On the Dodge Action

[Ovinomancer]

Roll 2d20 take highest causes you to have a 1/400 chance of rolling a 1.

Yes, but that wasn't the question.

 

[Ovinomancer]

That can’t be right (or I’m missing sometimes again) as that would give you 20 * 9.75% = 195% chance of getting a result.

The odds of rolling number N aren't balanced by rolling the other numbers, but by not rolling N. The specific question is about rolling N, not rolling all N. So, yes, you've missed something. The probability function isn't created by summing those odds for all possibile N, because it only exists for a specific value of N. It's formed of the odds of rolling N and rolling not N. You don't add the probabilities of Nsub1 and N sub2 because the odds of rolling Nsub1 negate the chance to roll Nsub2.

 

[FrogReaver]

The odds of rolling number N aren't balanced by rolling the other numbers, but by not rolling N. The specific question is about rolling N, not rolling all N. So, yes, you've missed something. The probability function isn't created by summing those odds for all possibile N, because it only exists for a specific value of N. It's formed of the odds of rolling N and rolling not N. You don't add the probabilities of Nsub1 and N sub2 because the odds of rolling Nsub1 negate the chance to roll Nsub2.

You are confused

 

[FrogReaver]

Yes, but that wasn't the question.

Is 1 a number that can be rolled?

Is advantage roll 2d20 take highest?

If so then the counterexample I provided shows the probability of rolling any umber is not 9.75%

 

[TallIan]

The odds of rolling number N aren't balanced by rolling the other numbers, but by not rolling N. The specific question is about rolling N, not rolling all N. So, yes, you've missed something. The probability function isn't created by summing those odds for all possibile N, because it only exists for a specific value of N. It's formed of the odds of rolling N and rolling not N. You don't add the probabilities of Nsub1 and N sub2 because the odds of rolling Nsub1 negate the chance to roll Nsub2.

That's still left me confused. I thought the sum of all possible outcomes had to equal 100%?

Even putting aside stat's for a minute, it doesn't make sense that all the probabilities increase. With a single die, the chance of any number is the same as any other number (you're just as likely to roll a 1 as you are a 20). Advantage is a mechanism to skew the distribution in favour of higher numbers. So the increased chance of rolling a 20 must come from a decreased chance of rolling a different number (or numbers).

With advantage getting a 1 as your final result only happens when both dice roll 1s (a 1 in 400 chance) you can roll a 20 if either dice rolls a 20 (slightly less than a 1 in 10 chance).

 

[TallIan]

Just for interest sake ... here is the math for advantage and disadvantage as a function of the number you need to roll to hit.

[snip]

The base probability to get a 10 or greater result without advantage or disadvantage is 55%

Thus in this case, disadvantage reduces the to hit by about 25% while advantage increases it by about 25%.

THIS is why passive skills are modified by +/-5 for advantage and disadvantage since for the average case advantage/disadvantage incur a +/-25% success probability change which is roughly equivalent to a static +/-5.

(so can folks stop talking about +/-3?)

[snip]

At the very extreme of the target numbers ... like needing a natural 20 to hit ... the effect is closer to that of a +1. However, the extremes do not come up as often as the middle of the distribution ... the game is balanced around typical target numbers in a standard encounter around 11. AC16 with +5 to hit at level 3 or maybe a typical AC20 with +9 to hit at level 11 ... sometimes the AC's are much easier or much harder to hit but then the creatures likely have varied hit points or other compensating abilities (like resistances).

Due to this, ascribing a static +/-3 to advantage/disadvantage isn't an accurate assessment.

[snip]

[/QUOTE]

+/-3 for ADV/DIS isn't accurate, but neither is +/-5, something that a lot of people seem to either think is the case or use a fact.

Your points about mid range rolls having a roughly +/-5 bonus suggests to me that this was chosen for passive checks as passive checks are more likely to matter when the roll is mediocre. EG, if you rolled 11 (including bonuses) on your stealth roll, the sentries passive perception is more likely to matter than if you rolled 21. Therefor giving passive skills a +5 bonus makes sense but saying the Advantage give a +anything bonus to all rolls is not that helpful except in the roughest guesstimates of what might happen.

