Numeric fair mapping from a 3 dice roll into a 2 dice roll
January 2nd, 2011 at 8:16:16 PM
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Apologies for the stupid poetry.
This problem took me 5 weeks to figure out, and I had to write a computer program to do so. I have since included this mapping in a pending U.S. patent. Please do not look at my patent for help to figure this one out. I will provide a few other clues further below.
First let's define the term "Fair mapping":
From a single 6-sided die roll, you could play a game based upon a 1 to 6 range, like "six flags".
You could also play a few other games at the same time:
You could play "high or low", which works by MAPPING the 1 to 6 range into a 1 to 2 range as follows:
1 high
2 high
3 high
4 low
5 low
6 low
You could play "high-low-middle", which works by MAPPING the 1 to 6 range into a 1 to 3 range as follows:
1 Low
2 Low
3 Middle
4 Middle
5 High
6 High
You could play "odd or even", which works by MAPPING the 1 to 6 range into another 1 to 2 range as follows:
1 Odd
2 Even
3 Odd
4 Even
5 Odd
6 Even
These are called "FAIR" mappings, meaning that the distributions have equal probibility in both ranges.
An UNFAIR map for "high-low-middle", for example, might look like this:
1 Low
2 Low
3 Middle
4 Middle
5 Middle
6 High
The problem: Develop a fair numeric mapping from a 3-dice roll using indistinguishable dice into 2 dice rolls; something like:
...
1 - 1 - 1 -> 1 - 1
1 - 1 - 2 -> 1 - 2
...
etc.
First clue: Anyone who has seen the game of Sic-Bo knows that this is an example of a game wherein the wagers being made upon a single 3-dice roll get mapped into the following three ranges:
3-dice rolls, for example, the point-sums from 3 to 18, and the 56 distinct roll combinations that permutate from 3 indistinguishable dice rolls.
2-dice rolls, for example, the point sums from 2 to 12, and the 21 distinct roll combinations that permutate from 2 indistinguishable dice rolls.
1-dice rolls based upon the numbers 1 to 6.
Sic-Bo accomplishes this by making one of the dice an off-color, making it the 1 to 6 range, leaving the other 2 colored dice to directly make up the 2 dice range, and allowing all 3 to provide the 3 dice range.
But in this problem, we are starting with 3 INDISTINGUISHBLE, dice!
Look through the list of US patents over the past 100 years or so, and you will find dozens of other ways to make a 2-dice range result from a 3-dice roll:
Throw one die, then throw two
Use one tiny die and two large dice
(my favorite) enclose 2 dice inside a large cube and toss it
etc..
No, No, No, I'm looking for a NUMERIC map.
Ideas?
OK, One Last BIG Clue: Read SOPRA LE SCOPERTE DEI DADI written by Galileo around 1623, but not published until 1718, found at:
http://spikersystems.com/FlashNet_Pointer/www/downloads/SpikerSystems/e-Gamers/AAA_Information/Galleleo_Dice_paper.htm
Good luck, I will watch this and provide more clues as needed...
OK, OK, One last clue... there is more than 1 fair map!
But I want a map that:
-Is symmetrical across the central point numbers (symmetrical around the number 7 in the 2-dice range)
-Optimizes the by - number mappings centrally around each number
-Allows a DIRECT JOIN between the 7 in the 2-dice game to a very small set of rolls in the 3-dice range, so players of 3-dice craps can enjoy the exact same set of table-out as being enjoyed in the 2 dice game, and so they both cheer for the same sets of dice to be thrown at the same time.
(marty)...
This problem took me 5 weeks to figure out, and I had to write a computer program to do so. I have since included this mapping in a pending U.S. patent. Please do not look at my patent for help to figure this one out. I will provide a few other clues further below.
First let's define the term "Fair mapping":
From a single 6-sided die roll, you could play a game based upon a 1 to 6 range, like "six flags".
You could also play a few other games at the same time:
You could play "high or low", which works by MAPPING the 1 to 6 range into a 1 to 2 range as follows:
1 high
2 high
3 high
4 low
5 low
6 low
You could play "high-low-middle", which works by MAPPING the 1 to 6 range into a 1 to 3 range as follows:
1 Low
2 Low
3 Middle
4 Middle
5 High
6 High
You could play "odd or even", which works by MAPPING the 1 to 6 range into another 1 to 2 range as follows:
1 Odd
2 Even
3 Odd
4 Even
5 Odd
6 Even
These are called "FAIR" mappings, meaning that the distributions have equal probibility in both ranges.
An UNFAIR map for "high-low-middle", for example, might look like this:
1 Low
2 Low
3 Middle
4 Middle
5 Middle
6 High
The problem: Develop a fair numeric mapping from a 3-dice roll using indistinguishable dice into 2 dice rolls; something like:
...
1 - 1 - 1 -> 1 - 1
1 - 1 - 2 -> 1 - 2
...
etc.
First clue: Anyone who has seen the game of Sic-Bo knows that this is an example of a game wherein the wagers being made upon a single 3-dice roll get mapped into the following three ranges:
3-dice rolls, for example, the point-sums from 3 to 18, and the 56 distinct roll combinations that permutate from 3 indistinguishable dice rolls.
2-dice rolls, for example, the point sums from 2 to 12, and the 21 distinct roll combinations that permutate from 2 indistinguishable dice rolls.
1-dice rolls based upon the numbers 1 to 6.
Sic-Bo accomplishes this by making one of the dice an off-color, making it the 1 to 6 range, leaving the other 2 colored dice to directly make up the 2 dice range, and allowing all 3 to provide the 3 dice range.
But in this problem, we are starting with 3 INDISTINGUISHBLE, dice!
Look through the list of US patents over the past 100 years or so, and you will find dozens of other ways to make a 2-dice range result from a 3-dice roll:
Throw one die, then throw two
Use one tiny die and two large dice
(my favorite) enclose 2 dice inside a large cube and toss it
etc..
No, No, No, I'm looking for a NUMERIC map.
Ideas?
OK, One Last BIG Clue: Read SOPRA LE SCOPERTE DEI DADI written by Galileo around 1623, but not published until 1718, found at:
http://spikersystems.com/FlashNet_Pointer/www/downloads/SpikerSystems/e-Gamers/AAA_Information/Galleleo_Dice_paper.htm
Good luck, I will watch this and provide more clues as needed...
OK, OK, One last clue... there is more than 1 fair map!
But I want a map that:
-Is symmetrical across the central point numbers (symmetrical around the number 7 in the 2-dice range)
-Optimizes the by - number mappings centrally around each number
-Allows a DIRECT JOIN between the 7 in the 2-dice game to a very small set of rolls in the 3-dice range, so players of 3-dice craps can enjoy the exact same set of table-out as being enjoyed in the 2 dice game, and so they both cheer for the same sets of dice to be thrown at the same time.
(marty)...
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.
January 2nd, 2011 at 8:41:24 PM
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Are you suggesting that a player, during the course of a live casino game, should look at a three-dice combination of 2-4-5 and think "hey, that maps to a two-dice result of 4-4?" Because that's going to be impossibly unwieldy both for players and dealers. Sorry to be blunt, but I know TGDs who would escort you out of their office if you proposed a game that required such mental gymnastics. The first thing they'd say is "use one differently-colored die and ignore it". Dice are cheap. Time (spent thinking) is not.
