Dice with Special Numbers

2,2,1,1

D6 Pipped

12,11,10,9,8,7

Opposite faces sum to 19

9,8,5,4,3,1

Non-transitive die

Miwin

9,7,6,5,2,1

Non-transitive die

Miwin

8,7,6,4,3,2

Non-transitive die

Miwin

8,6,5,4,3,1

Sicherman die

GameStation

6,6,6,6,6,6

wooden

6,6,3,3,2,2

Loaded die

Koplow

6,6,6,2,2,2

Loaded die

6,6,5,5,1,1

Loaded die

Koplow

6,6,4,4,2,2

Loaded die

Koplow

6,5,4,3,2,1

Regular D6

More types see here

6,5,4,3,2,blank

Type 1

6,5,4,3,2,blank

Type 2

6,5,4,2,blank,blank

6,3,3,3,3,3

Non-transitive die

Grand Illusions

5,5,5,5,5,5

Loaded die

5,5,5,2,2,2

Non-transitive die

Grand Illusions

5,5,4,4,3,3

Loaded die

Koplow

5,5,4,4,1,1

Loaded die

Koplow

5,5,3,3,1,1

Loaded die

Koplow

5,4,4,3,3,2

Averaging die

5,4,3,2,1,blank

Left handed

5,4,3,2,1,blank

Right handed

4,4,4,4,4,4

Cheater

4,4,4,4,4,1

Non-transitive die

Grand Illusions

4,3,3,2,2,1

Sicherman die

GameStation

3,3,3,3,3,3

Cheater

3,3,2,2,1,1

Plastic (left), wood (center), wood bi-color (right)

D6, Non-Neg Int

In order to uniquely describe the configuration of a die, the following nomenclature was defined. We start by pacing te die such that the highest number is on top and next highest number is on the right (clockwise). This is corresponds to the left photo. The right photo shows the die when it is rotated by 180 degrees along the horizontal axis which lies in parallel to the screen. In this way, the opposite faces are shown top-top, left-right and right-left.

Nomenclature: The orientations of the numbers are shown in the figure below

We list the numbers in the order shown below:

As an example, let’s look at this backgammon doubling die with numbers 64,32,16,8,4, and 2. The highest number, “64”, is on top, followed by “16” clockwise (note that “16” was chosen because “32” is opposite of “64”).

64,32,16,8,4,2

64UL16D4D32LL8U2U

If certain numbers appear more than once, the rule above may lead to more than one solution. For this case, use the following rules to place the die:

1) Highest number on top (position one)

2) Next highest possible number clockwise (position two)

3) Next highest possible number in position 3

If this is still ambiguous:

4) Place the die such that the top number (position one) looks (in decreasing order of priority) in direction UL, UR, LR, LL

If this is still ambiguous:

5) Place the die such that the number in position two looks (in decreasing order of priority) in direction U, R, D, L

If this is still ambiguous:

6) Place the die such that the number in position three looks (in decreasing order of priority) in direction U, R, D, L

If this is still ambiguous, repeat steps 4) to 6) for the numbers in position 4) to 6)

Example: The following die is numbered 4,4,4,4,0,0. The two 0s are on opposite faces, hence there is no angle from where 3 4s can be seen. Hence the die is rotated such that 2 4s are on top and to the right (rules 1-2). Then a 0 is on the left. Find a rotation that the top 4 points to UL (rule). There are two possible orientations for the second 4: L and R. Choose R, as this has higher priority (rule)

4,4,4,4,0,0

4UL4R0R4LL4R0R

Non-transitive die

Grand Illusions

Above 64

971,872,773,377,278,179

971UL872L773U179UR278D377D

Trick die

971,872,773,377,278,179

971LL872L773R179UL377L278R

Trick die

Same numbers as yellow die above

960,762,663,564,366,168

960LL762D663R168LR564U366U

Trick die

960,663,564,366,267,168

960LL663L564L168UL366L267L

Slightly different numbers than green die above
(267 instead of 762)

