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Pen & Paper Roleplaying Central => Pen and Paper Roleplaying Games (RPGs) Discussion => Topic started by: Ladybird on August 18, 2013, 10:59:46 AM

Title: Alternate rolls with same probabilities as 2d6
Post by: Ladybird on August 18, 2013, 10:59:46 AM
Quick question which doesn't really belong anywhere specific on the forum.

There is an alternate way of distributing numbers across two (Not identical!) six-sided dice, which has the same result probabilities as rolling regular 2d6 (ie, 1/36 rolls will be a 2, 2/36 will be a 3, etc). This isn't actually a quiz, by the way, I'm pretty sure I have seen this somewhere (I know about this (http://www.chiark.greenend.org.uk/~sgtatham/dice/), btw).

I've got a dremel, some blank d6, and a slow afternoon, so I'd like to create some dice like this, but I can't for the life of me remember what the alternate distributions are, despite some googling. Does anyone remember what this alternate distribution is called, or what the numbers are?
Title: Alternate rolls with same probabilities as 2d6
Post by: Ladybird on August 18, 2013, 11:14:29 AM
GOT IT. Sicherman dice (http://en.wikipedia.org/wiki/Sicherman_dice).
Title: Alternate rolls with same probabilities as 2d6
Post by: 3rik on August 18, 2013, 11:16:55 AM
You're looking for the Sicherman dice: 1, 2, 2, 3, 3, 4 and 1, 3, 4, 5, 6, 8.

Sicherman dice - Wikipedia (http://en.wikipedia.org/wiki/Sicherman_dice)

EDIT: you beat me to it while I was posting
Title: Alternate rolls with same probabilities as 2d6
Post by: apparition13 on August 18, 2013, 02:17:40 PM
Which raises the obvious question, why? How will the different dice be helpful in accomplishing whatever it is you are trying to do? My assumption would be something to do with the actual numbers on the dice influencing things in some way, but it could easily be wrong.
Title: Alternate rolls with same probabilities as 2d6
Post by: Brad J. Murray on August 18, 2013, 02:23:04 PM
Quote from: apparition13;682711Which raises the obvious question, why? How will the different dice be helpful in accomplishing whatever it is you are trying to do? My assumption would be something to do with the actual numbers on the dice influencing things in some way, but it could easily be wrong.

Yes, the individual numerical distribution is different, so if you tied some effect to the value of the highest or lowest die, that would have a wider range than on 2d6 which might be interesting. Also, you have two dice with very different linear ranges, and those might each also be interesting -- one generates lower values on average and the other quite a bit higher.
Title: Alternate rolls with same probabilities as 2d6
Post by: Ladybird on August 18, 2013, 03:30:47 PM
Quote from: apparition13;682711Which raises the obvious question, why? How will the different dice be helpful in accomplishing whatever it is you are trying to do? My assumption would be something to do with the actual numbers on the dice influencing things in some way, but it could easily be wrong.

You're overthinking this. Sometimes, just doing something is it's own reward.

Anyway, now I have a variant 2d6 set, and I've learned a bit about engraving, so mission accomplished.

Quote from: Brad J. Murray;682713Yes, the individual numerical distribution is different, so if you tied some effect to the value of the highest or lowest die, that would have a wider range than on 2d6 which might be interesting. Also, you have two dice with very different linear ranges, and those might each also be interesting -- one generates lower values on average and the other quite a bit higher.

The original Mongoose Traveller combat rules did something interesting with the 2d6 rolled (Like, one became your initiative next turn, and the other became your damage, or something). Baking that sort of question into variant dice themselves could be interesting; a 2d6 system where total indicated binary success / fail, one die indicated speed, and the other indicated quality of result, say.
Title: Alternate rolls with same probabilities as 2d6
Post by: Dirk Remmecke on August 18, 2013, 04:40:30 PM
Quote from: Ladybird;682731Anyway, now I have a variant 2d6 set, and I've learned a bit about engraving, so mission accomplished.

Pictures, or it didn't happen!
Title: Alternate rolls with same probabilities as 2d6
Post by: noisms on August 18, 2013, 05:27:27 PM
Quote from: Ladybird;682731You're overthinking this. Sometimes, just doing something is it's own reward.

Anyway, now I have a variant 2d6 set, and I've learned a bit about engraving, so mission accomplished.



The original Mongoose Traveller combat rules did something interesting with the 2d6 rolled (Like, one became your initiative next turn, and the other became your damage, or something). Baking that sort of question into variant dice themselves could be interesting; a 2d6 system where total indicated binary success / fail, one die indicated speed, and the other indicated quality of result, say.

I really like that. A bit like the way ORE works except just with two dice.

Another thought: with the Sicherman dice you have one "low-average" dice and one "high but risky" dice. That has potential to me as a defence/offence pairing: you can assign one dice to defence and one to offence, either having a not very impressive offence score and a potentially very high defence score, and vice-versa.
Title: Alternate rolls with same probabilities as 2d6
Post by: Brad J. Murray on August 18, 2013, 05:37:40 PM
Quote from: noisms;682757Another thought: with the Sicherman dice you have one "low-average" dice and one "high but risky" dice. That has potential to me as a defence/offence pairing: you can assign one dice to defence and one to offence, either having a not very impressive offence score and a potentially very high defence score, and vice-versa.

I thought about that too, but there's nothing very risky about the high die. I'd roll it every time if I had the choice between the two.

Low die: mean 7.5; std dev 1.04
High die: mean 13.5; std dev 2.4
Title: Alternate rolls with same probabilities as 2d6
Post by: noisms on August 18, 2013, 05:41:30 PM
Quote from: Brad J. Murray;682761I thought about that too, but there's nothing very risky about the high die. I'd roll it every time if I had the choice between the two.

Low die: mean 7.5; std dev 1.04
High die: mean 13.5; std dev 2.4

Yeah, "high but risky" was the wrong phrase, but you get what I mean. Either a good attack and mediocre defence or a good defence and mediocre attack.
Title: Alternate rolls with same probabilities as 2d6
Post by: Brad J. Murray on August 18, 2013, 05:56:15 PM
Quote from: noisms;682762Yeah, "high but risky" was the wrong phrase, but you get what I mean. Either a good attack and mediocre defence or a good defence and mediocre attack.

I agree, as a trade-off it might be kind of cool.
Title: Alternate rolls with same probabilities as 2d6
Post by: noisms on August 18, 2013, 05:59:55 PM
Quote from: Brad J. Murray;682766I agree, as a trade-off it might be kind of cool.

I also like the idea of one dice being initiative and one damage, especially in, say OD&D. You can sacrifice initiative (i.e. use the low dice) in the interest of picking your moment and building momentum for a big knock-out blow (i.e. the high dice), or act quickly (use the high dice for initiative) but only deliver glancing blows as a result (low dice for damage).
Title: Alternate rolls with same probabilities as 2d6
Post by: Ladybird on August 18, 2013, 06:23:14 PM
Quote from: Dirk Remmecke;682746Pictures, or it didn't happen!

Tada. I need to find my model paint to do the dots properly, though.

The thing I learnt about engraving was "I need more practice, because this is awful" (I'm not going to show you the test dice I ruined trying this, but I had a lot of difficulty getting a straight, deep enough line, and had no faith in my ability to do curves for the 2 / 3 / 5 / 8), so I went with spots instead. They seem to roll reasonably despite the (Obvious) imperfections, so that's okay.