Under what circumstances do you envision such a technique being commercially useful? In other words, why did you bother spending the money on a U.S. patent application? There's nothing wrong with solving math problems for the sake of solving math problems, but patents should only be pursued for commercial gain. If there's no money to be made by monopolizing your invention, buying a patent is a terrible investment.
Under what circumstances do you envision such a technique being commercially useful? In other words, why did you bother spending the money on a U.S. patent application? There's nothing wrong with solving math problems for the sake of solving math problems, but patents should only be pursued for commercial gain. If there's no money to be made by monopolizing your invention, buying a patent is a terrible investment.
"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
January 2nd, 2011 at 8:46:22 PM
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I'm new to this post and dont want to offend anyone, like I apparently did with my stupid poem. My answer to this question is part of a bussiness idea of mine. IS IT OK TO DISCUSS SUCH THINGS or am I gonna get another letter from Jerry Logan calling me a pathetic dufus?
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.
January 2nd, 2011 at 9:35:03 PM
permalink
Anyway, without explaining the commercial need for it, can anyone even attempt to figure this out? It is NOT simple.
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.
January 2nd, 2011 at 10:06:22 PM
permalink
Quote: discflickerAnyway, without explaining the commercial need for it, can anyone even attempt to figure this out? It is NOT simple.
I've had a quick look at the numbers required and this is what I have come up with:-
These are based purely on mapping to 2-dice TOTALS.
Using 3 dice then if you throw:-
2 1's or 2 2's - COUNTS as a '6'
2 3's or 2 4's OR ANY 3 of a kind - COUNTS as a '7'
2 5's or 2 6's - COUNTS as a '8'
1, 2, 3 - COUNTS as a '2'
4, 5, 6 - COUNTS as a '12'
From the remaining 3 dice totals (of which all 3 dice will be different):-
If the lowest die is a '1' then subtract the middle die total from 7 to give your score.
For example, 1, 3, 6 - COUNTS as a '4' (7-3)
Any other combination, use the middle die to give you the total where 3=10, 4=9 and 5=11.
For example, 2, 4, 6 - COUNTS as a '9'.
I'm not keen on the last rule as I would like to perform a simple calculation to give the total rather than just converting. I'm sure it could be done but I've run out of time :-)
January 2nd, 2011 at 10:56:16 PM
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It looks promising, but the point sum alone wont help, because what if somebody needs to "hop the 5-4", it needs to be distinguished from the "hop 6-3".
I really want a chart that shows that is a fair mapping, by counting the relative ratio probabilities of each 2-d number and proving that only those 3-d numbers that map exclusively to them occur in the same rations, (multiplied by 6) in the 3-d set. Like, if we're mapping to the 'yo, and we know the yo' only appears 2 out of 36 times in the 2-d set, it had better map to 3-d combinations exclusively, and these combinations had better occur 12 out of the 216 possible 3-dice rolls, and cannot be ambiguosly mapped from any other 2-d combinations other than the yo.
Any takers?
Hey while were at it, lets go right ahead and map some more useful ranges. To make things easy, here is the header of the chart I'm talking about:
Starting from the distinct combinations from an indistinguishable 3-dice roll, we map to the following ranges:
a 2-dice roll
a 1 to 18 range
a 1 to 12 range
a 1 to 9 range
a 1 to 6 range, (I.E. a 1-die roll)
a 1 to 4 range
a 1 to 3 range
a 1 to 2 range
3-Dice (3-D Point) 1 to 36 2-dice (2-D Point) 1 to 18 1 to 12 1 to 9 1 to 6 1 to 4 1 to 3 1 to 2
-----------------------------------------------------------------------------------------------------------------------------------------
1 1-1-1 ( 3) ...
I really want a chart that shows that is a fair mapping, by counting the relative ratio probabilities of each 2-d number and proving that only those 3-d numbers that map exclusively to them occur in the same rations, (multiplied by 6) in the 3-d set. Like, if we're mapping to the 'yo, and we know the yo' only appears 2 out of 36 times in the 2-d set, it had better map to 3-d combinations exclusively, and these combinations had better occur 12 out of the 216 possible 3-dice rolls, and cannot be ambiguosly mapped from any other 2-d combinations other than the yo.
Any takers?
Hey while were at it, lets go right ahead and map some more useful ranges. To make things easy, here is the header of the chart I'm talking about:
Starting from the distinct combinations from an indistinguishable 3-dice roll, we map to the following ranges:
a 2-dice roll
a 1 to 18 range
a 1 to 12 range
a 1 to 9 range
a 1 to 6 range, (I.E. a 1-die roll)
a 1 to 4 range
a 1 to 3 range
a 1 to 2 range
3-Dice (3-D Point) 1 to 36 2-dice (2-D Point) 1 to 18 1 to 12 1 to 9 1 to 6 1 to 4 1 to 3 1 to 2
-----------------------------------------------------------------------------------------------------------------------------------------
1 1-1-1 ( 3) ...
Last edited by: discflicker on Feb 23, 2018
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.
January 2nd, 2011 at 11:44:54 PM
permalink
Quote: discflickerAnyway, without explaining the commercial need for it, can anyone even attempt to figure this out? It is NOT simple.
First off, yes it's okay to discuss new game ideas. There's an entire section on it, and you'll get some good feedback if you post your ideas -- just make sure they're properly protected first since this is a public forum. You'll see why by the time you finish reading this message.
On the other hand, don't confuse tedious with difficult. Mapping 3d6 to 2d6 is tedious but very straightforward, and it can be done in a very large number of ways. Consider that each 2d6 combination occurs with p=1/36, or 6/216 times. The individual combinations of 3d6 occur either 1/216 (triples, occurs 6C1=6 different ways), 3/216 (doubles, occurs 2C1*6C2=30 ways), or 6/216 (3 unique, occurs 6C3=20 ways). Therefore, mapping 3d6 to 2d6 can be done as follows:
all 6 triples = 1 2d6 outcome
two different doubles = 1 2d6 outcome (x 15)
one 3-unique outcome = 1 2d6 outcome (x 20)
Total is 36 outcomes.
The above structure will always give a "fair mapping" under your definition.
"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
January 3rd, 2011 at 12:57:26 AM
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Yes, absoultely, the key is to breakdown the 216 combinations into those 3 classes and map them to a 1 to 36 range and then map THAT back into the 2-dice ranges from there. The thing about the tripples needing to go to the 7 is because no other combination works! I donno how you figured THAT one out so fast!
Ok, but we still need to account for the fact that some of these sets must map properly to the same 2-d number. For example, the "62C" comprising the "5-4 hop" must be mapped to the same 2-d (9), as must the "62C" comprising the "6-3" hop. And with some numbers, there is a mixture of "62C" and "63C" classes.
But anyway, yea, this is well underway and I am really impressed.
Wow you are good! Did you read that out of the Galileo Galilei_Dice paper? Did you play Ricochet out at the Reserve (Fiesta) in Henderson?
Heck, the gol dern thing took me a full 5 weeks, and I mean FULL, like 21 hours a day and sleepin on the floor next to the box with mouse in hand (tedious = difficult for me, but persistence wins out in the end).
Actually I figured that 3-class part out in a week or so (mostly trying to understand galie's jibberish), but I also needed to find the sweetest map possible. And so I needed to write this ugly monster piece of code that pre-loaded the tripples and a few of the endpoints, and then went throught all of the combinations dropping these 2 remaining classes into the slots like it was playing a game of Tetris. I started zero-ing in on a few, but then the sweetest map suddenly popped out. I say sweetest, because, like the previous critic implied, nobody wants to memorize a complex 56 to 21 position map. A sweet map minimizes the number of combinations that each number maps to, and attempts to keep things lined up, like 2-d 3s underneath 3-d 3s, and 2-d yo's lined up under 3-d 17s.
