Miwin's Dice were invented in 1975 by the physicist Michael Winkelmann in Vienna. They consist of three different dice with faces bearing numbers from 1 to 9, with opposite sides summing to 9, 10, or 11. The numbers on each die give the sum of 30 and have an arithmetic mean of 5. |

Who creates a good new game with miwin's dice, will get a set of miwin's dice and the game will be published here! |
---|

Designer | Dr. Michael G.F. Winkelmann |

Publisher | Arquus Verlag Vienna |

Years active | 1994 |

Players | 1–9 |

Age range | 6+, depending on game |

Playing time | 5–60 minutes depending on game |

Website | http://www.miwin.com |

Miwins's dice have 6 sides like standard dice, and each side shows different numbers. The standard set is made of wood; special designs are made of titanium (see picture) or other materials (gold, silver). The numbers (dots) on each die are colored blue, red or black.

Each die is named for the sum of its 2 lowest numbers.Die III | with blue dots |
1 | 2 | 5 | 6 | 7 | 9 | |||

Die IV | with red dots |
1 | 3 | 4 | 5 | 8 | 9 | |||

Die V | with black dots |
2 | 3 | 4 | 6 | 7 | 8 |

Numbers 1 and 9, 2 and 7, and 3 and 8 are on opposite sides. Additional numbers are 5 and 6 on die III, 4 and 5 on die IV, and 4 and 6 on die V. The dice are designed in such a way that for every die there exists one that will win against it. A given die will have a higher number with a probability of 17/36, or a lower number with a probability of 16/36. III wins against IV, IV against V, and V against III. Such dice are known as nontransitive.

Though the three intransitive dice A, B, C (first set of dice)

A: 2, 2, 6, 6, 7, 7

B: 1, 1, 5, 5, 9, 9

C: 3, 3, 4, 4, 8, 8

P(A > B) = P(B > C) = P(C > A) = 5:4

A': 2, 2, 4, 4, 9, 9

B': 1, 1, 6, 6, 8, 8

C': 3, 3, 5, 5, 7, 7

P(A' > B') = P(B' > C') = P(C' > A') = 5:4

win against each other with equal probability they are not equivalent.

While the first set of dice (A, B, C) has a ,highest' die the second set of dice has a 'lowest' die.

Rolling the three dice of a set and using always the highest score for evaluation will show a different winning pattern

for the two sets of dice.

With the first set of dice, die B will win with the highest probability (88/216) and dice A and C will each win with a probability of 64/216.

With the second set of dice, die C' will win with the lowest probability (56/216) and dice A' and B' will each win with a probability of 80/216.

Each of the Dice has similar attributes like having no double number, the sum of the numbers is 30, and having each number from 1 to 9 two times spread over the 3 dice. This attribute characterize the implementation of intransitive Dice enabling all the different game variants. All the games need only 3 dice in difference to other theoretical nontransitive dice designed in view of mathematics such as Efrons Dice.

Because of these special attributes Miwin's Dice used also in the area of education. Miwin's Dice help to develop the mathematical highlights and enhances the ability to calculate probability as happened in the summer semester 2007 during a seminar at the University Siegen.

Since the middle of the eighties the press wrote about the games -> see the Austrian paper "Das Weihnachtsorakel, Spieltip "Ein Buch mit zwei Seiten", the Standard 18.Dez..1994, page 6, Pöppel-Revue 1/1990 page 6 and Spielwiese 11/1990 page 13, 29/1994 page 7. Winkelmann presents his games also himself, for example in Vienna at the "Österrechischen Spielefest, "Stiftung Spielen in Österreich", Leopoldsdorf, where "Miwin's dice" 1987 won the price "novel independent dice game of the year".

1989 the games have been reviewed by the periodical "Die Spielwiese" ( 29/1989 page 6). At that time 14 alternatives of gambling and strategic games existed for Miwin's dice. Also the periodical "Spielbox" had in the category "Unser Spiel im Heft" (now known as "Edition Spielbox") two variants of games for Miwin's dice to be taken out of the magazine. It was the solitaire game 5 to 4 and the strategic game Bitis for two persons.

1994 Winkelmann published in Vienna's Arquus publishing house his game Miwin's Dice consisting of the book "Göttliche Spiele", containing 92 games, a master copy for 4 game board and a documentation about the mathematical attributes of the dice and a set of Miwin's dice. Now you can find about 120 variants of games for free at his homepage.

With Miwin's dice strategic games gambles are possible. Variants with both elements exist also. The intrinsic attributes of the dice cause well defined probabilities and mathematical phenomena's.

Solitaire games and games for up to nine people beginning with the age of 6 available. Some of the games need a game board. Playing time is from 5 minutes to 60 minutes.

- 1/3 of the sum of dots of all dice can be divided by 3 without carry over.
- 1/3 of the sum of dots of all dice can be divided by 3 having a carry over of 1.
- 1/3 of the sum of dots of all dice can be divided by 3 having a carry over of 2.

