One of the new mechanics in the DnD Basic ruleset is the concept of being advantaged or disadvantaged. It’s a simple mechanic reminiscent of GURPS’ Luck advantage (though a tetch less powerful) or bonus point expenditures (where it’s basically the same concept).

The key bit is if you’re advantaged or disadvantaged on a roll, you roll twice and pick the best or worst result, depending.

This mechanic skews an otherwise flat distribution (a d20 of course has 5% probability of landing on each number) to one side.

The net impact is interesting, in that the equivalent bonus depends on what you need to roll. For advantaged rolls, at the low end (because you’re picking the best of two), the equivalent bonus can be as large as about +5, meaning your odds of rolling that number or higher are about 25% higher with advantage. The plot above shows the difference between the curves is the percentage boost you get by being advantaged relative to a flat  d20 roll versus a typical target number from 1-20, such as ascending armor class.

Perhaps a table is easier. Thanks to a commenter, I realized what I’d been doing wrong at just shy of midnight, and fixed it. The conclusions are similar – the bonuses range from zero (at the low end; you can always roll 1 or higher on 1d20) to about +5, and the best equivalent bonuses are in the middle. The average bonus is precisely 3, but that’s not the equivalent of a +3 bonus all over, because of the skewed nature of the distribution. Still, if you’re borrowing mechanics from the DnD Basic Rulebook for an OSR game, just treat the “advantaged/disadvantaged” condition as worth +/-3.

Note that is is possible to roll quite poorly on an advantaged roll. You’ve got a 1 in 400 chance of rolling a 1 (lower even than GURPS’ 1 in 216 chance of a critical 3), about 1% of blowing a roll on 2 or higher, and at 5% chance of failure (2 or higher on 1d20 raw), you have that same probability with a target number of 5. So being advantaged against middle-of-the road combatants (target numbers of 10 or so) is a big deal. Likewise, being disadvantaged would be a big deal.

Well, unless you’re +Tim Shorts using Roll20. Then you’re guaranteed to roll low, no matter what the probabilities are.

When all is said and done, the advantaged/disadvantaged mechanic is kinda neat. It’s more than just a flat +3 would be, which would still be a fairly straight-forward distribution (0% for 1, 2, 3, 5% for a 4, and a 15% chance of hitting a 20). In reality, that roll mostly impacts the middle of the distribution; if you’re looking to roll high, and you hit a 19-20 on your first roll, the odds of improvement are small. But if that raw roll is 6-16 (55% of the entire distribution), you’re looking at that second roll being typically 4-5 higher, which is darn nice insurance against screw-ups.

1. you pass the same probability (5%) of rolling a 1 on 1d20. Unless you're +Tim Shorts using Roll20

ROFL!

In fairness though, in the context of the Monday Night Ubergoobers' rolls, he throws only slightly more 1's than the rest of the group. All our dice rolls suck pretty badly in that band of players. ðŸ™‚

2. The presentation of your results are not quite accurate. For a Raw Roll of 1, the Equiv Adv would fall in the range of 1-4. The exact probability of 4 being the highest result from rolling 2 20 sided dice is 7/400, or slightly lower than 2%. Thus the Adv Bonus would be much closer to 2. Some of the other results have similar issues. Some do not.

1. Fair, but I think while my words might be a tetch off, the overall message is fair. I did use cumulative distributions for both, so they are both directly comparable: what's the probability of rolling the raw roll or less, vs the number that's the equivalent probability for the advantaged roll.

DnD is a "roll X or higher" game, obviously, so in fairness (and this is my my results are wonky) the best way to do this would be to show it as 1-cum probability. So the probability of rolling 1 or higher raw is 100%, 2 or higher is 95%, etc. Then I can present the advantaged numbers in the same way.

That's a better idea; I'll amend the post. I was quite tired when I wrote it, and GURPS uses the roll-under convention, which is why I didn't think to invert the numbers.

3. Great post. Thanks for sharing the insight on the bonus especially as it might apply to an OSR game.

1. Thanks! I play in Erik Tenkar's Swords and Wizardry game, so OSR is really all I experience of D&D these days. I did play in a Pathfinder game for a bit, though, so I'm somewhat familiar with that style of play, though I'm barely above playing at default level, to borrow a GURPS-ism.

4. I'm not sure if this is already taken into account in the chart above but another great aspect of advantage is the fact that you get two chances to roll a natural 20 on an attack (giving a critical hit). Two shots at a crit is way better than one, especially given the mechanics that allow that range to be expanded or give all sorts of fun side effects.

As someone who despaired at dnd 4e's mountain of bonuses I am a huge fan of the advantage / disadvantage mechanic. If I want something more gritty and reality-based I'll go play GURPS!

1. Andrew Hackard says:

Specifically, you have a 1/20 chance at rolling a crit on a single die, and a 39/400 chance at rolling with advantage. That's almost twice as likely. (Of course, the same is true with fumbles when you have disadvantage…)

2. Right! Thanks for mathing it out for me ðŸ˜‰