Here she is in all her glory, the end result of 10 weeks of research, and protected by pending US patent....
The full reverse ways table map is...
point 2: 1-1 1-1-2 1-1-3 1-2-1 1-3-1 2-1-1 3-1-1
point 3: 1-2 1-1-4 1-2-2 1-2-3 1-3-2 1-4-1 2-1-2 2-1-3 2-2-1 2-3-1 3-1-2 3-2-1 4-1-1 2-1 1-1-4 1-2-2 1-2-3 1-3-2 1-4-1 2-1-2 2-1-3 2-2-1 2-3-1 3-1-2 3-2-1 4-1-1
point 4: 1-3 1-1-6 1-3-4 1-4-3 1-6-1 2-2-4 2-4-2 3-1-4 3-4-1 4-1-3 4-2-2 4-3-1 6-1-1 2-2 1-2-5 1-5-2 2-1-5 2-5-1 5-1-2 5-2-1 3-1 1-1-6 1-3-4 1-4-3 1-6-1 2-2-4 2-4-2 3-1-4 3-4-1 4-1-3 4-2-2 4-3-1 6-1-1
point 5: 1-4 1-4-4 2-2-5 2-2-6 2-3-3 2-5-2 2-6-2 3-2-3 3-3-2 4-1-4 4-4-1 5-2-2 6-2-2 2-3 1-2-6 1-3-5 1-5-3 1-6-2 2-1-6 2-6-1 3-1-5 3-5-1 5-1-3 5-3-1 6-1-2 6-2-1 3-2 1-2-6 1-3-5 1-5-3 1-6-2 2-1-6 2-6-1 3-1-5 3-5-1 5-1-3 5-3-1 6-1-2 6-2-1 4-1 1-4-4 2-2-5 2-2-6 2-3-3 2-5-2 2-6-2 3-2-3 3-3-2 4-1-4 4-4-1 5-2-2 6-2-2
point 6: 1-5 1-3-6 1-6-3 2-3-4 2-4-3 3-1-6 3-2-4 3-4-2 3-6-1 4-2-3 4-3-2 6-1-3 6-3-1 2-4 1-4-5 1-5-4 2-4-4 3-3-4 3-4-3 4-1-5 4-2-4 4-3-3 4-4-2 4-5-1 5-1-4 5-4-1 3-3 2-3-5 2-5-3 3-2-5 3-5-2 5-2-3 5-3-2 4-2 1-4-5 1-5-4 2-4-4 3-3-4 3-4-3 4-1-5 4-2-4 4-3-3 4-4-2 4-5-1 5-1-4 5-4-1 5-1 1-3-6 1-6-3 2-3-4 2-4-3 3-1-6 3-2-4 3-4-2 3-6-1 4-2-3 4-3-2 6-1-3 6-3-1
point 7: 1-6 1-1-1 1-1-5 1-5-1 2-2-2 2-6-6 3-3-3 4-4-4 5-1-1 5-5-5 6-2-6 6-6-2 6-6-6 2-5 1-2-4 1-4-2 2-1-4 2-4-1 4-1-2 4-2-1 4-4-6 4-5-5 4-6-4 5-4-5 5-5-4 6-4-4 3-4 1-3-3 2-2-3 2-3-2 3-1-3 3-2-2 3-3-1 3-5-6 3-6-5 5-3-6 5-6-3 6-3-5 6-5-3 4-3 1-3-3 2-2-3 2-3-2 3-1-3 3-2-2 3-3-1 3-5-6 3-6-5 5-3-6 5-6-3 6-3-5 6-5-3 5-2 1-2-4 1-4-2 2-1-4 2-4-1 4-1-2 4-2-1 4-4-6 4-5-5 4-6-4 5-4-5 5-5-4 6-4-4 6-1 1-1-1 1-1-5 1-5-1 2-2-2 2-6-6 3-3-3 4-4-4 5-1-1 5-5-5 6-2-6 6-6-2 6-6-6
point 8: 2-6 1-4-6 1-6-4 3-4-5 3-5-4 4-1-6 4-3-5 4-5-3 4-6-1 5-3-4 5-4-3 6-1-4 6-4-1 3-5 2-3-6 2-6-3 3-2-6 3-3-5 3-4-4 3-5-3 3-6-2 4-3-4 4-4-3 5-3-3 6-2-3 6-3-2 4-4 2-4-5 2-5-4 4-2-5 4-5-2 5-2-4 5-4-2 5-3 2-3-6 2-6-3 3-2-6 3-3-5 3-4-4 3-5-3 3-6-2 4-3-4 4-4-3 5-3-3 6-2-3 6-3-2 6-2 1-4-6 1-6-4 3-4-5 3-5-4 4-1-6 4-3-5 4-5-3 4-6-1 5-3-4 5-4-3 6-1-4 6-4-1
point 9: 3-6 1-5-5 2-5-5 3-3-6 3-6-3 4-4-5 4-5-4 5-1-5 5-2-5 5-4-4 5-5-1 5-5-2 6-3-3 4-5 1-5-6 1-6-5 2-4-6 2-6-4 4-2-6 4-6-2 5-1-6 5-6-1 6-1-5 6-2-4 6-4-2 6-5-1 5-4 1-5-6 1-6-5 2-4-6 2-6-4 4-2-6 4-6-2 5-1-6 5-6-1 6-1-5 6-2-4 6-4-2 6-5-1 6-3 1-5-5 2-5-5 3-3-6 3-6-3 4-4-5 4-5-4 5-1-5 5-2-5 5-4-4 5-5-1 5-5-2 6-3-3
point 10: 4-6 1-6-6 3-4-6 3-5-5 3-6-4 4-3-6 4-6-3 5-3-5 5-5-3 6-1-6 6-3-4 6-4-3 6-6-1 5-5 2-5-6 2-6-5 5-2-6 5-6-2 6-2-5 6-5-2 6-4 1-6-6 3-4-6 3-5-5 3-6-4 4-3-6 4-6-3 5-3-5 5-5-3 6-1-6 6-3-4 6-4-3 6-6-1
point 11: 5-6 3-6-6 4-5-6 4-6-5 5-4-6 5-5-6 5-6-4 5-6-5 6-3-6 6-4-5 6-5-4 6-5-5 6-6-3 6-5 3-6-6 4-5-6 4-6-5 5-4-6 5-5-6 5-6-4 5-6-5 6-3-6 6-4-5 6-5-4 6-5-5 6-6-3
point 12: 6-6 4-6-6 5-6-6 6-4-6 6-5-6 6-6-4 6-6-5
Please see the table in section 20 in this very informative text file...
Or if you like, visit my web site and you can download the program that generates the text file, and I can get you the sources, including the monster code segment.
But to see it actually work in a live demo, please trust me that this program won't hurt your box, I wrote every line of code in it! Now this is a Really COOL PROGRAM, FOR SURE!!!
Play with it, but dont use the cancel bet button. Start by pressing the 216 test and then cranking the speed up. See how it maps everything perfectly and how several game ranges can be played CONCURRENTLY!
Next, change the number of dice from 3 to 2, and then press all bets down.. see how it switches into 2-dice entry mode?
