rules.mechanic
Craft homebrewer
Certainly could. The reason for odds/evens was crits and you could make a case for that either way.
Level Up (A5E) Minor Advantage and Minor Disadvantage
Leatherhead
Possibly a Idiot.
My question is:
Why is there not a Passive minor (dis)advantage? When you have normal (dis)advantage on a passive check, it's +/- 5.
Why is there not a Passive minor (dis)advantage? When you have normal (dis)advantage on a passive check, it's +/- 5.
That's a good point, (minor)advantage/disadvantage should mesh better with passive checks as the current interaction makes it feel like one is a poorly bolted on houserule. Anyone who has ever played a character with the observant feat or payed attention while gm'ing with a player who has it will notice how badly passive checks mesh with other parts of the system.
take the feat and you literally get 25% worse at perception/investigate checks by trying than simply existing with any given check having a 50% chance of being up to around 75% worse. If a feat or some other ability gives a bonus to passive checks it should do the same to active checks. even worse is "becaue you $reason give me a investigate/perception check with advantage" still has significant odds of being worse than "no I'm just gonna chill"
Edge: Roll 2d20 and use the even value. If no even value, use the higher one.
An Edge is half of an Advantage.
Handicap: Roll 2d20 and use the odd value. If no odd value, use the lower one.
A Handicap is half of a Disadvantage.
Result: ~50% of the time this is 1d10*2 (-1 for disadvantage), which is a lot like 1d20.
50% of the time it is basically advantage/disadvantage (both odd, both even).
This requires 0 rerolls, and produces a something half way between Advantage and a Normal roll.
The odd/even difference is required to ensure that Edge increases crit chance (by about x1.5), and Handcap decreases it (by about x0.5).
If you roll a 17 and a 4 with Edge, you get a 4.
If you roll a 17 and a 4 with Handicap, you get 17.
If you roll an 16 and a 4 with Edge, you get an 16.
If you roll an 16 and a 4 with Handicap, you get a 4.
If you roll a 17 and a 3 with Edge, you get a 17.
If you roll a 17 and a 3 with Handicap, you get a 3.
If you roll an 16 and a 3 with Edge, you get an 16.
If you roll an 16 and a 3 with Handicap, you get a 3.
These are 4 representative cases. Edge has 3/4 good rolls, Handicap has 1/4. (Advantage would have 4/4, Disadvantage would have 0/4).
One little (psychological) downside is that there are cases where Handicap gives a higher value than Edge for the same roll; a high odd and low even roll.
Edge works out to: 1/2 1d10*2 + 1/4 (2d10*2 pick best) + 1/4(1d10*2 pick best +1)
Handicap works out to: 1/2 1d10*2-1 + 1/4 (2d10*2 pick worst) + 1/4(1d10*2 pick worst +1)
An Edge is half of an Advantage.
Handicap: Roll 2d20 and use the odd value. If no odd value, use the lower one.
A Handicap is half of a Disadvantage.
Result: ~50% of the time this is 1d10*2 (-1 for disadvantage), which is a lot like 1d20.
50% of the time it is basically advantage/disadvantage (both odd, both even).
This requires 0 rerolls, and produces a something half way between Advantage and a Normal roll.
The odd/even difference is required to ensure that Edge increases crit chance (by about x1.5), and Handcap decreases it (by about x0.5).
If you roll a 17 and a 4 with Edge, you get a 4.
If you roll a 17 and a 4 with Handicap, you get 17.
If you roll an 16 and a 4 with Edge, you get an 16.
If you roll an 16 and a 4 with Handicap, you get a 4.
If you roll a 17 and a 3 with Edge, you get a 17.
If you roll a 17 and a 3 with Handicap, you get a 3.
If you roll an 16 and a 3 with Edge, you get an 16.
If you roll an 16 and a 3 with Handicap, you get a 3.
These are 4 representative cases. Edge has 3/4 good rolls, Handicap has 1/4. (Advantage would have 4/4, Disadvantage would have 0/4).
One little (psychological) downside is that there are cases where Handicap gives a higher value than Edge for the same roll; a high odd and low even roll.
Edge works out to: 1/2 1d10*2 + 1/4 (2d10*2 pick best) + 1/4(1d10*2 pick best +1)
Handicap works out to: 1/2 1d10*2-1 + 1/4 (2d10*2 pick worst) + 1/4(1d10*2 pick worst +1)
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Something like this might work, while it still requires a little brain work "you have to look at odd/even on the die and then possibly assess high or low", its still a pretty low impact mental activity and has the advantage of still rolling the 2d20 at the same time, which is my issue with a lot of reroll mechanics.
I'm trying to break that asymmetry where the same roll is better with Handicap than Edge.
Here is another stab at it:
Edge: 2d20, take the higher one unless both are odd; then take the lower one.
Handicap: 2d20, take the lower one unless both are even; then take the higher one.
Edge is then 75% advantage 25% disadvantage, and vice versa for Handicap.
Math:
So a neutral roll is 50% advantage/50% disadvantage on this scale.
I think I like this one better. For a given roll, going up the Disadvantage -> Handicap -> (Skip Neutral) -> Edge -> Advantage always makes the roll better (well, no worse). And unless you land on Neutral, the same roll can be interpreted as any of those.
