Alternate (but statistically equal) system for 2d6 [Archive] - Wizards Community

Alternate (but statistically equal) system for 2d6 [Archive] - Wizards Community

Post/Author/DateTime Post
DMMagic
04-18-05, 09:12 PM I was playing one night awhile back and someone was telling me about a set of six-sided dice that instead of the typical 1 2 3 4 5 6 values, had values like 1 1 3 5 7 8 or something. I completely made up those last numbers but I'm pretty sure there were two 1's and values up to 8. Apparently, when two of these dice are thrown, they're statistically identical to throwing 2 regular d6. Apparently it's the only other number system on six-sided dice that does this.

I hope that all made some sense. Anyone know the name of these dice?
Sarella Starshine
04-18-05, 10:27 PM well considering that the totals for 2d6 range from 2-12, i don't see how a single 6-sided die can give the same values statistcally, especially since as you stated it has 2 1's listed which is pysically impossible on 2d6.
Prgrmr@wrk
04-18-05, 10:46 PM I have no idea what those dice are called, but I found 2 combinations of numbers that can give the same average results as a standard d6.
1,1,2,3,6,8
1,1,2,4,5,8
There are several more combinations possible if you don't mind duplicating any extra digits (such as 1,1,2,4,4,8).
I did check to make the averages still work out the same when you roll 2 dice of each number system, and they both end up with an average of 7 when you count all 36 possible results.

If you really want a set of dice like this for some reason, you can buy blank dice and write on them, or put masking tape on normal d6s, and write on them.
Solaris
04-18-05, 11:15 PM They're called Sicherman Dice, and they are numbered {1,2,2,3,3,4} and {1,3,4,5,6,8}.

http://mathworld.wolfram.com/SichermanDice.html
http://www.qbyte.org/puzzles/p041s.html
Plastik
04-18-05, 11:32 PM 2 1s on each die wouldn't work. You'd have 4 possabilities of 2, and the 2d6 setup only has 2. This system would polarize the rolls.
Solaris
04-18-05, 11:55 PM 2 1s on each die wouldn't work. You'd have 4 possabilities of 2, and the 2d6 setup only has 2. This system would polarize the rolls.

Not only that, but it has outcomes outside the range of 2-12, such as 16. The correct (and unique) solution is above.
Manyfist
04-18-05, 11:58 PM 2d6... that suck if you roll two 1's. Also Wouldn't this put your char. with LOW stats? Since the Highest is 12, 2-12, that sounds low.
Prgrmr@wrk
04-19-05, 12:15 AM I was just working with what I was given, which was that the dice were something like "1,1,?,?,?,8".
That, and my misconception that "Statistically Equal" in this case simply meant "Same Average Total".
BeyondFated
04-19-05, 07:51 AM 2d6... that suck if you roll two 1's. Also Wouldn't this put your char. with LOW stats? Since the Highest is 12, 2-12, that sounds low.

I don't think he was talking about character stats. Or rolling 2d6 and comparing it to one dice.

Or maybe he is, I dunno.
Alcari Ambaron
04-19-05, 09:21 AM a single d6 that has the averange equivalent of 2d6??
i know, it could go like 7,7,7,7,7,7....you'll find that this is EXACTLY the averange of 2d6
Da Dinictus
04-19-05, 09:52 AM 2d6... that suck if you roll two 1's. Also Wouldn't this put your char. with LOW stats? Since the Highest is 12, 2-12, that sounds low.
Most likely, rolls like these are for damage rolls :)
DMMagic
04-19-05, 03:32 PM They're called Sicherman Dice, and they are numbered {1,2,2,3,3,4} and {1,3,4,5,6,8}.

http://mathworld.wolfram.com/SichermanDice.html
http://www.qbyte.org/puzzles/p041s.html

Thank you! That's exactly what I was looking for.

I was just working with what I was given, which was that the dice were something like "1,1,?,?,?,8".
That, and my misconception that "Statistically Equal" in this case simply meant "Same Average Total".

I'm pretty sure the Sicherman Dice are in fact statistically equal for every number possible with 2d6. There are probably a few ways to create 2d6 that have an average roll of 7. The Sicherman Dice, however, are the only solution that gives the same odds for each number.

