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View Full Version : The d20 Collection of Dice, now with only d6s and coins.

Reinboom
2008-02-05, 10:41 PM
Here is a slightly convoluted method at emulating the dice required in a standard d20 session without actually having no more than six sided dice and coins.
In case you are ever stuck in such a unsettling situation, that is.
These methods should all produce the same theoretical probability as the normal dice (no bell curve).

The setup is:
Desired Dice in bold.
What you roll to produce them afterwards.
r means reroll that, or higher, on that dice.
and if something is in curly brackets, you use those for the values of the dice.
a d2 is a coin.
For example,
d100
d6 (r6); d6 (r6) {+0,+5,+10,+15,+20}; d2 {+0,+25}; d2 {+0,+50}

Would mean, roll a d6, reroll a 6.
Then roll another d6, and reroll the 6s.
Except, instead of 1,2,3,4,5 being the possible routes, use 0 for 1, 5 for 2, 10 for 3, 15 for 4, and 20 for 5. Add this number to the first roll.
Flip a coin. A "1" (tails, maybe) is 0. A "2" (heads, maybe) is 25.
Flip another coin. A "1" is a 0. A "2" is 50.

This should produce a random range between 1-100 with no possible outcome occurring more than once.

Now, the dice:
d4
d6 (r5)
d2; d2 {+0,+2}

d8
d6 (r5); d2 {+0,+4}

d10
d6 (r6); d2 {+0,+5}

d12
d6; d2 {+0,+6}

d20
d6 (r6); d2 {+0,+5}; d2 {+0,+10}

d100
d6 (r6); d6 (r6) {+0,+5,+10,+15,+20}; d2 {+0,+25}; d2 {+0,+50}

As I said, convoluted. Handy in times of desperation, however? maybe. :smalltongue:

DementedFellow
2008-02-05, 11:06 PM
not for nothing but wouldn't it be just as simple to flip a coin twice for the d4?
1=TT
2=TH
3=HT
4=HH

Chronos
2008-02-05, 11:41 PM
For that matter, if you're willing to accept re-rolls, you can do it all with nothing but coins. The downside, of course, is that you can't guarantee any finite number of rolls.

If you do want to guarantee any particular finite number of rolls, and you want to simulate all of the standard dice, you need a d2, a d3, and a d5 (or dice which are integer multiples of those).

Reinboom
2008-02-05, 11:59 PM
Aye, I had just the 2d2 thing written down before in my look at doing all coins.
However, since there would be an insane amount of "reflipping" amount involved with d10 (since it would require a 'd16') and d20 ('d32') I decided to scrap the idea - and thus - forgot about just two coins.
This is also an answer to Chronos.

Chronos
2008-02-06, 12:30 AM
However, since there would be an insane amount of "reflipping" amount involved with d10 (since it would require a 'd16') and d20 ('d32') I decided to scrap the idea - and thus - forgot about just two coins.It's not actually quite that bad, if you can keep track of the math. A d10 will only take an average of 3.322 flips for a "roll", and a d20 would take 4.322 . The general method is to divide the interval from 0 to 1 into n equal pieces, and then generate a random number between 0 and 1 using the coin. Keep generating bits until you're certain which segment of the interval you're in, and assign one number to each segment. Assuming that the bookkeeping is cheap but that random number generation is expensive (as is the case in a computer, for example), this is the most efficient method possible.

Whoops, sorry about that, SweetRein... I hope that wasn't a relative of yours.

Magnor Criol
2008-02-06, 01:05 AM
Psh. You crazy kids. What are you trying to do, put math in DnD or something? Pshaw I say! Pshaw!

On a serious note, nice job with the number crunching. Impressive stuff, at least to me; that's well beyond my ken. I think I'll stick with my bag o' dice, though. :D

Project_Mayhem
2008-02-06, 05:57 AM
you can do everything with just d10s too. Work out the highest multiple of your number (say d12) that goes in to 100 (in this case 96). Then roll, reroll anything higher than this, and divide the answer by whatever you multiplyed the original number by (in this case 8)

Sounds complicated, but its easy, especially to emulate d20s. I used to play like this before I bought dice other than d6 and d10

Jack Zander
2008-02-06, 02:09 PM
you can do everything with just d10s too. Work out the highest multiple of your number (say d12) that goes in to 100 (in this case 96). Then roll, reroll anything higher than this, and divide the answer by whatever you multiplyed the original number by (in this case 8)

Sounds complicated, but its easy, especially to emulate d20s. I used to play like this before I bought dice other than d6 and d10

Doesn't that give you a bell curve though?

Chronos
2008-02-06, 05:38 PM
Doesn't that give you a bell curve though?Nope, still perfectly uniform.

Lupy
2008-02-06, 09:04 PM
Nooooo! It hurts! I heard this game was magic! Not math!

Seriously, I think someone passes their math test.

BTW :elan: got a D- this time! He passed!