You also make a good point about the game assuming mid level rolls and therefor weighting the passive check mechanic in favour of mid level rolls, but I find that AC's tend to trend upwards MUCH slower than to hit bonuses and skill check DC's should remain the same through the whole game (in theory at least).

 

[Ovinomancer]

That's still left me confused. I thought the sum of all possible outcomes had to equal 100%?

Even putting aside stat's for a minute, it doesn't make sense that all the probabilities increase. With a single die, the chance of any number is the same as any other number (you're just as likely to roll a 1 as you are a 20). Advantage is a mechanism to skew the distribution in favour of higher numbers. So the increased chance of rolling a 20 must come from a decreased chance of rolling a different number (or numbers).

With advantage getting a 1 as your final result only happens when both dice roll 1s (a 1 in 400 chance) you can roll a 20 if either dice rolls a 20 (slightly less than a 1 in 10 chance).

Yes, the odds add to 1. The confusion you're under is what the question is. The question is "what are the odds of rolling at least one number N on 2d20?" The odds that sum to 1 here are tge odds you roll at least one N abd tge odds you don't. It isnt the odds of rolling N plus the odds of rolling M plus the odds of rolling K... which is what you did. It's just N or not N.

Now, though, it may be that your asking what the odds of rolling N are if I take the highest roll on 2d20. If so, maybe that is what that chart does. It would not have occurred to me to ask that question, as it's of no real interest to the game. I never need to roll an 11 exactly, for instance, I need an 11+.

 

[FrogReaver]

Yes, the odds add to 1. The confusion you're under is what the question is. The question is "what are the odds of rolling at least one number N on 2d20?" The odds that sum to 1 here are tge odds you roll at least one N abd tge odds you don't. It isnt the odds of rolling N plus the odds of rolling M plus the odds of rolling K... which is what you did. It's just N or not N.

No wonder you are confused. That was never the question.

Now, though, it may be that your asking what the odds of rolling N are if I take the highest roll on 2d20. If so, maybe that is what that chart does. It would not have occurred to me to ask that question, as it's of no real interest to the game. I never need to roll an 11 exactly, for instance, I need an 11+.

The question asked was what are the odds of rolling exactly number X using roll 2d20 take highest. That’s a very interesting question because with that info what you are ultimately wanting to get at (the probability of rolling x or higher) becomes a trivial problem.

 

[Ovinomancer]

That's still left me confused. I thought the sum of all possible outcomes had to equal 100%?

Even putting aside stat's for a minute, it doesn't make sense that all the probabilities increase. With a single die, the chance of any number is the same as any other number (you're just as likely to roll a 1 as you are a 20). Advantage is a mechanism to skew the distribution in favour of higher numbers. So the increased chance of rolling a 20 must come from a decreased chance of rolling a different number (or numbers).

With advantage getting a 1 as your final result only happens when both dice roll 1s (a 1 in 400 chance) you can roll a 20 if either dice rolls a 20 (slightly less than a 1 in 10 chance).

Yes, the odds add to 1. The confusion you're under is what the question is. The question is "what are the odds of rolling at least one number N on 2d20?" The odds that sum to 1 here are tge odds you roll at least one N abd tge odds you don't. It isnt the odds of rolling N plus the odds of rolling M plus the odds of rolling K... which is what you did. It's just N or not N.

Now, though, it may be that your asking what the odds of rolling N are if I take the highest roll on 2d20. If so, maybe that is what that darechart does. It would not have occurred to me to ask that question, as it's of no real interest to the game. I never need to roll an 11 exactly, for instance, I need an 11+.

 

[Ovinomancer]

No wonder you are confused. That was never the question.



The question asked was what are the odds of rolling exactly number X using roll 2d20 take highest. That’s a very interesting question because with that info what you are ultimately wanting to get at (the probability of rolling x or higher) becomes a trivial problem.

Nope, it's totally uninteresting. I don't care what the odds of rolling exactly 11 are, I would care what the odds of rolling 11 or more are (or 11 or less for disadvantage). Knowing the odds of rolling an 11 is pointless. Finding the odds of rolling exactly 11, then exactly 12, then exactly 13 and so on just to sum the odds when I can do a simple formula instead that delivers the interesting information is an unnecessary amount of work that has, as a middle point, useless information.

Hopefully, this post will not double post. Strange occurrences lately.