Binary dice, has it been done before?
Atabet2
I came up with this idea after reading the various posts about dice on this
newsgroup. Does anyone know if there exists a set of binary dice? My vision of
them would simply be a number of coins, or better yet, flattened gems, that had
a zero on one side and a number on the other. For instance, in a set there
would be a coin with 0 on one side and 1 on the other, then there would be one
with a 2 and a 0, then a 4/0, an 8/0, a 16/0 and so on. When you roll, you
could just roll all the necessary coins and total the result. This could be
used to generate a completely random number in a certain range. There would
never be any number rolled more than others, as happends when you roll more
than one die together. One could use the notation dB to represent the roll.
Lets say you need the number from 0 - 23 randomly generated. You would roll
what is called 23dB and use the coins 0/1, 0/2, 0/4, 0/6, 0/8, and 0/16 (the
highest die rolled should always be lower than the highest nubmer required,
notice we stopped at 0/16 and not 0/32). Then you simply start adding up the
numbers starting with the lowest one. If, while adding, the next highest die
puts you over the max possible roll, simply ignore the rest of the higer dice.
For instance, rolling 23dB lets say you get the numbers (starting from lowest
coin and working up) 0 2 4 0 16. This would give you a total of 22. Then let's
say you roll 0 2 4 8 16. This is only worth 14 since adding the sixteen puts
you over. I'm pretty sure this system would be completely random. It would also
be very useful in a number of cases. It also allows you to roll really large
numbers without too many dice. Rolling 200dB only requires 7 dice. I thought it
was pretty cool since it's haighly versatile and pretty unique. I essance you
could have D17 D294 D302, and have them be completely random and fair. Please
let me know what you think.
Aaron Day
>
> I came up with this idea after reading the various posts about dice on this
> newsgroup. Does anyone know if there exists a set of binary dice? My vision of
> them would simply be a number of coins, or better yet, flattened gems, that had
> a zero on one side and a number on the other. For instance, in a set there
> would be a coin with 0 on one side and 1 on the other, then there would be one
> with a 2 and a 0, then a 4/0, an 8/0, a 16/0 and so on. When you roll, you
> could just roll all the necessary coins and total the result. This could be
> used to generate a completely random number in a certain range. There would
> never be any number rolled more than others, as happends when you roll more
> than one die together. One could use the notation dB to represent the roll.
> Lets say you need the number from 0 - 23 randomly generated. You would roll
> what is called 23dB and use the coins 0/1, 0/2, 0/4, 0/6, 0/8, and 0/16 (the
> highest die rolled should always be lower than the highest nubmer required,
If you actually check the number you'll find that this methods doens't
create an even spread. For example, by your explanation if wanted to do
a D10 this way I'd roll 0/1, 0/2, 0/4, and 0/8. However, these dice will
actually give me 16 results. The results above 10 (1011 -> 1111) would
result in 3 through 7 if you ignored the high die. With some numbers
apearing twice, you've got a pretty screwed up probability curve.
Aaron
john v verkuilen
dice to get anywhere, at least a lot more than if you allow for other bases.
It's easier just to figure out the right representation to get close and just
use that. For instance, if I need a D27, the easiest thing to do is roll a
D4 and a D8, taking 8*(D4 - 1) + D8, rerolling entirely if 28 comes up. This
would probably be a lot more efficient than binary dice.
Also, like dedicated D3s or D4s made like a D8, I think it could be hard
to tell them apart from other dice unless you made them different shapes
or colors.
Jay
--
J. Verkuilen ja...@staff.uiuc.edu
There is no such thing as the Law of Small Numbers.
Frank J. Perricone
> For instance, rolling 23dB lets say you get the numbers (starting from lowest
> coin and working up) 0 2 4 0 16. This would give you a total of 22. Then let's
> say you roll 0 2 4 8 16. This is only worth 14 since adding the sixteen puts
> you over.
Then there's two different ways to roll a 14 (at least), but only one way
to roll a 22, which means the dice aren't "fair" (not an equal probability
of any of the rolls, and it's non-obvious, without stopping to think about
it, how the probabilities are skewed in a specific case). The only way to
make them fair on something like 23dB would be to reroll anything over 23.