The probability for a given number with all 3 dice is 11/36, for a given rolled double is 1/36, for any rolled double 1/4. The probability obtain a rolled double is only 50% compared to normal dice.

Cumulative frequency type III und V | Cumulative frequency type IV und V | Cumulative frequency type III und IV |

Cumulative frequency type IX and X | Cumulative frequency type X and X | Cumulative frequency type IX and X |

Cumulative frequency type III and IV and V | Cumulative frequency type IX and X and XI |

Removing the common dots of Miwin's Dice reverses intransitivity.

Miwin's dice allow to create several equal distributions. Adding a constant changes the range.

**1 – 9 (rolling dice one time)** P(1-9) = 1/9

*take one of Miwins dice by random*

**0 – 80 (roll the dice 2 times)** P(0-80) = 1/9² = 1/81

- ) Take one dice by random, roll it and lay it back: 1st throw!
- ) Take one dice by random, roll it and lay it back: 2nd throw!

1st throw * 9 - 2nd throw

Examples1st throw | 2nd throw | Equation | Result |
---|---|---|---|

9 | 9 | 9 times 9 - 9 | 72 |

9 | 1 | 9 times 9 - 1 | 80 |

1 | 9 | 9 times 1 - 9 | 0 |

2 | 9 | 9 times 2 - 9 | 9 |

2 | 8 | 9 times 2 - 8 | 10 |

8 | 4 | 9 times 8 - 4 | 68 |

1 | 3 | 9 mal 1 - 3 | 6 |

This variant provides numbers from 0 - 80 with a probability of (1/9)², 81 = 9²

- ) Take one dice by random, roll it and lay it back: 1st throw!
- ) Take one dice by random, roll it and lay it back: 2nd throw!

1st throw = 9 gives 10 * 2nd throw - 10 all others 10 * 1st throw + 2nd throw - 10

Examples1st throw | 2nd throw | Equation | Result |
---|---|---|---|

9 | 9 | 10 times 9 - 10 | 80 |

9 | 1 | 10 times 1 -10 | 0 |

8 | 4 | 10 times 8 + 4 - 10 | 74 |

1 | 3 | 10 times 1 + 3 - 10 | 3 |

This variant provides numbers from 0 - 80 with a probability of (1/9)², 81 = 9²

- ) Take one dice by random, roll it and lay it back: 1st throw!
- ) Take one dice by random, roll it and lay it back: 2nd throw!

Both throws with 9 gives 0 1st throw = 9 and 2nd throw not 9 gives 10 * 2nd throw 1st throw = 8 gives 2nd throw all other give 10 * 1st throw - 2nd throw

Examples1st throw | 2nd throw | Equation | Result |
---|---|---|---|

9 | 9 | - | 0 |

9 | 3 | 10 times 3 | 30 |

8 | 4 | 1 times 4 | 4 |

5 | 9 | 5 times 10 + 9 | 59 |

**0 – 90 (throw 3 times)** P(0-90) = 8/9³ = 8/729

To obtain a equal distribution with numbers from 0 - 90 throw 3 times.

- ) Take one dice by random, roll it and lay it back: 1st throw!
- ) Take one dice by random, roll it and lay it back: 2nd throw!
- ) Take one dice by random, roll it and lay it back: 3nd throw!

1st throw = 9, 3rd throw is not 9 gives 10 * 2nd throw (10, 20, 30, 40, 50, 60, 70, 80, 90) 1st throw is not 9 gives 10 times 1st throw plus 2nd throw 1st throw is equal to the 3rd throw gives 2nd throw (1, 2, 3, 4, 5, 6, 7, 8, 9) All dice equal gives 0 All dice 9 repeat the procedure

Examples1st throw | 2nd throw | 3rd throw | Equation | Result |
---|---|---|---|---|

9 | 9 | not 9 | 10 times 9 | 90 |

9 | 1 | not 9 | 10 times 1 | 10 |

8 | 4 | not 8 | 10 times 8 + 4 | 84 |

1 | 3 | not 1 | 10 times 1 + 3 | 13 |

7 | 8 | 7 | 78 gives 8 | 8 |

4 | 4 | 4 | three equals | 0 |

9 | 9 | 9 | repeate | - |

This gives 91 numbers from 0 - 90 with the probability of 8 / 9³, 8 * 91 = 728 = 9³ - 1

**0 – 103 (throw 3 times)** P(0-103) = 7/9³ = 7/729 This gives 104 numbers from 0 - 103 with the probability of 7 / 9³, 7 * 104 = 728 = 9³ - 1

**0 – 728 (throw 3 times)** P(0-728) = 1/9³ = 1/729

This gives 729 numbers from 0 - 728 with the probability of 1 / 9³

- ) Take one dice by random, roll it and lay it back: 1st throw!
- ) Take one dice by random, roll it and lay it back: 2nd throw!
- ) Take one dice by random, roll it and lay it back: 3nd throw!

