Dice: generating "Zocchi results" using "normal" polyhedrons

goodmangames · **Posted:** Mon Jun 13, 2011 7:39 am

Several people have asked this, so here is my simple summary of how to achieve "Zocchi results" with "normal" polyhedrons. (Funny that the d4 is now "normal" -- it sure seemed weird when I was a kid!) In other words, this is how to simulate a d3, d5, d7, etc. with your normal dice.

What's a control die? Several of the examples below require a "control die." A control die means you roll 1d6 along with the first die, and the 1d6 result indicates whether you add to the first die. For example, to simulate 1d24, you can roll 1d12 with a control die. If the control die is even, take the 1d12 result "straight"; if the control die is odd, take the 1d12 result and add 12.

How to simulate Zocchi dice results:
d3: Roll 1d6 and divide by 2.
d5: Roll 1d10 and divide by 2.
d7: (Option A) Roll 1d8 and re-roll on an 8. (Option B) Roll 1d14 and divide by 2 (if you have a d14, which you probably don't if you're reading this, but just in case...)
d14: Roll 1d20 and re-roll on 16-20.
d16: (Option A) Roll 1d8 with a control die (add +0 or +8 depending on the control die). (Option B) Roll 1d20 and re-roll on 17-20.
d24: (Option A) Roll 1d12 with a control die (add +0 or +12 depending on the control die). (Option B) Roll 1d30 and re-roll on 25-30.
d30: Roll 1d10 with a 6-sided control die (add +0 on 1-2, +10 on 3-4, or +20 on 5-6).

Note: There are multiple ways to achieve the Zocchi dice results. The ones noted above are just the simplest ones I've personally come across. If you have an even better preferred method, let us know by posting here!

GnomeBoy · **Posted:** Mon Jun 13, 2011 9:29 am

Good idea for a thread, but

goodmangames wrote:

d30: Roll 1d20 with a 6-sided control die (add +0 on 3-4, or +10 on 5-6).

whothewhatnow? :?:

What do you do with a control result of 1-2?

I'd use d30: Roll 1d10 with a control die (1-2 add zero, 3-4 add 10, 5-6 add 20).

For what it's worth, I make the control high/low to match the end result high/low (rather than even/odd = high/low).

jmucchiello · **Joined:** Mon Mar 14, 2011 5:28 am **Posts:** 779

This is my edit, fixing d30 and adding "options" to the control die explanation.

goodmangames wrote:

Several people have asked this, so here is my simple summary of how to achieve "Zocchi results" with "normal" polyhedrons. (Funny that the d4 is now "normal" -- it sure seemed weird when I was a kid!) In other words, this is how to simulate a d3, d5, d7, etc. with your normal dice.

What's a control die? Several of the examples below require a "control die." If you have ever rolled a d100 using two 10-sided dice, you have already mastered the use of the control die. A control die means you roll a second die (usually a 1d6) along with the first die, and the 1d6 result indicates whether you add to the first die. For example, to simulate 1d24, you can roll 1d12 with a control die. (OPTION A) If the control die is even, take the 1d12 result "straight"; if the control die is odd, take the 1d12 result and add 12. (OPTION B) If the control die is low (1, 2, or 3), take the 1d12 result "straight"; if the control die is high (4, 5, or 6), take the 1d12 result and add 12. Choose between OPTION A and OPTION B at the beginning of the evening and stick with that choice so everyone looking at your die rolls gets the same result. I prefer OPTION B because sometimes there are more than two results needed on the control die (see d30 below).

How to simulate Zocchi dice results:
d3: Roll 1d6 and divide by 2.
d5: Roll 1d10 and divide by 2.
d7: (Option A) Roll 1d8 and re-roll on an 8. (Option B) Roll 1d14 and divide by 2 (if you have a d14, which you probably don't if you're reading this, but just in case...)
d14: (Option A) Roll 1d20 and re-roll on 16-20. (Option B) Roll a d8 and re-roll on an 8 plus a control die (add +0 or +7 depending n the control die) Roll the control die after knowing the d8 did not roll an 8.
d16: (Option A) Roll 1d8 with a control die (add +0 or +8 depending on the control die). (Option B) Roll 1d20 and re-roll on 17-20.
d24: (Option A) Roll 1d12 with a control die (add +0 or +12 depending on the control die). (Option B) Roll 1d30 and re-roll on 25-30.
d30: Roll 1d10 with a 6-sided control die (add +0 on 1-2, +10 on 3-4, or +20 on 5-6).

finarvyn · **Posted:** Mon Jun 13, 2011 10:01 am

GnomeBoy wrote:

goodmangames wrote:

d30: Roll 1d20 with a 6-sided control die (add +0 on 3-4, or +10 on 5-6).

whothewhatnow? :?:

What do you do with a control result of 1-2? I'd use d30: Roll 1d10 with a control die (1-2 add zero, 3-4 add 10, 5-6 add 20).