Finally, try changing to wheel while in 2-dice mode and press all bets down.. now its a roulette wheel entry. Press the "show dice mappings" and you can now begin understand why I paid my lawyer for this whole thing..
This RollStation accept multiple input randomization ranges and outputs all of the ranges possibly mapped from it, off to various DIFFERENT computer games that require them.
And as to WHY I would do that?
Ask and I will tell. Its a cool story.
Thanks, MathEx !!!
marty
discflicker.com
Ok, but we still need to account for the fact that some of these sets must map properly to the same 2-d number. For example, the "62C" comprising the "5-4 hop" must be mapped to the same 2-d (9), as must the "62C" comprising the "6-3" hop. And with some numbers, there is a mixture of "62C" and "63C" classes.
But anyway, yea, this is well underway and I am really impressed.
Wow you are good! Did you read that out of the Galileo Galilei_Dice paper? Did you play Ricochet out at the Reserve (Fiesta) in Henderson?
Heck, the gol dern thing took me a full 5 weeks, and I mean FULL, like 21 hours a day and sleepin on the floor next to the box with mouse in hand (tedious = difficult for me, but persistence wins out in the end).
Actually I figured that 3-class part out in a week or so (mostly trying to understand galie's jibberish), but I also needed to find the sweetest map possible. And so I needed to write this ugly monster piece of code that pre-loaded the tripples and a few of the endpoints, and then went throught all of the combinations dropping these 2 remaining classes into the slots like it was playing a game of Tetris. I started zero-ing in on a few, but then the sweetest map suddenly popped out. I say sweetest, because, like the previous critic implied, nobody wants to memorize a complex 56 to 21 position map. A sweet map minimizes the number of combinations that each number maps to, and attempts to keep things lined up, like 2-d 3s underneath 3-d 3s, and 2-d yo's lined up under 3-d 17s.
Here she is in all her glory, the end result of 10 weeks of research, and protected by pending US patent....
The full reverse ways table map is...
point 2: 1-1 1-1-2 1-1-3 1-2-1 1-3-1 2-1-1 3-1-1
point 3: 1-2 1-1-4 1-2-2 1-2-3 1-3-2 1-4-1 2-1-2 2-1-3 2-2-1 2-3-1 3-1-2 3-2-1 4-1-1 2-1 1-1-4 1-2-2 1-2-3 1-3-2 1-4-1 2-1-2 2-1-3 2-2-1 2-3-1 3-1-2 3-2-1 4-1-1
point 4: 1-3 1-1-6 1-3-4 1-4-3 1-6-1 2-2-4 2-4-2 3-1-4 3-4-1 4-1-3 4-2-2 4-3-1 6-1-1 2-2 1-2-5 1-5-2 2-1-5 2-5-1 5-1-2 5-2-1 3-1 1-1-6 1-3-4 1-4-3 1-6-1 2-2-4 2-4-2 3-1-4 3-4-1 4-1-3 4-2-2 4-3-1 6-1-1
point 5: 1-4 1-4-4 2-2-5 2-2-6 2-3-3 2-5-2 2-6-2 3-2-3 3-3-2 4-1-4 4-4-1 5-2-2 6-2-2 2-3 1-2-6 1-3-5 1-5-3 1-6-2 2-1-6 2-6-1 3-1-5 3-5-1 5-1-3 5-3-1 6-1-2 6-2-1 3-2 1-2-6 1-3-5 1-5-3 1-6-2 2-1-6 2-6-1 3-1-5 3-5-1 5-1-3 5-3-1 6-1-2 6-2-1 4-1 1-4-4 2-2-5 2-2-6 2-3-3 2-5-2 2-6-2 3-2-3 3-3-2 4-1-4 4-4-1 5-2-2 6-2-2
point 6: 1-5 1-3-6 1-6-3 2-3-4 2-4-3 3-1-6 3-2-4 3-4-2 3-6-1 4-2-3 4-3-2 6-1-3 6-3-1 2-4 1-4-5 1-5-4 2-4-4 3-3-4 3-4-3 4-1-5 4-2-4 4-3-3 4-4-2 4-5-1 5-1-4 5-4-1 3-3 2-3-5 2-5-3 3-2-5 3-5-2 5-2-3 5-3-2 4-2 1-4-5 1-5-4 2-4-4 3-3-4 3-4-3 4-1-5 4-2-4 4-3-3 4-4-2 4-5-1 5-1-4 5-4-1 5-1 1-3-6 1-6-3 2-3-4 2-4-3 3-1-6 3-2-4 3-4-2 3-6-1 4-2-3 4-3-2 6-1-3 6-3-1
point 7: 1-6 1-1-1 1-1-5 1-5-1 2-2-2 2-6-6 3-3-3 4-4-4 5-1-1 5-5-5 6-2-6 6-6-2 6-6-6 2-5 1-2-4 1-4-2 2-1-4 2-4-1 4-1-2 4-2-1 4-4-6 4-5-5 4-6-4 5-4-5 5-5-4 6-4-4 3-4 1-3-3 2-2-3 2-3-2 3-1-3 3-2-2 3-3-1 3-5-6 3-6-5 5-3-6 5-6-3 6-3-5 6-5-3 4-3 1-3-3 2-2-3 2-3-2 3-1-3 3-2-2 3-3-1 3-5-6 3-6-5 5-3-6 5-6-3 6-3-5 6-5-3 5-2 1-2-4 1-4-2 2-1-4 2-4-1 4-1-2 4-2-1 4-4-6 4-5-5 4-6-4 5-4-5 5-5-4 6-4-4 6-1 1-1-1 1-1-5 1-5-1 2-2-2 2-6-6 3-3-3 4-4-4 5-1-1 5-5-5 6-2-6 6-6-2 6-6-6
point 8: 2-6 1-4-6 1-6-4 3-4-5 3-5-4 4-1-6 4-3-5 4-5-3 4-6-1 5-3-4 5-4-3 6-1-4 6-4-1 3-5 2-3-6 2-6-3 3-2-6 3-3-5 3-4-4 3-5-3 3-6-2 4-3-4 4-4-3 5-3-3 6-2-3 6-3-2 4-4 2-4-5 2-5-4 4-2-5 4-5-2 5-2-4 5-4-2 5-3 2-3-6 2-6-3 3-2-6 3-3-5 3-4-4 3-5-3 3-6-2 4-3-4 4-4-3 5-3-3 6-2-3 6-3-2 6-2 1-4-6 1-6-4 3-4-5 3-5-4 4-1-6 4-3-5 4-5-3 4-6-1 5-3-4 5-4-3 6-1-4 6-4-1
point 9: 3-6 1-5-5 2-5-5 3-3-6 3-6-3 4-4-5 4-5-4 5-1-5 5-2-5 5-4-4 5-5-1 5-5-2 6-3-3 4-5 1-5-6 1-6-5 2-4-6 2-6-4 4-2-6 4-6-2 5-1-6 5-6-1 6-1-5 6-2-4 6-4-2 6-5-1 5-4 1-5-6 1-6-5 2-4-6 2-6-4 4-2-6 4-6-2 5-1-6 5-6-1 6-1-5 6-2-4 6-4-2 6-5-1 6-3 1-5-5 2-5-5 3-3-6 3-6-3 4-4-5 4-5-4 5-1-5 5-2-5 5-4-4 5-5-1 5-5-2 6-3-3
point 10: 4-6 1-6-6 3-4-6 3-5-5 3-6-4 4-3-6 4-6-3 5-3-5 5-5-3 6-1-6 6-3-4 6-4-3 6-6-1 5-5 2-5-6 2-6-5 5-2-6 5-6-2 6-2-5 6-5-2 6-4 1-6-6 3-4-6 3-5-5 3-6-4 4-3-6 4-6-3 5-3-5 5-5-3 6-1-6 6-3-4 6-4-3 6-6-1
point 11: 5-6 3-6-6 4-5-6 4-6-5 5-4-6 5-5-6 5-6-4 5-6-5 6-3-6 6-4-5 6-5-4 6-5-5 6-6-3 6-5 3-6-6 4-5-6 4-6-5 5-4-6 5-5-6 5-6-4 5-6-5 6-3-6 6-4-5 6-5-4 6-5-5 6-6-3
point 12: 6-6 4-6-6 5-6-6 6-4-6 6-5-6 6-6-4 6-6-5
Please see the table in section 20 in this very informative text file...