Creating a number system with base 9:

(1st throw - 1) * 81 + (2nd throw - 1) * 9 + (3rd throw - 1) * 1 gives a maximum from: 8 * 9² + 8 * 9 + 8 * 9° = 648 + 72 + 8 = 728 (throw - 1) because we have only 9 digits ( 0,1,2,3,4,5,6,7,8 )

Examples1st throw | 2nd throw | 3rd throw | Equation | Result |
---|---|---|---|---|

9 | 9 | 9 | 8 * 9² + 8 * 9 + 8 | 728 |

4 | 7 | 2 | 3 * 9² + 6 * 9 + 1 | 298 |

2 | 4 | 1 | 1 * 9² + 4 * 9 + 0 | 117 |

1 | 3 | 4 | 0 * 9² + 3 * 9 + 3 | 30 |

7 | 7 | 7 | 6 * 9² + 6 * 9 + 6 | 546 |

1 | 1 | 1 | 0 * 9² + 0 * 9 + 0 | 0 |

4 | 2 | 6 | 3 * 9² + 1 * 9 + 5 | 257 |

This gives 729 numbers (0 - 728), each with a probability of 1 / 9³ = 1 / 729 728 = 9³ - 1

Variant | Equation | number of variants |
---|---|---|

one throw with 3 dice, types don't mind | - | 135 |

one throw with 3 dice, type is an additional attribute | (135 – 6 * 9) * 2 + 54 | 216 |

1 throw with each type, type is not used as attribute | 6 * 6 * 6 | 216 |

1 throw with each type, type is used as attribute | 6 * 6 * 6 * 6 | 1296 |

3 throws, random selection of one of the dice for each throw, type is not used as attribute | 9 * 9 * 9 | 729 |

3 throws, random selection of one of the dice for each throw, type is used as attribute:

Variant | Equation | number of alternatives |
---|---|---|

III, III, III / IV, IV, IV / V, V, V | 3 * 6 * 6 * 6 | 648 |

III, III, IV / III, III, V / III, IV, IV / III, V, V / IV, IV, V / IV, V, V | 6 * 3 * 216 | + 3888 |

III, IV, V / III, V, IV / IV, III, V / IV, V, III / V, III, IV / V, IV, III | 6 * 216 | + 1296 |

= 5832 |

5832 = 2 x 2 x 2 x 9 x 9 x 9 = 18³ numbers are possible.

die IX | with yellow dots |
1 | 3 | 5 | 6 | 7 | 8 | |||

die X | with white dots |
1 | 2 | 4 | 6 | 8 | 9 | |||

die XI | with green dots |
2 | 3 | 4 | 5 | 7 | 9 |

- Bitis in Ludings Game data base
- Game Tests

- Friedhelm Merz:
*Spiel ’89. Book for Gamblers, Game creators, Game producers and press*. Merz Verl., Bonn 1989, ISBN 3-926108-23-1, S. 477. - Michael Winkelmann:
*Göttliche Spiele*Arquus-Verl. Pahlich 1994*Göttliche Spiele*Arquus-Verl. Pahlich 1994, ISBN 3-901-388-10-9 - Strategie-Games: Esiema(deutsch), Esiema (english), Gulek(deutsch), Gulek (english) Myra(deutsch), Myra (english)

Literature:

• Michael Winkelmann: *Göttliche Spiele*. 1. Aufl., Arquus Verlag, Wien 1994, **ISBN 3-901-388-10-9**.

• Michael Engel: *Die schönsten Spiele für eine Person*. Orig.-Ausg., Humboldt, Baden-Baden 2003 (= Humboldt-Paperback, 4044: Freizeit & Hobby), ISBN 3-89994-044-X.

• Michael Winkelmann: *Spielerische Mathematik mit Miwin'schen Würfeln*. Bildungsverlag Lemberger, Wien 2012, **ISBN 978-3-85221-531-0**.

• spielbox. Heft 3, Seite 42, Juni 1989

• Spielcasino. Heft 26, Seite 31, Mai 1989

• Spielwiese. Ausgabe 29, Seite 6, Juni 1989

• spielraum. Heft 3, Seite 53, März/April 1989

• Pöppel Revue. Heft 1, Seite 6, 1990

• Spielwiese. Ausgabe 11, Seite 13, 1990

• EINKAUF. Seite 35, 17.3.1993

• Der Standard. Seite 6m 18.12.1994

• WIN-Spiele Magazin 174. Seite 14, 6. 11. 1994

• Bücher News. Nr 45, Seite 46, 1994

• Kurier. Seite 23, 7.5.1995

• EINKAUF. Nr. 37, Seite 4, 16.12.1996

• Die Presse. Seite 22, 28.10.1997

• Der Standard. Seite A 39, 13.12.1999

• U-Express. Seite 15, 9.4.2001