I've always done it as you suggested with the d10.

jmucchiello · **Joined:** Mon Mar 14, 2011 5:28 am **Posts:** 779

finarvyn wrote:

I think it was supposed to be +0 on a 1-4, or +10 on a 5-6

I hope not, that would be non-linear.

d20+0 on 1-4 and d20/2+20 on 5-6 works, but has high potential for confusion.

Harley Stroh · **Posted:** Mon Jun 13, 2011 10:17 am

Traveller over on the Acaeum offered up these formulas:

Traveller wrote:

d3 = 1d6/2. round up
d5 = 1d20/4, round up or 1d10/2, round up (thanks to Sardan for the d10 version)
d7 = 2d4-1
d14 = (1d8+2d4)-2 or (2d6+1d4)-2
d16 = 3d6-2
d24 = (1d10+2d8)-2 or (2d10+1d6)-2
d30 = (1d20+2d6)-2, (1d12+2d10)-2, or (2d12+1d8)-2

//H

jmucchiello · **Joined:** Mon Mar 14, 2011 5:28 am **Posts:** 779

Harley Stroh wrote:

Traveller over on the Acaeum offered up these formulas:

Traveller wrote:

d3 = 1d6/2. round up
d5 = 1d20/4, round up or 1d10/2, round up (thanks to Sardan for the d10 version)
d7 = 2d4-1
d14 = (1d8+2d4)-2 or (2d6+1d4)-2
d16 = 3d6-2
d24 = (1d10+2d8)-2 or (2d10+1d6)-2
d30 = (1d20+2d6)-2, (1d12+2d10)-2, or (2d12+1d8)-2

//H

And most of the are non-linear. What good are non-linear equations for simulating Zocchie dice?

meinvt · **Posted:** Mon Jun 13, 2011 1:26 pm

jmucchiello wrote:

Harley Stroh wrote:

Traveller over on the Acaeum offered up these formulas:

Traveller wrote:

d3 = 1d6/2. round up
d5 = 1d20/4, round up or 1d10/2, round up (thanks to Sardan for the d10 version)
d7 = 2d4-1
d14 = (1d8+2d4)-2 or (2d6+1d4)-2
d16 = 3d6-2
d24 = (1d10+2d8)-2 or (2d10+1d6)-2
d30 = (1d20+2d6)-2, (1d12+2d10)-2, or (2d12+1d8)-2

//H

And most of the are non-linear. What good are non-linear equations for simulating Zocchie dice?

Agreed! This only adds to the confusion unless you are telling folks what not to do.

GnomeBoy · **Posted:** Mon Jun 13, 2011 8:18 pm

Reboot?

birthright · **Joined:** Thu Jun 09, 2011 3:44 am **Posts:** 8

Buy a set of BLANK polyhedral dice (i.e. a set of blank d4, d6, d8, d10, d12, d20) then:

For:
d3 use the blank d6 and label it: 1,2,3,1,2,3
d5 use the blank d10 and label it: 1,2,3,4,5,1,2,3,4,5
d7 use the blank d8 and label it: 1,2,3,4,5,6,7,R (R means re-roll the die)
d14/d16 use the blank d20 and label it: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,R/15,R/16,R,R,R,R (when rolling for d14 treat the R/15 and R/16 faces as re-rolls)
d24 use the blank d4 and label it: 0,0,12,12 then throw it alongside a standard d12 and add the two results
d30 use the blank d12 and label it: 0,0,0,0,10,10,10,10,20,20,20,20 then throw it alongside a standard d10 and add the two results (treat 0+0 as 30 of course!)

