I love DW. One thing I miss from my OD&D experience in DW is the d20. There’s a way to use d20’s in the game, but it’s a bit of a shift to the probabilities. Rolling 2d6 for moves DW standard we get (assume +0)
~42% chance of a 2-6/miss
~42% chance of a 7-9/soft hit
~16% chance of a 10+/hard hit
My proposed change, roll 3d20, keep the median value, then add your modifier. Assuming a +0 to the roll, we get the following:
~42% of a miss (1-9)
~42% chance of a soft hit (10-15)
~16% chance of a hard hit (16+)
To my eye, given the odds are the same, there should be no difference in play? However, before I made that change, I wanted to ask the community: what am I missing? Is there something about this change that could potentially break the game?
TL’DR: if I change from rolling 2d6+MOD to rolling the median value on 3d20+MOD, will anything in the game break?
What about modifiers? What’s the equivalent of a +1 or +3?
I’m not a pro with math but the idea of dividing each roll by three does not sound fun to me.
I was pointed to a really interesting post on dice stats in PbtA games recently, I’ll see if I can find the link! It covers what you’re after, and shows success rates with modifiers (+1 etc).
Matt, if I understand what the OP means, there’s no math required. You’re thinking of the “mean” (adding all the numbers up them dividing). The median means the number in the middle. You roll three dice and take the middle value. For example, if you rolled a 2, 11, and 20, you’d take the 11 because it’s the middle. Another example: 1, 2, and 20, you’d take the 2. Does that make sense?
I gotcha! Thanks for clarifying!
John Bogart has it right. Giovanni Lanza , yes, that’s where the ‘feel’ and the actual odds differ. a +1 rolling sum of 2d6 is ~2x the value it would be in my scheme – but I’m not sure if that’s consistent across all situations (still doing some rough math to figure that out). If I kept the bonuses the same, it’d make any modifiers/bonuses less impactful.
James Hawthorne , if you find the post, I’d love to see it.
This could be a pretty cool system for modifiers.
Standard rolls = take middle die.
If you have advantage = take highest die.
If you have disadvantage = take lowest die.
Ryan M. Danks , that’s neat. I’ll have to look at the probabilities. Off the top of my head, I like it conceptually.
It’s amazing how how dice aesthetics/mechanics nostalgia in general are so powerful, so much so that we’ll avoid systems entirely just because of the dice they use.
Michael Prescott , just to be clear, I’ve been playing DW Rules As Written for some time. Now, after having run a couple of multi-session arcs (including 1 that took characters to level 10) and a handful of 1-shot delves, I’m looking to add back in my collection of neglected d20s.
Oh yes, wasn’t meaning to sound critical of you, I did get that. Nostalgia is so wonderfully mysterious – I have nostalgia for games in my collection that I’ve never played, merely pored over a lot. I’ve realized I yearn to ‘recreate’ an experience I’ve never actually had. 🙂
Jason Leigh, it’s buried somewhere in my notifications! Unfortunately I launched a kickstarter last week, so my notifications are pretty ridiculous to sort through. There were definitely other people involved in the discussion who saw the link to dice statistics, I think Wynand Louw might have been one of them?
The link was to a post in the Apocalypse World Google+ group from the 30th October, commented on by Vincent and exploring the range of results (with the same conclusion as yours!), though it had an interesting look at how adding +1 or subtracting 1 shifted the balance of probabilities.
Sub
ah! I’ve got you dice statistics post!
http://apocalypse-world.com/forums/index.php?topic=2787.msg16696#msg16696
I toyed with using d20s too, but it doesn’t seem feasible. Modifiers screw everything around and the balance between miss/weak hit/strong hit is basically what gets the whole game going.
Turns out, rolling 3d20, taking the median (or middle) value, and using double modifiers would produce close to the same results distribution (not perfectly, but very very close).
The other possibility is that modifiers having less impact will make the game feel ‘gritty’. Dunno.
So, define a miss as 1-9, a weak hit as 10 to 15, and a strong hit as 16+.
With a +0 mod, here are the chances of each:
Miss (m): ~42%
Weak Hit (w): ~42%
Strong Hit (s): ~16%
With a +1 mod, here are the chances of each:
(m): ~35%
(w): ~43%
(s): ~22%
With a +2 mod, here are the chances of each:
(m): ~28%
(w): ~44%
(s): ~28%
So we see that balance shift, just a bit shallower than with the 2d6+MOD roll from standard DW/AW.
Fully testing out the hypothesis, a +4 mod should reverse the chances between (m) and (s) we see from +0 mod from above. Here are the actuals with a +4 mod:
(m): ~16%
(w): ~44%
(s): ~40%
Again, a bit of a shallower shift.
So, if I’m going to do this, if I have my MODs be +2, +4, +6, +8 instead of +1, +2, +3, +4, I get roughly the same odds (not quite) using my choose the middle of 3d20.
Or, I could stick with +1,+2,+3,+4 mods and have such modifiers not tip the balance as much, which could produce a ‘grittier’ feel.
I really like that idea of median 3d20, but taking the lowest die for a disadvantage and the highest die for an advantage. It feels much more interesting than carry +1 forward. Here’s a link to a dice probability calculator. http://topps.diku.dk/torbenm/troll.msp
Use “median 3d20”, “min 3d20”, and “max 3d20” to see the results. Seems like max3d20 is 65% likely to give a success (>15), and min3d20 is 87% likely to give a failure (<10).
Curse all of you… I woke up this morning thinking about the possibilities of this… My biggest gripe about DW is, surprisingly, the difficulty of giving small mechanical benefits (e.g., a +1 magical sword ) without wonkiness creeping in pretty quickly. This solves all of it…
Stephen Danic, yep. I suspect, however, the big shifts in probability in play vs DW Raw will make it ‘feel’ like a different game, which is totally cool. I suspect only play testing will reveal the truth.
+Brennan OBrien, I didn’t mean to infect your mind. 🙂 I’m sorry. I too think this opens up use of a whole raft of mechanical widgets for DW. And like I said before, play testing is in order (which I’m going to undertake).
I’m tempted to combine this with the concept of running DW “torchbearer” style as +Tim Frankze suggested.
Jason Leigh completely agree. Theres also some interesting crossover with the non mechanical and semi mechanical elements of 13th Age… one unique thing, backgrounds, icon relationships and even the escalation die.
Quick shout out to Tavern Tales: http://taverntalesrpg.com/, which uses the 3d20 median rule. Otherwise it’s a bit of a cross between DW and D20. It’s free, so definitely worth checking out.