Trick die

954,855,756,657,558,459

954LL855D657R459LR558U756U

Trick die

954,855,756,657,558,459

954LL855D657D756UL459U558U

Same numbers as yellow die above

Trick die

913,814,616,517,418,319

913UR814R319L616LR517R418L

Trick die

902,803,704,605,506,209

902LR803L605R506UR704L209R

Trick die

840,741,642,543,345,147

840UL741R543L642LL147L345D

Trick die

840,741,642,543,345,147

840UR741R345R642LR147R543R

Same numbers as black die above

Trick die

780,681,483,384,285,186

780UL681U285L483LL384D186L

Same numbers as red die below

Trick die

780,681,483,384,285,186

780UR681D483R384UR186D285R

Trick die

690,591,492,393,294,195

690UR591R195D492LR393R294U

Trick die

500,200,200,100,50,50

500UR200L50U100UL200L50L

Monopoly Express

400,300,250,200,200,200

400LR300L200L200UL250U200L

Monopoly Express

400,300,250,200,200,200

400LL300D200U200LL250R200U

Monopoly Express

300,280,260,240,220,200

300UR260R200D280LR240R220U

260,240,220,200,180,160

260LL240L220D160UL180L200U

Opposite faces sum to 420

250,225,200,175,150,125

250U200UL150LL225R175LR125UR

Diagonal numbers!

200,190,190,180,170,160

200LL190L160D190UL170U180U

Additional “4” on each face

The Golf Game

200,180,160,140,120,100

200LR180D120D100UR140U160R

150,150,100,100,100,100

150UL100U100U150UL100U100D

bulb
Monopoly Express

150,150,100,100,100,100

150UL100U100L150UR100R100R

tap
Monopoly Express

81,72,54,36,18,9

81_UL72U36_L18_LL9_U54L

Backgammon Doubling Dice

There are surprisingly many configurations of D6 Backgammon doubling dice. Most “normal” (1..6) D6 are numbered such that opposite faces sum to 7. An analogy for doubling dice would be to print the numbers such that opposite faces multiply to 128 (64x2, 32x4, 16x8). However there are only few such doubling dice in my. Most of the dice use a numbering scheme 64-32, 16-8, 4-2.

64-2, 32-4, 16-8, 64/32/16

If the die is placed such that “64” is on top and “32” on the right, the third number that can be seen is “16”.

64,32,16,8,4,2

Backgammon

64UR32R16U2UL4L8U

Opposite faces multiply to 128

64,32,16,8,4,2

Backgammon

64UR32D16U2UL4U8U

Opposite faces multiply to 128

64,32,16,8,4,2

Backgammon

64LR32L16R2UR4L8R

Opposite faces multiply to 128

64,32,16,8,4,2

Backgammon

64LL32L16L2UL4L8D

Opposite faces multiply to 128

64-2, 32-4, 8-16, 64/32/16

If the die is placed such that “64” is on top and “32” on the right, the third number that can be seen is “8”.

64,32,16,8,4,2

Backgammon

64LL32R8L2UL4L16R

Opposite faces multiply to 128

64,32,16,8,4,2

Backgammon

64LL32L8L2UL4L16R

Opposite faces multiply to 128

64-16, 32-8, 4-2, 64/32/4

64,32,16,8,4,2

Backgammon

64LR32R4U16LR8D2L

Italic font

64-4, 32-16, 2-8, 64/32/2

64,32,16,8,4,2

Backgammon

64LR32R2L4UL16D8U

64,32,16,8,4,2

Backgammon

64LR32R2D4UL16D8U

64-4, 32-16, 8-2, 64/32/8

64,32,16,8,4,2

Backgammon

64LL32R8D4UL16L2D

64-32, 16-8, 4-2, 64/16/4

If the die is placed such that “64” is on top and “16” on the right, the third number that can be seen is “4”.

