 for a total of 24 outcomes and then 3-12 for the other 10). This leaves a 2/34 chance for a 1-2 and a 3/34 chance for 3-12). Add the damage values for each category and multiply by the chance for each category and that should give you the right answer. Incidentally, I'm getting about 6.79. Considering your method is averaging average numbers, being off a half a point isn't bad.
I know that's a method is an option, but I figured creating a tree diagram for all the options would be an absolute pain
I don't quite understand your text explanation but the numbers are correct. You basically want to take the average of all the numbers on the die, but replace 1 and 2 with the average of the dice roll. For a d12, that'd be (6.5 + 6.5 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12)/12 = 7.33, which can be rearranged into the same formula you used.
That seems slightly faster than how I had thought through it
In my written explanation I had calculated the value of landing on any number other than 1 or 2 separately from the expected value of landing on a 1 or 2 (and then dividing that by the % chance of getting it).
It's actually pretty easy, 3x dice size minus 2 gives you the sample size for all of the 1dx dice. (1+2)*(2/sample size) + (3+4+...)*(sample size minus 4/dice size minus 2). For the 2dx, just multiply the 1dx by 2. I think. I'll have to work through it in the morning and see if it holds true.
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Hey, I was messing around and trying to calculate how GWF effects the expected damage output of a weapon.
So far, after a bit of testing, my method is to take the expected damage of a normal roll / % chance of rolling a 1-2 plus the expected damage of a weapon without adding 1-2.
So for example I calculated a 1d12 as (3 through 12 / 12) + (6.5 / 6) which came out to an expected damage of 7.33
Does this method make sense? Is there anything I am not considering?
I don't quite understand your text explanation but the numbers are correct. You basically want to take the average of all the numbers on the die, but replace 1 and 2 with the average of the dice roll. For a d12, that'd be (6.5 + 6.5 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12)/12 = 7.33, which can be rearranged into the same formula you used.
This link has a method of doing this in AnyDice.
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The other way to look at it (which just takes a little longer to figure out) would be that you have 34 possible outcomes (roll a 1 followed by 1-12 and roll a 2 followed by 1-12 for a total of 24 outcomes and then 3-12 for the other 10). This leaves a 2/34 chance for a 1-2 and a 3/34 chance for 3-12). Add the damage values for each category and multiply by the chance for each category and that should give you the right answer. Incidentally, I'm getting about 6.79. Considering your method is averaging average numbers, being off a half a point isn't bad.
I know that's a method is an option, but I figured creating a tree diagram for all the options would be an absolute pain
That seems slightly faster than how I had thought through it
In my written explanation I had calculated the value of landing on any number other than 1 or 2 separately from the expected value of landing on a 1 or 2 (and then dividing that by the % chance of getting it).
It's actually pretty easy, 3x dice size minus 2 gives you the sample size for all of the 1dx dice. (1+2)*(2/sample size) + (3+4+...)*(sample size minus 4/dice size minus 2). For the 2dx, just multiply the 1dx by 2. I think. I'll have to work through it in the morning and see if it holds true.