Roll Twice, Take the Best?

[MesiDoomstalker]

So I was just browsing through Drow of the Underdark and found a nifty Item called the Ring of Anticipation, which grants some minor buffs to Spot and Listen but also the ability to roll initiative twice, taking the best result. It got me thinking, how useful are such abilities? To be able to roll twice, take the best. I suppose it depends on what your double rolling. For its cost, the Ring of Anticipation is pretty good.

[Inevitability]

5e uses 'roll twice, take the best' quite a lot (it's called Advantage there) and it comes down to increasing your average roll from 10 to 13.8, which is useful but not too major (Nerveskitter is better). If your DM uses critical fumbles or successes, though, it becomes a lot better.

[Twurps]

Comparing averages isn't really doing the ability justice though.
If I nead 6 or higher to 'succeed' on a d20 roll, rolling twice increases my chances from 75% to 93,75%. Effectively turning 3 out of every 4 failures into a succes. That's pretty big, and much better than the averages suggest.

Also: The fewer dice you roll, the less usefull an 'average' is. A single d20 will roll a 1 just as often as it will roll a 10 or 20. no matter what the 'averages' say. Adding dice rolls significantly increases the predictive power of averages (Ever tried rolling a total of 6 on 6d20?), and so reduces risks. Something I greatly value both in D&D and real life.

[ben-zayb]

Comparing averages isn't really doing the ability justice though.
If I nead 6 or higher to 'succeed' on a d20 roll, rolling twice increases my chances from 75% to 93,75%. Effectively turning 3 out of every 4 failures into a succes. That's pretty big, and much better than the averages suggest.

Also: The fewer dice you roll, the less usefull an 'average' is. A single d20 will roll a 1 just as often as it will roll a 10 or 20. no matter what the 'averages' say. Adding dice rolls significantly increases the predictive power of averages (Ever tried rolling a total of 6 on 6d20?), and so reduces risks. Something I greatly value both in D&D and real life.

And in the above context of a 2d20b1 to initiative being compared to Nerveskitter, that's still worse because getting +5 now means you auto-succeed.

Really, the best feature of 2d20b1 is reducing the chance of getting a 1 from 5% to 0.25%, which means it is best being utilized on attack rolls and saves.

[Twurps]

And in the above context of a 2d20b1 to initiative being compared to Nerveskitter, that's still worse because getting +5 now means you auto-succeed.

Really, the best feature of 2d20b1 is reducing the chance of getting a 1 from 5% to 0.25%, which means it is best being utilized on attack rolls and saves.

Very true.
I'd prefer the nerveskitter. (Or at least: an item of nerveskitter, to make a better comparison to the ring of anticipation)
My point however wasn't to compare it to nerveskitter. It's just that averages aren't the best way to go about comparing these things.
I think the argument has been made before by people better versed in the math behind this than I am: http://www.giantitp.com/forums/showthread.php?237281-Ring-of-Anticipation-Initiative-bonus-math
short version: The bonus, comparing means, of the ring is closer to 5 than it is to 3. (And I still prefer the flat bonus of nerverskitter)

[Chronos]

On a roll where your base chance of success is 50%, roll-twice-take-best is worth the equivalent of +5 (aside from special effects on specific die values like natural 1 or critical range). If your base chance of success was higher or lower than that, then its value is less than that.

On the other hand, there are those rolls where specific die values, without considering modifiers, are relevant. If you have a threat range of, say, 15-20 (the highest you can get without extreme optimization), no amount of bonus in the world will turn a 14 into a critical threat. Rolling twice, however, can.

[ben-zayb]

^ Yep. I guess the proper way of saying it is that 2d20b1 is best for rolls that already have binary effects independent of the opposing check or DC (e.g. likelier autosuccess on a 20, less likelier autofail on a 1, more crit opportunities, etc.)

[prufock]

5e uses 'roll twice, take the best' quite a lot (it's called Advantage there) and it comes down to increasing your average roll from 10 to 13.8, which is useful but not too major (Nerveskitter is better). If your DM uses critical fumbles or successes, though, it becomes a lot better.

It's 10.5 to 13.8 to be more precise, so a +3.3 equivalent. It has higher variability though, which can be good or bad.

[Spore]

Also the usefulness depends if you can activate this at will AFTER the first roll is made and if it is a binary effect (save made or not) or some linear effect (like Initiative or damage).

[MesiDoomstalker]

Also the usefulness depends if you can activate this at will AFTER the first roll is made and if it is a binary effect (save made or not) or some linear effect (like Initiative or damage).

On making the second roll AFTER the first, most of these abilities I see are of the "take second result" type, where you can roll worse. Roll Twice, Take Best is strictly better than these types of double rolls. I think another thing is if you have flat bonuses to whatever roll your Doubling, they explicitely stack (since the bonus applies whatever the final result is).

[Spore]

On making the second roll AFTER the first, most of these abilities I see are of the "take second result" type, where you can roll worse. Roll Twice, Take Best is strictly better than these types of double rolls. I think another thing is if you have flat bonuses to whatever roll your Doubling, they explicitely stack (since the bonus applies whatever the final result is).

I'm referring to items worded as such: "If saved is failed then roll twice, take second result even if worse."

You wouldn't activate them unless you botched your save anyway.

[MesiDoomstalker]

I'm referring to items worded as such: "If saved is failed then roll twice, take second result even if worse."

You wouldn't activate them unless you botched your save anyway.

Even then, Roll Twice, Take Best is still better (if only marginally). Because you always get 2 rolls and always get the better result, you'll have statistically better chance of success. How much depends a lot on what kind of roll your doing and the relative difficulty.