--
* Frank J. Perricone * hawt...@sover.net * http://www.sover.net/~hawthorn
Prism: http://www.sover.net/~hawthorn/Prism/
Just because we aren't all the same doesn't mean we have nothing in common
Just because we have something in common doesn't mean we're all the same
John Kim
Atabet2 <ata...@aol.com> wrote:
>Does anyone know if there exists a set of binary dice? My vision of
>them would simply be a number of coins, or better yet, flattened gems,
>that had a zero on one side and a number on the other.
Well, you can just use coins. The _Prince Valiant_ RPG
(from Chaosium, by Greg Stafford) did this. It is essentially a
"dice pool" mechanism where the player tosses a number of coins
equal to his stat and counts the "heads" as successes which must
be greater than the required number.
Personally, I find that in most circumstances rolling a
few dice (i.e. 2d6 or 3d6) is easier than tossing a number of coins.
The exception would be when you are outdoors and thus lacking a
flat surface. However, in these cases picking up tossed coins is
something of a pain. I think for outdoors a millisecond stopwatch
or cards are the best bet.
-*-*-*-*-*-*-
>
[...skipping binary number rolling...]
>
>I'm pretty sure this system would be completely random. It would also
>be very useful in a number of cases. It also allows you to roll really
>large numbers without too many dice. Rolling 200dB only requires 7 dice.
>I thought it was pretty cool since it's haighly versatile and pretty
>unique. I essance you could have D17 D294 D302, and have them be
>completely random and fair.
Others have pointed out that your system as described doesn't
give flat results. In order to be fair, you need to reroll all the
dice if the expanded number is over the maximum. I would point out
that most of these are more easily done using d10s. For those of us
using arabic numerals, at least, d10's are much easier to use for
these purposes than d2's.
i.e. For d294, roll a d3 (i.e. d6/2), a d10, and a d10
for the hundreds, tens, and ones digits, respectively. If the
result is 295-300, re-roll. For a d72, roll a d8 (tens) and
a d10 (ones), re-rolling if it is 73-80.
Ed Chauvin IV
rec.games.frp.misc, Frank J. Perricone used a less than adequate
newsreader Forte Agent 1.6/32.525
to describe Re: Binary dice, has it been done before?
>On 12 Nov 1999 21:07:43 GMT, ata...@aol.com (Atabet2) wrote:
>
>> For instance, rolling 23dB lets say you get the numbers (starting from lowest
>> coin and working up) 0 2 4 0 16. This would give you a total of 22. Then let's
>> say you roll 0 2 4 8 16. This is only worth 14 since adding the sixteen puts
>> you over.
>
>Then there's two different ways to roll a 14 (at least), but only one way
>to roll a 22, which means the dice aren't "fair" (not an equal probability
>of any of the rolls, and it's non-obvious, without stopping to think about
>it, how the probabilities are skewed in a specific case). The only way to
>make them fair on something like 23dB would be to reroll anything over 23.
Or use 23 0/1 coins. : (
Sounds like a great idea on the surface, and actually works well for
certain numbers (2, 4, 8, 16...), but severely flawed for others.
Just a thought for the more mathematically inclined:
Would this work for 23 (and other numbers using the same principle),
use 0/2, 04, 0/8 and enough 0/1's (9 in this case) to add up to 23?
Or are there still some weird probabilities going on that I'm not
seeing?
Ed Chauvin IV
--
As our bodies are armoured with adamantium, our souls are protected
with our loyalty. As our bolters are charged with death for the
Emperor's enemies, our thoughts are charged with his wisdom. As our
ranks advance, so does our devotion, for are we not Marines? Are we
not the chosen of the Emperor, his loyal servants unto death?
-Chaplain Fergus Nils
An address to the defenders of Portrein.
Robin Lim
Atabet2 <ata...@aol.com> wrote in message
news:19991112160743...@ng-cm1.aol.com...