Or if you like, visit my web site and you can download the program that generates the text file, and I can get you the sources, including the monster code segment.
But to see it actually work in a live demo, please trust me that this program won't hurt your box, I wrote every line of code in it! Now this is a Really COOL PROGRAM, FOR SURE!!!
Play with it, but dont use the cancel bet button. Start by pressing the 216 test and then cranking the speed up. See how it maps everything perfectly and how several game ranges can be played CONCURRENTLY!
Next, change the number of dice from 3 to 2, and then press all bets down.. see how it switches into 2-dice entry mode?
Finally, try changing to wheel while in 2-dice mode and press all bets down.. now its a roulette wheel entry. Press the "show dice mappings" and you can now begin understand why I paid my lawyer for this whole thing..
This RollStation accept multiple input randomization ranges and outputs all of the ranges possibly mapped from it, off to various DIFFERENT computer games that require them.
And as to WHY I would do that?
Ask and I will tell. Its a cool story.
Thanks, MathEx !!!
marty
discflicker.com
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.
January 3rd, 2011 at 5:38:18 AM
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Here is a mapping to two distinct numbers. I throw down the challenge to come up with something easier to remember.
If the three dice represent two different numbers, for example 3-3-5, then you would represent the 2-dice roll with the two types of numbers, in this case 3-5.
If the three dice represent three different numbers, for example 136, then you have to use the following table. I know it isn't that elegant, so try to think of something better.
If you get any three of a kind, then the 2-dice roll is a 1,1.
If the three dice represent two different numbers, for example 3-3-5, then you would represent the 2-dice roll with the two types of numbers, in this case 3-5.
If the three dice represent three different numbers, for example 136, then you have to use the following table. I know it isn't that elegant, so try to think of something better.
| Die 1 | Die 2 | Die 3 | 2-Dice Roll |
|---|---|---|---|
| 1 | 2 | 3 | 1,2 |
| 1 | 2 | 4 | 1,4 |
| 1 | 2 | 5 | 1,5 |
| 1 | 2 | 6 | 1,6 |
| 1 | 3 | 4 | 1,3 |
| 1 | 3 | 5 | 3,5 |
| 1 | 3 | 6 | 3,6 |
| 1 | 4 | 5 | 4,5 |
| 1 | 4 | 6 | 4,6 |
| 1 | 5 | 6 | 5,6 |
| 2 | 3 | 4 | 2,3 |
| 2 | 3 | 5 | 2,5 |
| 2 | 3 | 6 | 2,6 |
| 2 | 4 | 5 | 2,4 |
| 2 | 4 | 6 | 2,2 |
| 2 | 5 | 6 | 5,5 |
| 3 | 4 | 5 | 3,4 |
| 3 | 4 | 6 | 6,6 |
| 3 | 5 | 6 | 3,3 |
| 4 | 5 | 6 | 4,4 |
If you get any three of a kind, then the 2-dice roll is a 1,1.
Last edited by: Wizard on May 18, 2016
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 3rd, 2011 at 5:57:27 AM
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I'm still wondering what the purpose is. Craps is difficult enough for a novice. This makes it difficult for everyone.
I think you meant 1,1.Quote: WizardIf you get any three of a kind, then the 2-dice roll is a 6,6.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
January 3rd, 2011 at 6:26:50 AM
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Quote: DJTeddyBearI think you meant 1,1.
You're right. I changed the last column in that table, but forgot to update the trips outcome.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 3rd, 2011 at 8:59:18 AM
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Wizard and DJTeddyBear, thanks for your input, but the method cannot be simplified and still work. The class desciptions given by MathEx are required to solve this problem.
As to why, if you bothered reading through the US patant application or the .txt document, I give some solid reasons why.
Of course, I already knew the answers to this question, and only asked it to stir some interest in my mapping technology.
At this point, I would like to start another post in the Game Development area. My games are all based upon these mapping ranges being concurrently generated and feeding them as such. So my 2-dice craps games dont care if the 2-dice "roll" comes from an actual 2-dice throw, or from a roulette wheel spin, or from 3 indistinguishable dice, or even from 3 dice, each with a different color.
Now why would I do that?
If you run the safe litte program above (BTW, I showed The Wizard this program last Thursday at the Red Rock Casino), you can see it working in action.
Why, Why, Why???
Imagine being able to run an entire casino with LIVE action, running any number of 3-dice games, 2-dice games and Roullette games (and electronic combination games) WITH ONLY ONE DEALER. Players dont need to memorize the map, they just need to know that it is correct and that it is fair. Which it is.
Please see my new post to see the 26 games I have developed thus far based upon this technolgy, including complex games and games so simple, a cave-man could use them. "Craps is difficult enough for a novice", well I have some games with ONLY 5 choices, and 3 of them pay out at true odds. I have made True Odds betting simple and accessible to players who dont understand the dynamcs of craps.
Thanks again
marty
discflicker.com
As to why, if you bothered reading through the US patant application or the .txt document, I give some solid reasons why.
Of course, I already knew the answers to this question, and only asked it to stir some interest in my mapping technology.
At this point, I would like to start another post in the Game Development area. My games are all based upon these mapping ranges being concurrently generated and feeding them as such. So my 2-dice craps games dont care if the 2-dice "roll" comes from an actual 2-dice throw, or from a roulette wheel spin, or from 3 indistinguishable dice, or even from 3 dice, each with a different color.
Now why would I do that?
If you run the safe litte program above (BTW, I showed The Wizard this program last Thursday at the Red Rock Casino), you can see it working in action.
Why, Why, Why???
Imagine being able to run an entire casino with LIVE action, running any number of 3-dice games, 2-dice games and Roullette games (and electronic combination games) WITH ONLY ONE DEALER. Players dont need to memorize the map, they just need to know that it is correct and that it is fair. Which it is.
Please see my new post to see the 26 games I have developed thus far based upon this technolgy, including complex games and games so simple, a cave-man could use them. "Craps is difficult enough for a novice", well I have some games with ONLY 5 choices, and 3 of them pay out at true odds. I have made True Odds betting simple and accessible to players who dont understand the dynamcs of craps.
Thanks again
marty
discflicker.com
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.
January 3rd, 2011 at 9:10:56 AM
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Quote: discflickerYes, absoultely, the key is to breakdown the 216 combinations into those 3 classes and map them to a 1 to 36 range and then map THAT back into the 2-dice ranges from there. The thing about the tripples needing to go to the 7 is because no other combination works! I donno how you figured THAT one out so fast!