Here is another stab at it:
Edge: 2d20, take the higher one unless both are odd; then take the lower one.
Handicap: 2d20, take the lower one unless both are even; then take the higher one.
Edge is then 75% advantage 25% disadvantage, and vice versa for Handicap.
Math:
With a base probability of success of P, advantage is 1-(1-P)^2 or 2P-P^2. Disadvantage is P^2.
K advantage and (1-K) disadvantage is then K(2P-P^2) + (1-K)P^2 = 2KP - KP^2 + P^2 - KP^2 = 2KP + (1-2K)P^2.
At K=0.5 this is P, aka no advantage or disadvantage.
At K=1 this is 2P-P^2, aka advantage.
At K=0 this is P^2, aka disadvantage.
d/dK is 2P - 2P^2 = 2P(1-P). This is always positive, and maximal at P=0.5 (where it is 1/2) and zero at P=1 and 0.
What this means is that for any case besides certain failure/success, Advantage > Edge > Normal > Handicap > Disadvantage in terms of probability of success.
By having double-odd be bad on Edge, it doesn't block crits; your crit chance is doubled. Your natural 1 chance is halved over a normal roll.
With advantage, your natural 1 chance is basically eliminated (1 in 400).
Similarly, for Handicap, your natural 1 chance is doubled (just like disadvantage), and your crit chance is halved over a normal roll.
With disadvantage, your crit chance is basically eliminated (1 in 400).
This assumes crit on a 20; on a 19-20 the math changes a bit.
Chance of a 20: 1- .95 * .95 = 9.75%.
Chance of a 19 but not a 20: Die 1 lands on an even value that isn't 20 (9/20 chance) times die 2 lands on 19 (1/20), and vice versa (*2), for 18/400, plus double 19 (1/400).
Total: 14.5%
With real advantage it would be 19%.
With a normal roll it would be 10%.
Crit on a 18-20 with edge.
Same for 20 and 19.
For an 18 but not 19 or 20, it is die 1 on an 18, plus die 2 from 1 to 18, plus die 2 on 18 and die 1 from 1 to 17, for 35/400.
Total is 23.25%.
With real advantage it is 27.75%
With a normal roll it is 15%
again, about half way in between.
K advantage and (1-K) disadvantage is then K(2P-P^2) + (1-K)P^2 = 2KP - KP^2 + P^2 - KP^2 = 2KP + (1-2K)P^2.
At K=0.5 this is P, aka no advantage or disadvantage.
At K=1 this is 2P-P^2, aka advantage.
At K=0 this is P^2, aka disadvantage.
d/dK is 2P - 2P^2 = 2P(1-P). This is always positive, and maximal at P=0.5 (where it is 1/2) and zero at P=1 and 0.
What this means is that for any case besides certain failure/success, Advantage > Edge > Normal > Handicap > Disadvantage in terms of probability of success.
By having double-odd be bad on Edge, it doesn't block crits; your crit chance is doubled. Your natural 1 chance is halved over a normal roll.
With advantage, your natural 1 chance is basically eliminated (1 in 400).
Similarly, for Handicap, your natural 1 chance is doubled (just like disadvantage), and your crit chance is halved over a normal roll.
With disadvantage, your crit chance is basically eliminated (1 in 400).
This assumes crit on a 20; on a 19-20 the math changes a bit.
Chance of a 20: 1- .95 * .95 = 9.75%.
Chance of a 19 but not a 20: Die 1 lands on an even value that isn't 20 (9/20 chance) times die 2 lands on 19 (1/20), and vice versa (*2), for 18/400, plus double 19 (1/400).
Total: 14.5%
With real advantage it would be 19%.
With a normal roll it would be 10%.
Crit on a 18-20 with edge.
Same for 20 and 19.
For an 18 but not 19 or 20, it is die 1 on an 18, plus die 2 from 1 to 18, plus die 2 on 18 and die 1 from 1 to 17, for 35/400.
Total is 23.25%.
With real advantage it is 27.75%
With a normal roll it is 15%
again, about half way in between.
I think I like this one better. For a given roll, going up the Disadvantage -> Handicap -> (Skip Neutral) -> Edge -> Advantage always makes the roll better (well, no worse). And unless you land on Neutral, the same roll can be interpreted as any of those.
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jmucchiello
Hero
Psychologically, the Edge is counterintuitive. I have a 17 and a 4 when I'm at some form of advantage and the 4 is chosen? Yes, the math overall says this is a partial advantage but it look like I just lost out on my 17.
nod. Which is why the second one is a bit better.
With Edge v2, you have advantage unless both dice are odd (then you get disadvantage). It still comes up, but less often.
With Handicap v2, you have disadvantage unless both dice are even (then you get advantage).
Hopefully the "3/4 chance at advantage and 1/4 chance at disadvantage" still feels like semi-advantage.
@NotAYakk what problem are you trying to "solve" & what concrete improvements do you think your suggestion brings to the table? That might work ok for your 5 & 8 year old kids, but keep in mind that they are really a bit on the young end for d&d let alone a crunchier "advanced" version. More importantly your change seems to be change for the sake of change without bringing anything particular to the table
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