Gaming Discussion > General D&D Discussion
Estimating the Best of Two Rolls
Garryl:
So, for the longest time, I had it in my head that when rolling 2d20 and taking the better result (2d20b1), the average result was 15. I don't know where I got this number from (probably from extrapolating from the far more trivial case of 2d2b1, a pair of coins), but suffice it to say, it's wrong. Today I learned of my mistake and a better estimator.
As it turns out, a good estimator is that for rolling a d20 twice and taking the better result, the average result is actually 13.825. A good estimation for die-rolling (and the actual exact average result if working with a random number generator not restricted to whole numbers only) is that the average = (min + 2*max) / 3, or that average = min + (max - min)*2/3.
Now, I haven't double-checked my math, but I think that the generalized case of XdNb1 (rolling X N-sided dice and taking the best result) has an average of approximately (1 + X*N) / (X+1). Again, dice only give integer results, so this is only an estimate; with a random number generator that could give any result from A to B, not just whole numbers, the average would be exactly (A + X*B) / (X+1), assuming my napkin math is right. If anybody feels like double-checking me, I'd appreciate it.
SorO_Lost:
I haven't checked it but I did want to plug AnyDice in here. It's a really old site but it calculates odds for you.
For example,
--- Code: ---output [highest 1 of 2d20]
--- End code ---
Gives you the odds of rolling any certain face along with a two point decimal value of its average which is 13.82.
If you want the formulas, you can just read the source code.
Keldar:
The 4E Avenger rolled best of 2d20 for attack rolls, it was generally thought of as analogous to a +4 in guides. I didn't pay attention to the math then, but it does further support your arithmetic. :cheers
Garryl:
--- Quote from: SorO_Lost on August 30, 2018, 07:35:04 PM ---I haven't checked it but I did want to plug AnyDice in here. It's a really old site but it calculates odds for you.
For example,
--- Code: ---output [highest 1 of 2d20]
--- End code ---
Gives you the odds of rolling any certain face along with a two point decimal value of its average which is 13.82.
If you want the formulas, you can just read the source code.
--- End quote ---
Yeah, AnyDice is an awesome tool. I've used it for some surprisingly complex calculations in the past.
--- Quote from: Keldar on September 03, 2018, 02:27:30 AM ---The 4E Avenger rolled best of 2d20 for attack rolls, it was generally thought of as analogous to a +4 in guides. I didn't pay attention to the math then, but it does further support your arithmetic. :cheers
--- End quote ---
If you need anywhere from a 7 to a 15 to succeed on your attack roll, 2d20b1 is actually slightly better than a +4 bonus (topping out at being equal to a +5 bonus if you need exactly 11 to hit) in terms of your odds of success. It's slightly worse than +4 outside of that range, although 7-15 should cover most situations. However, rolling twice also gets you better odds of rolling a natural 20 or whatever you need for a crit, so that's an extra benefit to account for.
(click to show/hide)Target number to hit2d20b1 success rateEquivalent roll bonus1100%+0299.75%+0.95399%+1.8497.75%+2.55596%+3.2693.75%+3.75791%+4.2887.75%+4.55984%+4.81079.75%+4.951175%+51269.75%+4.951364%+4.81457.75%+4.551551%+4.21643.75%+3.751736%+3.21827.75%+2.551919%+1.8209.75%+0.95
awaken_D_M_golem:
ninja'd except this detail , iirc the +5 is the actual value for Passive checks, perhaps PHB p175 or there'bouts.
--- Quote from: Keldar on September 03, 2018, 02:27:30 AM ---The 4E Avenger rolled best of 2d20 for attack rolls, it was generally thought of as analogous to a +4 in guides. I didn't pay attention to the math then, but it does further support your arithmetic. :cheers
--- End quote ---
bolded ... but that sorta didn't matter, you either played without having the right math, or somebody blew money on the paid-for-errata and was auto-part of a build.
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