Triples don't necessarily need to map to a 7 -- they just need to map to a single 2d6 outcome. Or perhaps be split 3-and-3 with one of the pairs outcomes each. But yes, I played Ricochet when it was at the Fiesta Henderson, and I'm well aware of the Galileo paper. You should also review Scarne's New Complete Guide to Gambling Games, ch. 11.
You should look at the Wizard's mapping in this thread. His establishes a significantly easier-to-remember mapping than the one you presented. It is also more consistent in that at least two of the numbers in the 3d6 outcome always appear (with one exception - triples) in the 2d6 outcome. Your mapping, on the other hand, has a 3-dice roll of 4-2-2 mapped to a 2-dice outcome of 1-3. To me, that's strange.
Quote:And as to WHY I would do that?
Ask and I will tell. Its a cool story.
I reviewed your website but it doesn't give any details about the new game you've developed. It's also very out-of-date.
"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
January 3rd, 2011 at 9:38:40 AM
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The first game I wrote this software for WAS RICOCHET actually, THE REASON I CREATED THE SYSTEM IN THE FIRST PLACE was to automate the payouts in the game of Ricochet!!!
The reason my map is complex is because of a game I invented called "TDC_7_14_Trips_Outs"... That is Three Dice Craps, 7, 14 and Trips Outs.
The game plays exactly like 2 dice craps, but uses 3 dice, and the table-outs include all of the 7s, all of the 14's, and all of the tripples. By mapping all of these 3-d table outs to the 2-d 7s, we now have 2 games in which the set of table-outs is the same, and so players of these 2 games will cheer for the same numbers at the same time; the phases of these 2 games will always be in-synch between TDC_7_14_Trips_Outs and 2-d Crapless-Craps, but when played with along with 2-D Traditional Craps, there are a few situations where they wont be.. when the 3-dice game is still on a point, but the 2-dice game is on a come-out roll. I have taken advangtage of the situation and created a set of BONUS bets for when it occurs!!!
Without using the mapping, it would not occur. So, now, as a player, you are presented with 2 games: one in which you get free bonuses, and one without them.
The bonuses reflect the savings the Casino has by not needing to deciate a sperate dealer to every game and game range in the casino. Players still never need to know that numbers are mapped or what the map is.
I am starting a new thred in games describing these, and the first game in the list is not tic-tac-toe it is Ricochet!!!!
Thanks for your input, MathEx!!!
The reason my map is complex is because of a game I invented called "TDC_7_14_Trips_Outs"... That is Three Dice Craps, 7, 14 and Trips Outs.
The game plays exactly like 2 dice craps, but uses 3 dice, and the table-outs include all of the 7s, all of the 14's, and all of the tripples. By mapping all of these 3-d table outs to the 2-d 7s, we now have 2 games in which the set of table-outs is the same, and so players of these 2 games will cheer for the same numbers at the same time; the phases of these 2 games will always be in-synch between TDC_7_14_Trips_Outs and 2-d Crapless-Craps, but when played with along with 2-D Traditional Craps, there are a few situations where they wont be.. when the 3-dice game is still on a point, but the 2-dice game is on a come-out roll. I have taken advangtage of the situation and created a set of BONUS bets for when it occurs!!!
Without using the mapping, it would not occur. So, now, as a player, you are presented with 2 games: one in which you get free bonuses, and one without them.
The bonuses reflect the savings the Casino has by not needing to deciate a sperate dealer to every game and game range in the casino. Players still never need to know that numbers are mapped or what the map is.
I am starting a new thred in games describing these, and the first game in the list is not tic-tac-toe it is Ricochet!!!!
Thanks for your input, MathEx!!!
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.
January 3rd, 2011 at 12:18:18 PM
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If the idea is to create a map easy to remember, that is really hard to accomplish. The way The Wizard shows allows you to associate the dice patterns in a SOMEWHAT straightforward manner, but here is what happens... lets start with the doubles... here is an actual photo of the Ricochet table at the Fiesta, and YES, I got into big trouble taking it!!!
Ricochet!!
Damn, I miss playing that game on that table. I LOVED it. ANYONE WANT TO HELP ME AND JAMES BOWLING RESSURECT THIS GAME USING AUTOMATED BETTING???
OK, looking at the table, lets jut go through some the doubles and map 'em back using the Wizard's map..
112 ( 4) -> 3 113 (5) -> 4
122 ( 5) -> 3 223 (7) -> 5
133 ( 7) -> 4 233 (8) -> 5
144 ( 9) -> 5 244 (11) -> 6
155 (11) -> 6 255 (12) -> 7
166 (13) -> 7 266 (14) -> 8
Just here alone, we have already 2 different 3-d POINT numbers (7 from 133 and 5 from 113) mapping to the 2-d 4 point. It becomes obvious that the idea of relating POINT numbers accross ranges is not the way to fly in the Wizzard's system, although, if you ARE a math wiz, yup, you could do some spiffy-fast calculating in your head on the fly...
In my map, and I know its a bit much at first, try to think of it as the game of 2-d craps.. OK, next, think about the table outs... 7s (of course), 14s (2 x 7 is a good hint), and all tripples (i have no way to paste that in someone's brain, but maybe the game name might help, you know, TDC_7_14_TRIPS_Outs)
Now for the individual points, for example, the 4 2-d point results from 1-3 and 2-2, and in my map these point to:
1-3 1-1-6, 1-3-4, 2-2-4
2-2 1-2-5
so,
4 8, 8, 8
4 8
and thus, 4 comes exclusively from 8!!!
If we look at the 2-d 5 point, it results from 1-4 and 2-3:
1-4 1-4-4, 2-2-5, 2-2-6, 2-3-3
2-5 1-2-6, 1-3-5
and thus,
5 9, 9, 10, 8
5 9, 9
and so 5s only come from 8, 9, and 10, and you can think about the exceptions here, all 5 come from the 3d 9 except for part of the 1-4 comming from 2-2-6, and the other from 2-3-3.
Isnt that simpler to remember?
My map focuses on POINT relations, and in that respect, it is SWEET, again, meaning that THE MINUMUM number of different 3-D points map accross to the 2-d points. The Wizard's map is the oppopside, requireing on-the-fly conversion.
Here is the POINT mapping of my map, and it is soooo sweeeetttt both forwards;
3 7
4 2 2 2
5 2 3 2 3 3 2
6 3 3 3 3 3 7 3 3 3 3
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
8 4 4 4 4 4 4 4 4 5 4 4 4 5 5 4 4 4 4 4 4 4
9 5 5 5 5 5 5 5 6 6 5 5 5 6 7 6 5 5 6 6 5 5 5 5 5 5
10 6 6 6 6 5 6 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 6
11 8 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 8 8 8 9 8 8 8 8
12 9 9 9 9 9 9 8 8 9 9 8 7 8 9 9 9 8 8 9 9 9 9 9 9 9
13 10 10 10 10 10 10 10 9 9 10 10 10 9 10 10 10 10 10 10 10 10
14 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
15 11 11 11 11 7 11 11 11 11 11
16 12 11 11 12 11 12
17 12 12 12
18 7
AND BACKWARDS!!
point 2: 4 5
point 3: 6 5
point 4: 8
point 5: 9 10 8
point 6: 10 9
point 7: 3 7 6 14 9 12 15 18
point 8: 11 12
point 9: 11 12 13
point 10: 13
point 11: 15 16
point 12: 16 17
I MUST SAY that you guys ARE REALLY SMART to come up with these answers so fast.
