Advantageously
2021-07-13

Advantageously

I read somewhere that giving the advantage on a d20 was similar to giving a +5. I ran the numbers, thanks to AnyDice and here are the results, arranged in a table:

target1d20adv~dis~
295%99.75%+190.25%-1
390%99.00%+281.00%-2
485%97.75%+372.25%-3
580%96.00%+364.00%-3
675%93.75%+456.25%-4
770%91.00%+449.00%-4
865%87.75%+542.25%-5
960%84.00%+536.00%-5
1055%79.75%+530.25%-5
1150%75.00%+525.00%-5
1245%69.75%+520.25%-5
1340%64.00%+516.00%-5
1435%57.75%+512.25%-5
1530%51.00%+49.00%-4
1625%43.75%+46.25%-4
1720%36.00%+34.00%-3
1815%27.75%+32.25%-3
1910%19.00%+21.00%-2
205%9.75%+10.25%-1

Thus a +1 attack against an AC of 16, targets 15. A regular roll has 30% chances of success. With the advantage, it becomes 51%, the delta of 21% is equivalent to a +4.

The above mentioned +5 is for the targets ranging from 8 to 14 included.

 

In Stars Without Number and friends, skill check resolution is done with 2d6. Yes, bell curve.

Some foci give an advantage. I can't remember if there is a disadvantage possibility, let's compute it anyway.

target2d6adv~dis~
2100.00%100.00%+0100.00%0
397.22%99.54%+192.59%-1
491.67%98.15%+180.09%-1
583.33%94.91%+264.35%-2
672.22%89.35%+247.69%-2
758.33%80.56%+231.94%-2
841.67%68.06%+219.44%-2
927.78%52.31%+210.65%-2
1016.67%35.65%+25.09%-2
118.33%19.91%+11.85%-1
122.78%7.41%+10.46%0

A skill check targetting 8 at 2d6+1 becomes a 2d6 targetting 7. A regular roll has 58.33% chance of success. Giving it the advantage (highest 2 of 3d6) turns it into 80.56% chance of success. That is roughly equivalent to a +2.

Turning an advantage to a modifier for a d20 is easy, 5% per increment. But for a 2d6, I went with comparing the advantage percent with a regular percent. Hence, the example above advantages at 80.56% which is close to a target 5 roll, two rows above, thus the +2.