There. Zochii dice simulated for under $3. You just need to re-roll occasionally - the worst offender being the d14 where you'll need to re-roll 6 of 20 rolls (30% of the time).

Machpants · **Posted:** Tue Jun 14, 2011 1:54 am

Hehe I was going to quote you from RPGNet here, but ... you beat me too it

birthright · **Joined:** Thu Jun 09, 2011 3:44 am **Posts:** 8

Machpants wrote:

Hehe I was going to quote you from RPGNet here, but ... you beat me too it

Heh. Yeah, I thought the idea might get more oxygen here.

jmucchiello · **Joined:** Mon Mar 14, 2011 5:28 am **Posts:** 779

birthright wrote:

Buy a set of BLANK polyhedral dice (i.e. a set of blank d4, d6, d8, d10, d12, d20) then:

For:
d3 use the blank d6 and label it: 1,2,3,1,2,3
d5 use the blank d10 and label it: 1,2,3,4,5,1,2,3,4,5
d7 use the blank d8 and label it: 1,2,3,4,5,6,7,R (R means re-roll the die)
d14/d16 use the blank d20 and label it: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,R/15,R/16,R,R,R,R (when rolling for d14 treat the R/15 and R/16 faces as re-rolls)
d24 use the blank d4 and label it: 0,0,12,12 then throw it alongside a standard d12 and add the two results
d30 use the blank d12 and label it: 0,0,0,0,10,10,10,10,20,20,20,20 then throw it alongside a standard d10 and add the two results (treat 0+0 as 30 of course!)

There. Zochii dice simulated for under $3. You just need to re-roll occasionally - the worst offender being the d14 where you'll need to re-roll 6 of 20 rolls (30% of the time).

+d9

Although writing R/15 onto the surface of d20 requires impeccable handwriting that I would lack.

smathis · **Joined:** Fri Jan 28, 2011 2:52 pm **Posts:** 960

jmucchiello wrote:

+d9

Although writing R/15 onto the surface of d20 requires impeccable handwriting that I would lack.

You could leave all the "R" sides blank and then reroll if you get a blank...

The only problem I see with the blank dice thing is determining which one is a d7 and which one is a d8. Other than that, it's awesome.

jmucchiello · **Joined:** Mon Mar 14, 2011 5:28 am **Posts:** 779

smathis wrote:

The only problem I see with the blank dice thing is determining which one is a d7 and which one is a d8. Other than that, it's awesome.

Buy the blank set in a color you don't already own, most likely flat white.

Hamel™ · **Posted:** Thu Jun 16, 2011 1:26 am

To generate a d7 you can always use 7 cards from a Poker Deck, shuffling them each time.

rabindranath72 · **Joined:** Wed Sep 06, 2006 6:21 am **Posts:** 109

jmucchiello wrote:

Harley Stroh wrote:

Traveller over on the Acaeum offered up these formulas:

Traveller wrote:

d3 = 1d6/2. round up
d5 = 1d20/4, round up or 1d10/2, round up (thanks to Sardan for the d10 version)
d7 = 2d4-1
d14 = (1d8+2d4)-2 or (2d6+1d4)-2
d16 = 3d6-2
d24 = (1d10+2d8)-2 or (2d10+1d6)-2
d30 = (1d20+2d6)-2, (1d12+2d10)-2, or (2d12+1d8)-2

//H

And most of the are non-linear. What good are non-linear equations for simulating Zocchie dice?

Apparently he created these rules to generate ranges from table, which are distribution-agnostic; but he used the notation for uniform distributions. So yes, one way or the other, he is wrong.

dkadera · **Posted:** Thu Jun 16, 2011 6:51 pm

Because more tables are always better

; not a perfect solution, there are still re-rolls, but it works.

http://dl.dropbox.com/u/10388550/Zocchi%20Dice%20Table.xls

finarvyn · **Posted:** Mon Jun 20, 2011 7:31 am

Here's another interesting take on the dice situation.

Quote:

If you've played Traveller, then you remember the d66, or rolling two six-sided dice reading the first result as 10's and the second as 1's. The d66 equals to a d36, in which on any other roll you have 36 possible combinations (6 times 6.) See the point? 16 is 4 times 4, thus a d44. 24 is 4 times 6 (or 6 times 4), thus a d46 or a d64. 30 is 6 times 5 (or 5 times 6), thus a d65 or a d56. You can also generates numbers between 1 and 30 by rolling 1d6 (or 1d3) and 1d10 reading 1-2 (1) as +0, 3-4 (2) as +10 and 5-6 (3) as +20.