AND I APPRECIATE YOUR EFFORTS!!!!
Thanks again.
Ricochet!!
Damn, I miss playing that game on that table. I LOVED it. ANYONE WANT TO HELP ME AND JAMES BOWLING RESSURECT THIS GAME USING AUTOMATED BETTING???
OK, looking at the table, lets jut go through some the doubles and map 'em back using the Wizard's map..
112 ( 4) -> 3 113 (5) -> 4
122 ( 5) -> 3 223 (7) -> 5
133 ( 7) -> 4 233 (8) -> 5
144 ( 9) -> 5 244 (11) -> 6
155 (11) -> 6 255 (12) -> 7
166 (13) -> 7 266 (14) -> 8
Just here alone, we have already 2 different 3-d POINT numbers (7 from 133 and 5 from 113) mapping to the 2-d 4 point. It becomes obvious that the idea of relating POINT numbers accross ranges is not the way to fly in the Wizzard's system, although, if you ARE a math wiz, yup, you could do some spiffy-fast calculating in your head on the fly...
In my map, and I know its a bit much at first, try to think of it as the game of 2-d craps.. OK, next, think about the table outs... 7s (of course), 14s (2 x 7 is a good hint), and all tripples (i have no way to paste that in someone's brain, but maybe the game name might help, you know, TDC_7_14_TRIPS_Outs)
Now for the individual points, for example, the 4 2-d point results from 1-3 and 2-2, and in my map these point to:
1-3 1-1-6, 1-3-4, 2-2-4
2-2 1-2-5
so,
4 8, 8, 8
4 8
and thus, 4 comes exclusively from 8!!!
If we look at the 2-d 5 point, it results from 1-4 and 2-3:
1-4 1-4-4, 2-2-5, 2-2-6, 2-3-3
2-5 1-2-6, 1-3-5
and thus,
5 9, 9, 10, 8
5 9, 9
and so 5s only come from 8, 9, and 10, and you can think about the exceptions here, all 5 come from the 3d 9 except for part of the 1-4 comming from 2-2-6, and the other from 2-3-3.
Isnt that simpler to remember?
My map focuses on POINT relations, and in that respect, it is SWEET, again, meaning that THE MINUMUM number of different 3-D points map accross to the 2-d points. The Wizard's map is the oppopside, requireing on-the-fly conversion.
Here is the POINT mapping of my map, and it is soooo sweeeetttt both forwards;
3 7
4 2 2 2
5 2 3 2 3 3 2
6 3 3 3 3 3 7 3 3 3 3
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
8 4 4 4 4 4 4 4 4 5 4 4 4 5 5 4 4 4 4 4 4 4
9 5 5 5 5 5 5 5 6 6 5 5 5 6 7 6 5 5 6 6 5 5 5 5 5 5
10 6 6 6 6 5 6 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 6
11 8 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 8 8 8 9 8 8 8 8
12 9 9 9 9 9 9 8 8 9 9 8 7 8 9 9 9 8 8 9 9 9 9 9 9 9
13 10 10 10 10 10 10 10 9 9 10 10 10 9 10 10 10 10 10 10 10 10
14 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
15 11 11 11 11 7 11 11 11 11 11
16 12 11 11 12 11 12
17 12 12 12
18 7
AND BACKWARDS!!
point 2: 4 5
point 3: 6 5
point 4: 8
point 5: 9 10 8
point 6: 10 9
point 7: 3 7 6 14 9 12 15 18
point 8: 11 12
point 9: 11 12 13
point 10: 13
point 11: 15 16
point 12: 16 17
I MUST SAY that you guys ARE REALLY SMART to come up with these answers so fast.
AND I APPRECIATE YOUR EFFORTS!!!!
Thanks again.
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.
January 3rd, 2011 at 12:55:46 PM
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Quote: discflickerThe reason my map is complex is because of a game I invented called "TDC_7_14_Trips_Outs"... That is Three Dice Craps, 7, 14 and Trips Outs.
Please don't try to market a game called "TDC_7_14_Trips_Outs". That looks more like an error message than a brand name. At a minimum, game brands should be easy to pronounce and remember, like blackjack or roulette.
As for the rules being complex, don't do it. Requiring that the player "simply trust that the mapping is fair" means that you're catering more to a slot player than a table game player. With very few exceptions, table players want to understand what's happening in their game. Telling them that the 2-5-6 they just rolled is really a "hard 10" isn't going to fly, in my opinion. In table game design, simplicity trumps just about everything else. The cost to the casino in hiring an extra dealer is insignificant compared to the reduced revenue they'd get from slowing the game down while people try to figure out what's going on. Also, you're ignoring a big part of the draw of live table play -- interaction with the dealer. By making the dealer a remote telecast, you lose all the banter.
F2Systems was showing a single-dealer terminal-based system this year at G2E where the live dealer had a roulette wheel, deck of cards and automatic dice bubble by the dealer's podium, and terminal players could bet on whatever combination of bets they wanted. To me, that's the way to go if you're looking at this model.
"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
January 3rd, 2011 at 1:32:21 PM
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Thanks again for reading and taking the time to think it out and respond!
I missed G2e this year, but it sounds like these guys have stolen my idea! That is EXACTLY what I am designing, and why my US patent (pending) calls this invention the RollStation. The little program you can run (above) exactly demonstrates this, and now that you have told me about this, it gives me even more confidence that I am doing something worthwhile.
I have ALL THIS STUFF running RIGHT NOW, WORLD-WIDE and you are welcome to take it for a test ride if you like right now.
I demmoed all of this for the Wizard last Thursday.
I AM taking all of your suggestions seriously.
My answer to "dont name a game TDC..." is that MY stuff is targetted at ALL player levels. TDC7_14_Trips_Outs is for super-high-level cubes players like you and me. AT THE SAME TIME and FROM THE SAME ROLL, you can choose to play RouleDice, another complex game, or Crapless Craps, or Craps (I'm making them easier as I go down the list), or RouLevel (a simpler trade-off between craps and "hazzard" roulette), or Roulette, or Ricochet, or, and now they get really simple, "TruePlace_EasyGames"... and these are all designed and built for players who dont have a clue about how craps (or "hazzard roullete) works, but still want to play and make bets that payout at TRUE odds against a live game.
As far as sombody "trusting" the map, the map is fixed and will never change, and any time they dont trust a mapped number they're welcome to check it out. Its kind of like not trusting your multiplication tables once you learn them.
As far as telling me that the cost of another dealer is not worthwhile, I totally disagree! There are a lot of casinios that will soon be operating exactly like this, and I have had a vision for a long time now about a casino that only has ONE rollstation in it, up on a platform somewhere and the entire casino is all rootin' for the thrower all at the same time (talk abougt a roar!)
wanna see it work right now?
wanna play a live world-wide game right now?
I missed G2e this year, but it sounds like these guys have stolen my idea! That is EXACTLY what I am designing, and why my US patent (pending) calls this invention the RollStation. The little program you can run (above) exactly demonstrates this, and now that you have told me about this, it gives me even more confidence that I am doing something worthwhile.
I have ALL THIS STUFF running RIGHT NOW, WORLD-WIDE and you are welcome to take it for a test ride if you like right now.
I demmoed all of this for the Wizard last Thursday.
