Mathletes: Remind me: What happens to the probability of rolling a combined total of a six or less on:
three dice, take the worst two
two dice, take two
three dce, take the best two
four dice, take the best two
five dice, take the best two
Basically, what happens if "advantage" and "disadntange" replace bonuses in a 2d6 system?
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I usually use anydice.com - AnyDice to resolve these existential questions.
ReplyDeletethree dice, take the worst two: 68%
ReplyDeletetwo dice, take two: 41%
three dce, take the best two: 20%
four dice, take the best two: 9%
five dice, take the best two: 4%
Hmmm.
Or, this, so I'm not the guy that says google it...
ReplyDeleteChances of 6-, according to anydice:
5d6, keep worst 2: 90.57%
4d6, keep worst 2: 82.64%
3d6, keep worst 2: 68.06%
2d6, flat: 41.67%
3d6, keep best 2: 19.44%
4d6, keep best 2: 9.03%
5d6, keep best 2: 4.22%
Oh, we cross-posted while I was feeling like a butthead.
ReplyDeleteNo worries; I'd forgotten the name of any dice. :-)
ReplyDeleteIt's a bigger difference than +1 forward. 2d6+1 chances of 6- are 27.78%, and that 8% difference would be mirrored on the -1 side.
ReplyDeleteAlso, results are LESS swingy, the more dice are involved. They congregate even harder toward the 7-9 result. (Deviation for 2d6+1 is 2.4, for 3d6 keep 2 it's 2.2.)
Got code to show that on any dice?
ReplyDeleteClick on the summary button. It shows Mean, Deviation, Min and Max.
ReplyDeleteYeah, I see that. What i really want is to show the 6- options, so i can see a single chart with all the options and show chance of hard moves. Same for 7-9. I get all confuzzld trying to add them.
ReplyDeleteAh. You don't have to add. Use (ignore quotes) "output [highest 2 of 3d6]", or contrariwise "output [lowest 2 of 3d6]" and click on the "at most" button.
ReplyDeleteI saw that, too. I just want to see the percentage chance of a 6-. Not the others.
ReplyDeleteFor 7-9, I'd have to look at the documentation, but at least with the "at most" button, you'd only have 3 numbers to add.
ReplyDeleteIt's an interesting question that comes up often. I think I'll make something pretty tomorrow, built off the sweat of someone else's brow, if you're not deep into it at the moment.
ReplyDelete
ReplyDeleteI made this chart while working on my own design.
docs.google.com - Result percentage spead PBTA
I think in practical terms it could get annoying to try and visually spot the two lowest or two highest dice.
ReplyDeleteInstead, I think it might be easier to make one of the dice colored differently. That die is always part of the mix. The second die is chosen from the remaining dice (either highest result or lowest result).
This also simplifies the math dramatically. You just need to figure out the probability of getting the necessary second die roll for each of the 6 possible first die rolls, and average them.
For penalty it's:
(5/6)^n/6
+ (4/6)^n/6
+ (3/6)^n/6
+ (2/6)^n/6
+ (1/6)^n/6
+ 0
For bonus you subtract the probability of failure from 100%:
1.00
- (1/6)^n/6
- (2/6)^n/6
- (3/6)^n/6
- (4/6)^n/6
- (5/6)^n/6
- 1
I'm taking n to be the total number of dice minus 1.
I just spent half an hour trying to find a way of doing this and I don't think Anydice can do it. I think the best option is to run the various options and pull out the percentages yourself.
ReplyDeletehttps://lh3.googleusercontent.com/Z7IO0mBoo4cnVKz_SMVpoGUtTl-5QG_a2Qn0NWB1uSLtkU3kgqrkyo-MeH5IxVbM6JqSb0dw9Ok
ReplyDeleteThanks guys! This is all really neat!
ReplyDeleteI love that Brian did the math on paper. That reminds me of undergrad so much.
William Nichols
ReplyDelete30 mins, Googling and fiddling = no progress.
5 mins with pen & paper = problem solved.
Yep. Still nothing quite so flexible as dotted graph paper and a pencil.
ReplyDelete.
ReplyDelete