64,32,16,8,4,2

Backgammon

64ULI6U4U32UR8D2D

64,32,16,8,4,2

Backgammon

64UL16U4L32UR8R2L

64,32,16,8,4,2

Backgammon

64UL16R4L32LL8L2L

64,32,16,8,4,2

Backgammon

64UL16D4D32LL8U2U

64,32,16,8,4,2

Backgammon

64UL16D4D32LL8U2D

64,32,16,8,4,2

Backgammon

64UL16D4L32LL8U2L

Plastic, 18mm (top left), plastic, 17mm (top right),

wood,18mm (2nd left), wood 19mm (2nd right)

plastic 16mm (3rd left), plastic 12mm (3rd right)

plastic 18mm (bottom left), plastic 16mm (bottom right)

64,32,16,8,4,2

Backgammon

64UR16U4L32LL8L2U

64,32,16,8,4,2

Backgammon

64UR16R4U32UL8U2U

64,32,16,8,4,2

Backgammon

64UR16R4D32LR8D2R

Italic font

64,32,16,8,4,2

Backgammon

64UR16R4L32UL8L2L

Italic font

64,32,16,8,4,2

Backgammon

64UR16D4R32UL8D2L

64,32,16,8,4,2

Backgammon

64UR16D4L32UR8U2L

64,32,16,8,4,2

Backgammon

64LR16U4U32UR8D2D

64,32,16,8,4,2

Backgammon

64LR16D4D32UR8U2U

64,32,16,8,4,2

Backgammon

64LR16D4D32LL8U2U

64,32,16,8,4,2

Backgammon

64LR16L4L32UR8R2R

64,32,16,8,4,2

Backgammon

64LL16L4D32UL8L2U

64,32,16,8,4,2

Backgammon

64LL16L4L32UL8L2L

64-32, 16-8, 2-4, 64/16/2

If the die is placed such that “64” is on top and “16” on the right, the third number that can be seen is “2”.

64,32,16,8,4,2

Backgammon

64UL16U2U32LR8D4D

Special font

64,32,16,8,4,2

Backgammon

64UL16R2U32LL8L4D

64,32,16,8,4,2

Backgammon

64UL16R2R32LL8D4L

64,32,16,8,4,2

Backgammon

64UL16D2R32LL8D4L

64,32,16,8,4,2

Backgammon

64UR16R2U32UL8R4L

64,32,16,8,4,2

Backgammon

64UR16R2U32UR8R4D

64,32,16,8,4,2

Backgammon

64UR16D2L32LL8U4L

64,32,16,8,4,2

Backgammon

64UR16L2U32UL8L4U

64,32,16,8,4,2

Backgammon

64R16UR2LL32L8UL4LR

Note that numbers are diagonal!

64,32,16,8,4,2

Backgammon

64LR16U2U32UR8D4D

64,32,16,8,4,2

Backgammon

64LR16R2U32UR8R4D

Font with serifs (top row), sans serif (bottom row)

