Hey, probability folks:
If instead of rolling 2d6, we instead rolled 3d6 and kept the highest 2, how does that compare to rolling 2d6 and adding a modifier? What I’m hoping is that someone can tell me “rolling 3d6, keep and sum the highest 2, is mathematically the same as 2d6+X” (and I realize that X probably won’t be a whole number).
Thanks in advance.
I heard recently that it should average out at a general +1.5 but I have not done the calculations myself.
I was curious of this from a different angle; replacing +1 or -1 forward with a advantage/disadvantage roll like D&D 5e.
Rolling 3d6 and keeping the highest two and summing has a skewed distribution, so not only is the expectation higher than sum 2d6 (8.45 rather than 7.0), but the shape is different, with a longer tail down to 2 and a shorter tail up to 12.
What is the hoped-for feature that 3d6 keeping highest two might give you?
anydice.com is useful for this kind of thing. Here are the numbers for 2d6 vs 3d6 and keep 2: http://anydice.com/program/4238
The curves you get when you roll nd6 and sum the highest 2 are just about the best ever. AW almost worked that way, but I went with the more straightforward roll instead.
There’s all kinds of fun stuff you can do with roll & keep mechanics. It can be tempting to get too byzantine, of course.
I created a little function for calculating success/mixed/failure.
http://anydice.com/program/423e
Rob Donoghue has been playing with this:
“For the curious, the math is that an advantage or disadvantage equates to approximately +/- 1.5, so it’s a little more robust, but still in bounds.” http://walkingmind.evilhat.com/2014/07/13/deep-dive-into-dw-gming/
Here are a couple of good discussions on alternate dice mechanics:
http://apocalypse-world.com/forums/index.php?topic=6120.msg25676#msg25676
http://apocalypse-world.com/forums/index.php?topic=6034.5
I’m leaning towards giving the advantage/disadvantage (3d6 drop lowest/highest) since Rob Donoghue has reported that it has worked great for his group.
Also because Vincent Baker just said up there ^ that this was his preferred design (how cool is that)!
Here is a breakdown of various possible configurations of multiple dice:
http://redboxvancouver.files.wordpress.com/2014/07/aw-dice-probabilities.pdf
So much awesome help! Thanks, all!