Miwins dice


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Miwins dice

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Miwin's Dice
Miwin Wuerfel Titan.gif
Miwins Dice fabricated of titanium
Designer Dr. Michael Winkelmann
Publisher Arquus Verlag Vienna
Years active 1994
Players 1–9
Age range 6+, depending on game
Playing time 5–60 account depending on game
Website www.miwin.com

Miwin's Dice were invented in 1975 by the physicist Michael Winkelmann. They abide of three altered dice with faces address numbers from 1 to 9, with adverse abandon accretion to 9, 10, or 11. The numbers on anniversary die accord the sum of 30 and accept an addition beggarly of 5.

Contents

Description

Miwin's dice accept 6 abandon like accepted dice, and anniversary ancillary shows altered numbers. The accepted set is fabricated of wood; appropriate designs are fabricated of titanium (see picture) or added abstracts (gold, silver). The numbers (dots) on anniversary die are atramentous blue, red or black.

Each die is called for the sum of its 2 everyman 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 adverse sides. Added numbers are 5 and 6 on die III, 4 and 5 on die IV, and 4 and 6 on die V. The dice are advised in such a way that for every die there exists one that will usually win adjoin it. A accustomed die will accept a college amount with a anticipation of 17/36, or a lower amount with a anticipation of 16/36. III wins adjoin IV, IV adjoin V, and V adjoin III. Such dice are accepted as nontransitive.

Miwins dice IX, X, XI

Second set of Miwin's dice: IX, X, XI

Each die is called for the sum of its everyman and accomplished number.

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

Mathematical attributes

design of numbers of Miwins dice III, IV, V
design of numbers of Miwins dice IX, X, XI

Each of the dice has agnate attributes -- there is no bifold number, the sum of the numbers is 30, and anniversary amount from 1 to 9 is advance alert over the three dice. This aspect characterizes the accomplishing of intransitive dice, enabling all the altered bold variants. All the amateur charge alone 3 dice, in allegory to added abstract nontransitive dice advised in appearance of mathematics such as Efron's dice.1

Because of these appropriate attributes Miwin's dice are acclimated aswell in the breadth of education. Miwin's dice advice to advance the algebraic highlights and enhance the adeptness to account probability, as happened in the summer division 2007 during a academy at the University of Siegen.

Games

Since the average of the eighties the columnist wrote about the games.2 Winkelmann presents his amateur aswell himself, for archetype in Vienna at the "Österrechischen Spielefest, "Stiftung Spielen in Österreich", Leopoldsdorf, area "Miwin's dice" 1987 won the cost "novel absolute dice bold of the year".

In 1989 the amateur were advised by the journal "Die Spielwiese".3 At that time 14 alternatives of bank and cardinal amateur existed for Miwin's dice. Aswell the journal "Spielbox" had in the class "Unser Spiel im Heft" (now accepted as "Edition Spielbox") two variants of amateur for Miwin's dice to be taken out of the magazine. It was the anchoress bold 5 to 4 and the cardinal bold Bitis for two persons.

In 1994 Vienna's Arquus publishing abode appear Winkelmann's book "Göttliche Spiele",4 which independent 92 games, a adept archetype for 4 bold boards, affidavit about the algebraic attributes of the dice and a set of Miwin's dice. Now one can acquisition about 120 bold variants for free.5

With Miwin's dice cardinal amateur gambles are possible. Variants with both elements aswell exist. The built-in attributes of the dice could could cause able-bodied authentic probabilities and algebraic phenomena.

Solitaire amateur and amateur for up to nine humans alpha with the age of 6 available. Some of the amateur charge a bold board. Playing time is from 5 account to 60 minutes.


Features

The anticipation for a accustomed amount with all 3 dice is 11/36, for a accustomed formed bifold is 1/36, for any formed bifold 1/4. The anticipation to access a formed bifold is alone 50% compared to accustomed dice.

Cumulative frequency

Cumulative abundance blazon III and IV

Cumulative abundance blazon III and V

Cumulative abundance blazon IV and V

Cumulative abundance blazon III and IV and V = "Miwin-Distribution"

Reversed intransitivity

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

Equal administration of accidental numbers

Miwin's dice acquiesce to actualize several according distributions. Abacus a connected 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

Variants 0 - 80

1st Variant

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

1st bandy * 9 - 2nd throw

Examples
1st 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 alternative provides numbers from 0 - 80 with a anticipation of (1/9)², 81 = 9²


2nd Variant

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

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

Examples
1st 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 alternative provides numbers from 0 - 80 with a anticipation of (1/9)², 81 = 9²

3rd Variant

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

Both throws with 9 gives 0 1st bandy = 9 and 2nd bandy not 9 gives 10 * 2nd bandy 1st bandy = 8 gives 2nd bandy all added accord 10 * 1st bandy - 2nd throw

Examples
1st 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


Other distributions

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

To access an according administration with numbers from 0 - 90 bandy 3 times.

  1. ) Take one dice by random, cycle it and lay it back: 1st throw!
  2. ) Take one dice by random, cycle it and lay it back: 2nd throw!
  3. ) Take one dice by random, cycle it and lay it back: 3rd throw!

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

Examples
1st 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 anticipation 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 anticipation 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 anticipation of 1 / 9³

  1. ) Take one dice by random, cycle it and lay it back: 1st throw!
  2. ) Take one dice by random, cycle it and lay it back: 2nd throw!
  3. ) Take one dice by random, cycle it and lay it back: 3rd throw!

Creating a amount arrangement with abject 9:

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

Examples
1st 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), anniversary with a anticipation of 1 / 9³ = 1 / 729 728 = 9³ - 1

Combinations of numbers with Miwin's dice blazon III IV and V

Variant Equation number of variants
one bandy with 3 dice, types don't mind - 135
one bandy with 3 dice, blazon is an added attribute (135 – 6 * 9) * 2 + 54 216
1 bandy with anniversary type, blazon is not acclimated as attribute 6 * 6 * 6 216
1 bandy with anniversary type, blazon is acclimated as attribute 6 * 6 * 6 * 6 1296
3 throws, accidental alternative of one of the dice for anniversary throw, blazon is not acclimated as attribute 9 * 9 * 9 729

3 throws, accidental alternative of one of the dice for anniversary throw, blazon is acclimated 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.

Notes

  1. ^ http://www.miwin.com/ bang "Miwin'sche Würfel 2", again analysis attributes
  2. ^ Austrian cardboard "Das Weihnachtsorakel, Spieltip "Ein Buch mit zwei Seiten", the Accepted 18.Dez..1994, page 6, Pöppel-Revue 1/1990 page 6 and Spielwiese 11/1990 page 13, 29/1994 page 7
  3. ^ 29/1989 page 6
  4. ^ The book on the German adaptation of Amazon
  5. ^ Winkelmann's homepage

External links

Published games

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