> Greetings,
> could have D17 D294 D302, and have them be completely random and fair.
> let me know what you think.
Go to your museum store and pick up some Egyptian 'dice', or you can flip
over tarot cards and read for heads or tails.
rob
Rachel E. Taylor
wrote:
I'm no stats expert, but if there's a 50/50 chance your 0/16
"dice" comes up 0, that seems to indicate to me that there
must be a 50% chance of rolling 15 or less. Since 15 is
greater than 11.5 the resulting distribution is skewed
toward the high-end of the spread.
On the other hand, it seems to me that to get any
particularly number the dice HAVE to land in one pattern,
and one only, no matter what the number. There's only way
for each number to be created. That does sound pretty fair
and random to me.
But then I'm no stats expert.
That said, it is an interesting idea. And as you pointed
out, can be used to generate high ranges from only a few
dice.
I'd be interested to hear more mathematically aware people
give this the once-over.
>Greetings,
>I came up with this idea after reading the various posts about dice on this
>newsgroup. Does anyone know if there exists a set of binary dice? My vision of
>them would simply be a number of coins, or better yet, flattened gems, that had
>a zero on one side and a number on the other. For instance, in a set there
>would be a coin with 0 on one side and 1 on the other, then there would be one
>with a 2 and a 0, then a 4/0, an 8/0, a 16/0 and so on. When you roll, you
>could just roll all the necessary coins and total the result. This could be
>used to generate a completely random number in a certain range. There would
>never be any number rolled more than others, as happends when you roll more
>than one die together. One could use the notation dB to represent the roll.
>Lets say you need the number from 0 - 23 randomly generated. You would roll
>what is called 23dB and use the coins 0/1, 0/2, 0/4, 0/6, 0/8, and 0/16 (the
>highest die rolled should always be lower than the highest nubmer required,
>notice we stopped at 0/16 and not 0/32). Then you simply start adding up the
>numbers starting with the lowest one. If, while adding, the next highest die
>puts you over the max possible roll, simply ignore the rest of the higer dice.
>For instance, rolling 23dB lets say you get the numbers (starting from lowest
>coin and working up) 0 2 4 0 16. This would give you a total of 22. Then let's
>say you roll 0 2 4 8 16. This is only worth 14 since adding the sixteen puts
>you over. I'm pretty sure this system would be completely random. It would also
>be very useful in a number of cases. It also allows you to roll really large
>numbers without too many dice. Rolling 200dB only requires 7 dice. I thought it
>was pretty cool since it's haighly versatile and pretty unique. I essance you
>could have D17 D294 D302, and have them be completely random and fair. Please
>let me know what you think.
Rachel Taylor
Frank J. Perricone
wrote:
> Would this work for 23 (and other numbers using the same principle),
> use 0/2, 04, 0/8 and enough 0/1's (9 in this case) to add up to 23?
> Or are there still some weird probabilities going on that I'm not
> seeing?
There's only one way to get 23 this way, but there are lots and lots and
lots of ways to get 1, so the probabilities are way out of whack; and
again, it's non-intuitive what the probabilities are, for anyone but a real
math whiz, for any given "total die size".
One other problem with the binary dice is that it's possible to roll zero;
okay, that's not a problem, but it should be mentioned since people are
inclined to think of a "23-sided die" as having 23 possible outcomes, not
24.
Frank J. Perricone
<rachel-...@freeuk.com> wrote:
> On the other hand, it seems to me that to get any
> particularly number the dice HAVE to land in one pattern,
> and one only, no matter what the number. There's only way
> for each number to be created. That does sound pretty fair
> and random to me.
Unfortunately that's not the case. Here's two ways to roll 14: 0 2 4 8 16
and 0 2 4 8 0. But only one way to roll 22: 0 2 4 0 16.
Atabet2
of the system. Thanks for pointing out the errors (even though I didnt need 15
people restating the same thing : ) I'm going to try a few different things and
try to work out the double occurences. I think that mutli faceted jewels that
basically had only two sides that you could balance them on would be much
better than using coins and would be easier to roll and pickup. Again, thanks
for the advice.