I AM taking all of your suggestions seriously.
My answer to "dont name a game TDC..." is that MY stuff is targetted at ALL player levels. TDC7_14_Trips_Outs is for super-high-level cubes players like you and me. AT THE SAME TIME and FROM THE SAME ROLL, you can choose to play RouleDice, another complex game, or Crapless Craps, or Craps (I'm making them easier as I go down the list), or RouLevel (a simpler trade-off between craps and "hazzard" roulette), or Roulette, or Ricochet, or, and now they get really simple, "TruePlace_EasyGames"... and these are all designed and built for players who dont have a clue about how craps (or "hazzard roullete) works, but still want to play and make bets that payout at TRUE odds against a live game.
As far as sombody "trusting" the map, the map is fixed and will never change, and any time they dont trust a mapped number they're welcome to check it out. Its kind of like not trusting your multiplication tables once you learn them.
As far as telling me that the cost of another dealer is not worthwhile, I totally disagree! There are a lot of casinios that will soon be operating exactly like this, and I have had a vision for a long time now about a casino that only has ONE rollstation in it, up on a platform somewhere and the entire casino is all rootin' for the thrower all at the same time (talk abougt a roar!)
wanna see it work right now?
wanna play a live world-wide game right now?
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.
January 3rd, 2011 at 2:03:29 PM
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Quote: discflickerI missed G2e this year, but it sounds like these guys have stolen my idea! That is EXACTLY what I am designing, and why my US patent (pending) calls this invention the RollStation.
Many companies have built central outcome-generating machines for terminal-based games, and have been doing so for a long time. Roulette is especially popular in Europe. Those companies include Novomatic, Electroncek, F2System, ShuffleMaster, IGT, etc. You have lots of competition...
"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
January 3rd, 2011 at 4:12:45 PM
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Exactly! Thats Exactly why the mapping system is unique... I'm trying to set THE standard for the unique approach of multiply mapped games played from the same randomization source. Of course my lawer used terms like "applicable to any..", the idea of creating this complex and spiffy map was to make it unique enough and provide a bussiness case for it (the 7_14_Trips linkage to sharing 3-dice craps with the world's most popular dice game), and THEN, because of all of the other ranges I'm mapping to (which include EVERY POSSIBLE COMBINATION starting from 3-distinguishable dice all the way down to "coin-flip", each mapped and described with a bussiness case), the patent is to stake a claim that I am the king of concurrent gaming, and I swear, I just made that up just now.
...
...
That list of companies... all will run MY software if I can just keep my cat from waking me up...
He haw! But really, I plan to OFFER the entire package, with any mapping a casino needs to use (I'm getting kinda pissed now because I'm thinking about describing it and your descripition of what you saw at G2e pops up),
BUT, I don't actually expect any one to use the map in the way we have been using it thus far!!!
Which brings me to a real math question, and this one isnt to toot my own horn about my inventions either.
This is based upon another more recent alogorythm I came up with and also demonstrates (I think) why I need a numeric map... I think you guys can help me on this one. If the wizard solves it, I'll pay him off in disc golf discs!
I am starting another post to discuss this.... 3DD:1to38
Thnaks again for your thoughts and time
marty
...
...
That list of companies... all will run MY software if I can just keep my cat from waking me up...
He haw! But really, I plan to OFFER the entire package, with any mapping a casino needs to use (I'm getting kinda pissed now because I'm thinking about describing it and your descripition of what you saw at G2e pops up),
BUT, I don't actually expect any one to use the map in the way we have been using it thus far!!!
Which brings me to a real math question, and this one isnt to toot my own horn about my inventions either.
This is based upon another more recent alogorythm I came up with and also demonstrates (I think) why I need a numeric map... I think you guys can help me on this one. If the wizard solves it, I'll pay him off in disc golf discs!
I am starting another post to discuss this.... 3DD:1to38
Thnaks again for your thoughts and time
marty
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.
January 3rd, 2011 at 5:02:17 PM
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Quote: discflickerI am starting another post to discuss this.... 3DD:1to38
Obviously 38 doesn't go into 216 evenly. Can we throw out certain rolls if we wish, and roll again?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 3rd, 2011 at 6:17:08 PM
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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?
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.
May 18th, 2016 at 1:58:02 PM
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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:
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.
Comments?
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 |
Comments?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 18th, 2016 at 2:31:32 PM
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You don't need a mapping to a single die, there's a function:Quote: WizardI 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
Comments?
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
May 18th, 2016 at 2:48:51 PM
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Quote: MathExtremistYou 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...
http://spikersystems.com/FlashNet_Pointer/www/downloads/SpikerSystems/P1_Demo_Demo/SpikerSystems_Patent.htm
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.
May 18th, 2016 at 3:47:59 PM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 19th, 2016 at 7:30:32 PM
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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.
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 19th, 2016 at 8:31:12 PM
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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
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.
May 21st, 2016 at 4:01:39 PM
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Quote: discflickerTHANKS, 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?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 21st, 2016 at 5:06:18 PM
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Quote: WizardSince 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.
April 25th, 2020 at 4:37:28 PM
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Sorry to wake up an old thread (I'm really not sorry), but I Matt Parker made a second part to his video on this problem. You can see in the background he has screen shots from WoV! I am honored.
I set this link to the right time, or scroll to the 14:45 point.
I set this link to the right time, or scroll to the 14:45 point.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 14th, 2022 at 2:43:15 AM
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CORRECTION
Thank you for posting this, Wizard. The actual frames 4 WOV photos appear are at 14:26, 14:30, 14:31, 14:34. Then at 15:22 there is a photo of Wikipedia page for the Wizard of Vegas. In the video description (Show More), he has an entry for "Marty Wollner long description"
https://spikersystems.com/FlashNet_Pointer/www/downloads/SpikerSystems/P1_Demo_Demo/SpikerSystems_Patent.htm
In this document, I have a paragraph about original discussion thread featuring your "very simple" map...
"See also the Wizard of Vegas forum discussing this problem way back in 2011:
https://wizardofvegas.com/forum/questions-and-answers/math/3917-numeric-fair-mapping-from-a-3-dice-roll-into-a-2-dice-roll/ "
BTW, I also have a pointer to a .zip file that contains the full install of my full-blown "casino" featuring 26 games all based upon this mapping technology for Windows10 if anyone is interested, and I have YouTube videos that fully describe how to run the install and the "casino".
Thanks again!
Marty Wollner
Thank you for posting this, Wizard. The actual frames 4 WOV photos appear are at 14:26, 14:30, 14:31, 14:34. Then at 15:22 there is a photo of Wikipedia page for the Wizard of Vegas. In the video description (Show More), he has an entry for "Marty Wollner long description"
https://spikersystems.com/FlashNet_Pointer/www/downloads/SpikerSystems/P1_Demo_Demo/SpikerSystems_Patent.htm
In this document, I have a paragraph about original discussion thread featuring your "very simple" map...
"See also the Wizard of Vegas forum discussing this problem way back in 2011:
https://wizardofvegas.com/forum/questions-and-answers/math/3917-numeric-fair-mapping-from-a-3-dice-roll-into-a-2-dice-roll/ "
BTW, I also have a pointer to a .zip file that contains the full install of my full-blown "casino" featuring 26 games all based upon this mapping technology for Windows10 if anyone is interested, and I have YouTube videos that fully describe how to run the install and the "casino".
Thanks again!
Marty Wollner
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.