A couple of tables follow. You can find the blog post here:
http://theyaqqothlgrimoire.blogspot.com ... -free.html

wavemotion · **Joined:** Tue Jun 21, 2011 8:15 am **Posts:** 34

finarvyn wrote:

Here's another interesting take on the dice situation.

Quote:

If you've played Traveller, then you remember the d66, or rolling two six-sided dice reading the first result as 10's and the second as 1's. The d66 equals to a d36, in which on any other roll you have 36 possible combinations (6 times 6.) See the point? 16 is 4 times 4, thus a d44. 24 is 4 times 6 (or 6 times 4), thus a d46 or a d64. 30 is 6 times 5 (or 5 times 6), thus a d65 or a d56. You can also generates numbers between 1 and 30 by rolling 1d6 (or 1d3) and 1d10 reading 1-2 (1) as +0, 3-4 (2) as +10 and 5-6 (3) as +20.

A couple of tables follow. You can find the blog post here:
http://theyaqqothlgrimoire.blogspot.com ... -free.html

Random thoughts:

1. I'm not keen for the d44 nomenclature they used (I realize they are adapting the d66 from Traveller where it does make sense since a d6d6 is the same as d66 when the control die is a multiple of 10) - it's really a d4d4 (since d44 means something specific when you're talking about dice and die rollers... i.e. 44 equal probabilities... otherwise the table they showcase has a problem in that d44 and d16 are shown as table column headings and one means d4/d4 to produce 16 different outcomes and the other d16).

2. This is the same as the 'control die' method. The first die is the control die and determines if you add 0, 4, 8 or 12 ... or, for those astute readers: ((d4control - 1) * 4) + d4 yields the same as a d16. Thinking of it as a control die means you don't have to use a lookup table to get a result to use in potentially another look up table (too many indexes makes for less fun, IMO).

-Dave

Dreamslinger · **Posted:** Thu Jun 23, 2011 11:10 am

smathis wrote:

jmucchiello wrote:

+d9

Although writing R/15 onto the surface of d20 requires impeccable handwriting that I would lack.

You could leave all the "R" sides blank and then reroll if you get a blank...

The only problem I see with the blank dice thing is determining which one is a d7 and which one is a d8. Other than that, it's awesome.

Ink the highest result in a different color.

fred.thecimmerian · **Posted:** Sat Jun 25, 2011 9:32 pm

Just got my 12-pc Dice Set from Game Science with my d-7 extra. I looked at the d-7 for a few minutes before I figured out how the read it other than the 6 or 7.

DaveMage · **Posted:** Wed Jun 29, 2011 11:31 am

I know this is likely sacreligious, but for those with an iPad/iPhone, there is an app that will let you do d[x]:

http://itunes.apple.com/us/app/rpg-calc-hd/id371751276?mt=8

(Though I still prefer rolling dice.

)

sirhotalot · **Joined:** Thu Jun 30, 2011 4:40 pm **Posts:** 2

Have any of you been doing the math to compare the results of the actual die? You have to keep in mind the the die roll differently because of their shapes and therefor wont produce the same average.

You can calculate them here: http://www.wolframalpha.com/

These die produce a +1 on average compared to what the actual die would get (whereas a D30 might produce an average 14 a d20+d10 produces an average of 15).

The closest I could get was for a D30 roll 1d10 and 1d20 and add the results together.

For a d24 roll 2d12.

For a d16 roll 2d8.

finarvyn · **Posted:** Thu Jun 30, 2011 6:56 pm

sirhotalot wrote:

The closest I could get was for a D30 roll 1d10 and 1d20 and add the results together.

For a d24 roll 2d12.

For a d16 roll 2d8.

Sorry, but these are just wrong.
1. They produce a "bell" shape instead of a linear one. (This means that there is a higher chance of getting numbers in the middle than on the extremes.)
2. They don't produce the right range. For example, 2d12 produces numbers from 2-24, not 1-24.

See earlier parts of this thread for correct options, such as the use of the control die.

Goodman Games

Dice: generating "Zocchi results" using "normal" polyhedrons

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