discflicker
Joined: Jan 1, 2011
• Posts: 453
January 3rd, 2011 at 6:17:08 PM permalink
Thanks Wizard for responding and thanks for the use of this site. I hope Im not flooding it too much, let me know I have thick skin.

Please see the new post I crated for 3dd:1 to 38.

Tried out that comet yet?
The difference between zero and the smallest possible number? It doesn't matter; once you cross that edge, it might as well be the difference between zero and 1. The difference between infinity and reality? They are mutually exclusive.
Wizard

Joined: Oct 14, 2009
• Posts: 22702
May 18th, 2016 at 1:58:02 PM permalink
I don't think we've properly hashed out the case of a three-dice roll being mapped to one die. Below is my solution. I welcome ideas that are simpler.

1. If the three dice are the same, then the roll is a 6.

2. If the three dice contain a pair, then go with the whatever the pair is, with these exceptions:

Die 1 Die 2 Die 3 1-Die Roll
1 1 2 6
2 2 3 6
3 3 4 6
4 4 5 6
5 5 6 6

Note how the exceptions are all x-x-x+1, in which case it maps to a 6.

3. If the three dice are different, use this table.

Die 1 Die 2 Die 3 1-Die Roll
1 2 3 1
1 2 4 1
1 2 5 1
1 2 6 1
1 3 4 2
1 3 5 2
1 3 6 2
1 4 5 2
1 4 6 3
1 5 6 3
2 3 4 3
2 3 5 3
2 3 6 4
2 4 5 4
2 4 6 4
2 5 6 4
3 4 5 5
3 4 6 5
3 5 6 5
4 5 6 5

It's not whether you win or lose; it's whether or not you had a good bet.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
May 18th, 2016 at 2:31:32 PM permalink
Quote: Wizard

I don't think we've properly hashed out the case of a three-dice roll being mapped to one die. Below is my solution. I welcome ideas that are simpler.

1. If the three dice are the same, then the roll is a 6.

2. If the three dice contain a pair, then go with the whatever the pair is, with these exceptions:

Die 1 Die 2 Die 3 1-Die Roll
1 1 2 6
2 2 3 6
3 3 4 6
4 4 5 6
5 5 6 6

Note how the exceptions are all x-x-x+1, in which case it maps to a 6.

3. If the three dice are different, use this table.

Die 1 Die 2 Die 3 1-Die Roll
1 2 3 1
1 2 4 1
1 2 5 1
1 2 6 1
1 3 4 2
1 3 5 2
1 3 6 2
1 4 5 2
1 4 6 3
1 5 6 3
2 3 4 3
2 3 5 3
2 3 6 4
2 4 5 4
2 4 6 4
2 5 6 4
3 4 5 5
3 4 6 5
3 5 6 5
4 5 6 5

You don't need a mapping to a single die, there's a function:
Add the three dice, mod 6, add 1. That gets you a fair mapping to a single die. Works for any number of d6 dice, too.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
discflicker
Joined: Jan 1, 2011
• Posts: 453
May 18th, 2016 at 2:48:51 PM permalink
Quote: MathExtremist

You don't need a mapping to a single die, there's a function:

Add the three dice, mod 6, add 1. That gets you a fair mapping to a single die. Works for any number of d6 dice, too.

Hey, he got that from the Matt Parker video!

Just kidding, MathEx is smart enough to come up with that solution in his sleep.

Dang, I honestly forgot where this thread was, I would've mentioned it for sure. I'm gonna link to it from my document...

The difference between zero and the smallest possible number? It doesn't matter; once you cross that edge, it might as well be the difference between zero and 1. The difference between infinity and reality? They are mutually exclusive.
Wizard

Joined: Oct 14, 2009
• Posts: 22702
May 18th, 2016 at 3:47:59 PM permalink
Quote: MathExtremist

Add the three dice, mod 6, add 1. That gets you a fair mapping to a single die. Works for any number of d6 dice, too.

Wow! I didn't think of that. Clever.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard

Joined: Oct 14, 2009
• Posts: 22702
May 19th, 2016 at 7:30:32 PM permalink
Our own discflicker got quite into a solution to this problem, as posed in this video, which solicited video responses.

Diskflicker posted three lengthy responses:

Response # 1 (32:08)

Response # 2 (32:08)

Response # 3 (12:09). This one mentions WoV quite a bit.

Later the guy in the original video responds to the responses he got. He starts with Diskflicker around the 13:30 point.

It's not whether you win or lose; it's whether or not you had a good bet.
discflicker
Joined: Jan 1, 2011
• Posts: 453
May 19th, 2016 at 8:31:12 PM permalink
My apologies for the length, repetition, and stuttering. Thanks, Wizard, for posting this. I can't believe how much work Matt put into this project... I been on the YouTube channels, and thousands of people viewing and hundreds participated. I am SO grateful for him to spend all that time going through my work. He even sited links to my third response video, my patent and my graphical mapping summary in his video description. THANKS, Matt and thank you, WoV, the Wizard, and MathEx for everything you guys do.

Marty, 19-May-2016
Last edited by: discflicker on May 19, 2016
The difference between zero and the smallest possible number? It doesn't matter; once you cross that edge, it might as well be the difference between zero and 1. The difference between infinity and reality? They are mutually exclusive.
Wizard

Joined: Oct 14, 2009
• Posts: 22702
May 21st, 2016 at 4:01:39 PM permalink
Quote: discflicker

THANKS, Matt and thank you, WoV, the Wizard, and MathEx for everything you guys do.

You're welcome.

Since you have clearly thought about this problem a lot, do you have a way to map the roll of three dice to a single playing card?
It's not whether you win or lose; it's whether or not you had a good bet.
discflicker
Joined: Jan 1, 2011
• Posts: 453
May 21st, 2016 at 5:06:18 PM permalink
Quote: Wizard

Since you have clearly thought about this problem a lot, do you have a way to map the roll of three dice to a single playing card?

My knee-jerk response is to use 3 distinguishable dice, and map 4 of each of the 216 into each of the 54 playing cards, and that means using 2 jokers! Using the "deck" with jokers in a live game, you could just ignore 8 of the 216, and just use the rest.

To map into a true 1 to 52 range, I will have to give it some thought, and about doing it with 3 indistinguishable dice.... that would be a lot harder. Once the mapping strategy is figured, out, the next step is to try to find a way to map that is simple and visual. That might also be tricky.

Good question, Wizard!
The difference between zero and the smallest possible number? It doesn't matter; once you cross that edge, it might as well be the difference between zero and 1. The difference between infinity and reality? They are mutually exclusive.
Wizard