Cheers,
Matthew
woodelf
(Atabet2) wrote:
> numbers starting with the lowest one. If, while adding, the next highest die
> puts you over the max possible roll, simply ignore the rest of the higer dice.
[snip]
> could have D17 D294 D302, and have them be completely random and fair. Please
> let me know what you think.
to get completely fair, you need to just throw out the result and reroll
if it's over the max. otherwise, certain results will be more frequent,
since there's more than one way to generate them.
--
----sorry for typos; i'm switching to dvorak keyboard----
woodelf <*>
woo...@rpg.net
http://members.home.net/woodelph/
I did not realize that similarity was required for the exercise of
compassion. --Delenn
John Rudd (yes, that's really my email address)
You could use any even sided die, and just use the even sides as 0 and the
odd sides as 1. (Some of the Mutant Chronicles board games came with dice
that fit that bill... red d6's with white explosions on 3 sides). (the
specific games were "Siege of the Citadel" and "Fury of the Clansmen")
Also, there isn't really anything different between this technique and
using d10's for powers of 10 (percentile dice by having a 1's die and a
10's die, d1000 by rolling 3 d10, one for 1's, one for 10's, one for
100's). The only difference between what you're talking about and this is
the number base in quesiton.
Plus, the required number of d2's required goes up faster than d10's.
Desired range number of d2's number of d10's
1-10 4 (d16) 1 (d10)
1-100 7 (d128) 2 (d100)
1-1000 10 (d1024) 3 (d1000)
Now, obviously, the d10's have some advantage here because I choose powers
of 10.. but if we choose powers of 2, you still have d2's going up faster
than d10's.
Desired range number of d2's number of d10's
1-2 1 (d2) 1 (d10/5 (a d2))
1-4 2 (d4) 1 (d10/2 (a d5))
1-8 3 (d8) 1 (d10)
1-16 4 (d16) 2 (2d10 - 1 (1-19))
1-32 5 (d32) 2 (d10/2,d10 (a d50))
1-64 6 (d64) 2 (d100)
1-128 7 (d128) 3 (d10/5,d100 (a d200))
1-256 8 (d256) 3 (d10/2,d100 (a d500))
1-512 9 (d512) 3 (d1000)
(the d50, d200, and d500 work by using the d10/2 or d10/5 as your first
digit, and then using the other d10's as your 10's and 1's digits, like the
way an old fashined d20 works (roll a d6 and a d10, if the d6 is 4-6, add
10 to the d10), or the way a d100 and d1000 work)
In both cases, the off power (d2's in the first chart, d10's in the second)
have some useless (throw away/re-roll) values that alter the probabilities,
as others have pointed out ... but it's still apparent that if you use a
small base you require more dice as you go up in range than if you pick a
large base. Plus, d10's are readily available.
The disadvantage of d10's is you get larger throw-away ranges. You can get
smaller throw away/re-roll ranges by mixing in smaller dice (a d40 (d4 for
10's place, d10 for 1's place (d4*10 + d10), just like an old fashioned
d20) instead of the d50, a d80 (d8,d10) instead of d100, a d150 ((2d8-2)*10
+ d10) instead of the d200, a d300 (d3, d100) instead of the d500, and a
d600 (d6, d100) instead of the d1000). However, those throw away ranges
have something to do with why I think you don't tend to see many "powers of
N" dice systems.
Personally, I prefer dF's (Fudge), varying number of fixed success dice
(Shadowrun with d6's and Storyteller with d10's), or fixed dice (all d6's
or all d10's or all d100's, such as WEG's d6 system, Hero, Rolemaster's
almost exclusive use of d100's, etc) systems over trying to have N
different randomizers for nearly N different situations. Pick 1 flexible
randomizer and apply it usefully. :-)
(and, I prefer them in that order... Fudge first, Shadowrun/Storyteller
second (even acknowleging the probability weirdness of Storyteller), and
then WEG/Hero/RM type systems third, and N different randomizers type games
(like D&D) last. I'm not sure where in there to put games like Castle
Falkenstein, which uses a standard card deck, and I've never played a
randomizer-less game, like Amber .. nor an r-s-p based game.)
