What is the Best Roll?

[Yora]

When you crush your enemies, see them driven before you, and you hear the lamentations of their players!

 

[MarkB]

You're playing a game in which your goal, when it comes to determining the quality of outcomes, is to roll your d20 higher than the GM's d20. Each side has miscellaneous bonuses to add to its result due to favorable circumstances.

What is the result of your roll that indicates the best outcome?

20 on the die, since more is better?

One higher than the GMs result, since as you get more bonus points, it's actually harder to roll low and still win?

Tie with the GM, since that's the least likely result? Because if you have more or fewer (but not equal) bonus points than the GM, you are more likely to either win or lose - but odds of a tie diminish. Note that a tie, though rare, does not automatically indicate a win under these rules.

Or something else, like a result that equals your attribute score?

20 on the die is easiest to grasp. It's a simple case of "the higher the better." Any of the other options put you as a player in the weird position of wanting to roll "high, but not too high", which is going to tend to feel out of place for many players.

If you want something variable, you could go with something like "beat the GM's roll by 5 or more", which places more emphasis on the bonuses each side gets to their roll, as in some cases, if the GM rolled high enough, that super-good result may simply be unachievable.

 

[Deset Gled]

This seems wrong. To roll the same as the DM you need both rolls to be the same result. It's not the same as a single d20 result (5%) of 20.

There are 400 equally likely ways to roll two d20s (20x20=400). Of those 400 ways, 20 of them have paired results (1&1, 2&2, ... 19&19, 20&20). 20 out of 400 is 20/400 = 1/20 = 5%.

It may seem wrong, but I think to math holds up. Of course, this is assuming there are no modifiers to the rolls.

 

[GMMichael]

There are 400 equally likely ways to roll two d20s (20x20=400). Of those 400 ways, 20 of them have paired results (1&1, 2&2, ... 19&19, 20&20). 20 out of 400 is 20/400 = 1/20 = 5%. . . . Of course, this is assuming there are no modifiers to the rolls.

And the modifiers, or bonuses, are why getting a tie becomes less likely. If one side rolls d20 and the other side rolls d20+19, then there's a 1-in-400 chance of rolling a tie.

I have this weird notion that the best-outcome-roll should be less likely than other outcomes, which is why the tied roll (followed by a "confirmation" if you will) is a likely candidate. It's also why I'm not a fan of 20-is-best; you have the same odds of rolling any other number. If you add "and win" to the condition of "roll X" then winning in this way becomes less likely but...wait for it...rolling a 20 and winning is more likely than rolling a low number and winning when considering the results of the two rolls.

One of the Other candidates could be "roll a winning result that your opponent cannot achieve." This will only happen if your bonuses are higher than the GM, and requires some maths, but it answers the question "why are you neatly beating the GM on this roll?"