(I'm really not someone who should have an Associate's Degree in Mathematics :rolleye2: )
DMMagic
04-19-05, 03:56 PM Whoops... double posted my previous message. Sorry!

Post/Author/DateTime	Post
DMMagic 04-18-05, 09:12 PM	I was playing one night awhile back and someone was telling me about a set of six-sided dice that instead of the typical 1 2 3 4 5 6 values, had values like 1 1 3 5 7 8 or something. I completely made up those last numbers but I'm pretty sure there were two 1's and values up to 8. Apparently, when two of these dice are thrown, they're statistically identical to throwing 2 regular d6. Apparently it's the only other number system on six-sided dice that does this. I hope that all made some sense. Anyone know the name of these dice?
Sarella Starshine 04-18-05, 10:27 PM	well considering that the totals for 2d6 range from 2-12, i don't see how a single 6-sided die can give the same values statistcally, especially since as you stated it has 2 1's listed which is pysically impossible on 2d6.
Prgrmr@wrk 04-18-05, 10:46 PM	I have no idea what those dice are called, but I found 2 combinations of numbers that can give the same average results as a standard d6. 1,1,2,3,6,8 1,1,2,4,5,8 There are several more combinations possible if you don't mind duplicating any extra digits (such as 1,1,2,4,4,8). I did check to make the averages still work out the same when you roll 2 dice of each number system, and they both end up with an average of 7 when you count all 36 possible results. If you really want a set of dice like this for some reason, you can buy blank dice and write on them, or put masking tape on normal d6s, and write on them.
Solaris 04-18-05, 11:15 PM	They're called Sicherman Dice, and they are numbered {1,2,2,3,3,4} and {1,3,4,5,6,8}. http://mathworld.wolfram.com/SichermanDice.html http://www.qbyte.org/puzzles/p041s.html
Plastik 04-18-05, 11:32 PM	2 1s on each die wouldn't work. You'd have 4 possabilities of 2, and the 2d6 setup only has 2. This system would polarize the rolls.
Solaris 04-18-05, 11:55 PM	2 1s on each die wouldn't work. You'd have 4 possabilities of 2, and the 2d6 setup only has 2. This system would polarize the rolls. Not only that, but it has outcomes outside the range of 2-12, such as 16. The correct (and unique) solution is above.
Manyfist 04-18-05, 11:58 PM	2d6... that suck if you roll two 1's. Also Wouldn't this put your char. with LOW stats? Since the Highest is 12, 2-12, that sounds low.
Prgrmr@wrk 04-19-05, 12:15 AM	I was just working with what I was given, which was that the dice were something like "1,1,?,?,?,8". That, and my misconception that "Statistically Equal" in this case simply meant "Same Average Total".
BeyondFated 04-19-05, 07:51 AM	2d6... that suck if you roll two 1's. Also Wouldn't this put your char. with LOW stats? Since the Highest is 12, 2-12, that sounds low. I don't think he was talking about character stats. Or rolling 2d6 and comparing it to one dice. Or maybe he is, I dunno.
Alcari Ambaron 04-19-05, 09:21 AM	a single d6 that has the averange equivalent of 2d6?? i know, it could go like 7,7,7,7,7,7....you'll find that this is EXACTLY the averange of 2d6
Da Dinictus 04-19-05, 09:52 AM	2d6... that suck if you roll two 1's. Also Wouldn't this put your char. with LOW stats? Since the Highest is 12, 2-12, that sounds low. Most likely, rolls like these are for damage rolls :)
DMMagic 04-19-05, 03:32 PM	They're called Sicherman Dice, and they are numbered {1,2,2,3,3,4} and {1,3,4,5,6,8}. http://mathworld.wolfram.com/SichermanDice.html http://www.qbyte.org/puzzles/p041s.html Thank you! That's exactly what I was looking for. I was just working with what I was given, which was that the dice were something like "1,1,?,?,?,8". That, and my misconception that "Statistically Equal" in this case simply meant "Same Average Total". I'm pretty sure the Sicherman Dice are in fact statistically equal for every number possible with 2d6. There are probably a few ways to create 2d6 that have an average roll of 7. The Sicherman Dice, however, are the only solution that gives the same odds for each number. (I'm really not someone who should have an Associate's Degree in Mathematics :rolleye2: )
DMMagic 04-19-05, 03:56 PM	Whoops... double posted my previous message. Sorry!