--
John "kzin" Rudd kz...@domain.org http://www.domain.org/users/kzin
Truth decays into beauty, while beauty soon becomes merely charm. Charm
ends up as strangeness, and even that doesn't last. (Physics of Quarks)
-----===== Kein Mitleid Fu:r MicroSoft (www.kmfms.com) ======-----
Ed Chauvin IV
used a less than adequate newsreader Mozilla 4.61 [en] (Win98; U)
>You could use any even sided die, and just use the even sides as 0 and the
>odd sides as 1.
Hm. Barring the Egyptian "prism" style dice, I've never seen any dice
with an odd number of sides. Anybody?
John Rudd (yes, that's really my email address)
>
> John Rudd wrote:
>
> >You could use any even sided die, and just use the even sides as 0 and the
> >odd sides as 1.
>
> Hm. Barring the Egyptian "prism" style dice, I've never seen any dice
> with an odd number of sides. Anybody?
>
Yeah, according to http://hjem.get2net.dk/Klaudius/Dice.htm (which I
grabbed from another dice thread on here), the only odd dice are either
prismic/cigar/cylindrical type shapes, or a sphere (sides = 1). Though, if
you do it right, you can have any number of sides on a faceted sphere ...
you're just not guaranteed to have it be usable (spherical d100's were
really annoying).
Ed Chauvin IV
rec.games.frp.misc, John Rudd (yes, that's really my email address)
used a less than adequate newsreader Mozilla 4.61 [en] (Win98; U)
before?)
>Ed Chauvin IV wrote:
>>
>> John Rudd wrote:
>>
>> >You could use any even sided die, and just use the even sides as 0 and the
>> >odd sides as 1.
>>
>> Hm. Barring the Egyptian "prism" style dice, I've never seen any dice
>> with an odd number of sides. Anybody?
>>
>
>Yeah, according to http://hjem.get2net.dk/Klaudius/Dice.htm (which I
>grabbed from another dice thread on here), the only odd dice are either
>prismic/cigar/cylindrical type shapes, or a sphere (sides = 1). Though, if
>you do it right, you can have any number of sides on a faceted sphere ...
>you're just not guaranteed to have it be usable (spherical d100's were
>really annoying).
Hell, d30's are annoying. Of course, I get upset when the d10's roll
across the table on that one edge and don't seem to want to stop
before falling right off the table.
Grrr.
back...@my-deja.com
> I came up with this idea after reading the various posts about dice on this
> newsgroup. Does anyone know if there exists a set of binary dice? My vision of
> them would simply be a number of coins, or better yet, flattened gems, that had
> a zero on one side and a number on the other. For instance, in a set there
> would be a coin with 0 on one side and 1 on the other, then there would be one
> with a 2 and a 0, then a 4/0, an 8/0, a 16/0 and so on. When you roll, you
> could just roll all the necessary coins and total the result. This could be
> used to generate a completely random number in a certain range.
<snip>
Check out: http://www.hyperbooks.com/kiss
For the KISS d2 RPG rules which make use of Binary or d2 dice.
--
Wilf K. Backhaus
Sent via Deja.com http://www.deja.com/
Before you buy.
Torben AEgidius Mogensen
>Yeah, according to http://hjem.get2net.dk/Klaudius/Dice.htm (which I
>grabbed from another dice thread on here), the only odd dice are either
>prismic/cigar/cylindrical type shapes, or a sphere (sides = 1). Though, if
>you do it right, you can have any number of sides on a faceted sphere ...
>you're just not guaranteed to have it be usable (spherical d100's were
>really annoying).
Putting prisms on a sphere doesn't help you. In order for such a die
to be fair, the facets have to be evenly distributed. Apart from
putting the facets around the equator of the sphere, for most numbers
there doesn't exist even distributions. My guess is that Klaus'
enumeration of fair dice also covers spheres with facets.
Torben Mogensen (tor...@diku.dk)