64,32,16,8,4,2

Backgammon

64LR16R2U32UR8L4D

64,32,16,8,4,2

Backgammon

64LR16R2U32LR8R4D

64,32,16,8,4,2

Backgammon

64LR16R2U32LL8R4D

64,32,16,8,4,2

Backgammon

64LR16R2R32UR8R4D

64,32,16,8,4,2

Backgammon

64LR16D2U32LL8D4D

64,32,16,8,4,2

Backgammon

64LR16D2R32UR8U4U

64,32,16,8,4,2

Backgammon

64LR16D2R32LL8U4L

64,32,16,8,4,2

Backgammon

64LR16D2D32LL8U4U

64,32,16,8,4,2

Backgammon

64LR16L2U32UR8L4D

64,32,16,8,4,2

Backgammon

64LR16L2U32LR8R4D

64,32,16,8,4,2

Backgammon

64LL16R2U32UR8R4D

64,32,16,8,4,2

Backgammon

64LL16R2R32UL8D4L

64,32,16,8,4,2

Backgammon

64LL16R2R32LR8R4L

64,32,16,8,4,2

Backgammon

64LL16R2R32LR8D4L

64,32,16,8,4,2

Backgammon

64LL16R2L32LL8L4D

64,32,16,8,4,2

Backgammon

64LL16D2R32UL8U4L

64,32,16,8,4,2

Backgammon

64LL16D2R32UL8D4L

64,32,16,8,4,2

Backgammon

64LL16D2R32LR8D4L

64,32,16,8,4,2

Backgammon

64LL16D2D32LL8D4R

64-32, 16-4, 2-4, 64/16/2

64,32,16,8,4,2

Backgammon

64LL16D2D32LR8U4U

64-32, 16-2, 8-4, 64/16/8

64,32,16,8,4,2

Backgammon

64UL16D8R32UL2R4D

64-32, 16-4, 8-2, 64/16/8

64,32,16,8,4,2

Backgammon

64UL16U8U32UR4D2D

Below 64

60,50,40,30,20,10

60UR50D40U10UL20U30U

Opposite faces sum to 70

40,32,24,16,8,8

40UR24D8D32UL8U16_U

40,30,25,20,15,10

40UR25D10_D30UL15U20U

36,30,24,18,12,6

36UL24U6U30LL18D12D

MEGADICE

35,32,25,18,11,4

35UR25R4R32UR11L18L

35 red

Lotto die?

35,29,23,17,11,5

35UL23U5U29LL17D11D

MEGADICE

35,28,21,17,14,7

35LR28L21L17UL14R7R

17 red

Lotto die?

34,28,22,16,10,4

34UL22U4U28LL16D10D

MEGADICE

34,27,26,20,13,6

34LR27L20L26UL13R6.R

26 red

Lotto die?

33,31,24,17,10,3

33UR24R3R31UR10L17L

33 red

Lotto die?

33,28,26,19,12,5

33LR26L19L28LL12L5R

28red

Lotto die?

33,27,21,15,9,3

33UL21U3U27LL15D9_D

MEGADICE

32,26,20,14,8,2

32UL20U2U26LL14D8D

MEGADICE

31,25,19,13,7,1

31UL19U1U25LL13D7D

MEGADICE

30,30,20,20,10,10

30UR20R10L30UL20L10R

Opposite faces are identical

30,29,28,27,26,25

30LR29R27L25LR26D28U

Opposite faces sum to 55

Educational die

30,23,18,16,9,2

30UL23L16L18LL9.R2R

18red

Lotto die?

29,22,15,8,5,1

29LR22L15L5UL8R1R

5 red

Lotto die?

24,23,22,21,20,19

24LR23R21L19LR20D22U

Opposite faces sum to 43

Educational die

24,19,16,15,14,11

D6, Edged Cigar Shape

Kick Return Die

Football Fever

20,15,10,5,5,0

20LR15U5U10UR0U5D

Half-Time Football

18,17,16,15,14,13

18LR17U15D14LL13D16U

Educational die

16,15,14,13,12,11

16UL15U13D11UR12U14U

Opposite faces sum to 27

15,14,13,12,11,10

15UL14U12D10UR11U13U

Opposite faces sum to 25

15,14,9,8,4,2

15LR9.R4D14UR2L8R

15,12,10,7,5,2

15UL12R7U5LR10R2U

15,12,10,7,5,2

15UR10U2R12LR5R7L

15,12,10,7,4,2

15UL12U2D10UR7U4D

15,12,9,7,5,2

15UR9.U2R12LR5R7L

15,12,9,7,5,2

15UR9.L2L12LR5R7R

15,12,8,6,4,1

15UL12L4L1UR6_R8R

15,11,10,6,5,1

15UR11U1R10LR5R6.R

15,11,10,6,5,1

15UR10U1R11LR5R6.R

15,9,5,3,2,1

15LR9_D5U1LL3D2U

15,6,5,4,3,1

15UL6_U1D4UR5U3D

14,13,12,11,10,9

14UL13U11D9_UR10U12U

Opposite faces sum to 23

14,13,10,9,5,4

14LR13L10R4LR9.D5R

14,13,9,8,4,3

14UR9.U8L13UL4R3L

14,13,9,8,4,3

14LR9.L3L13LL4L8D

14,12,11,10,2,1

14UL11U1U12UR2U10U

14,12,9,7,4,2

14UR9.U7R12LR4R2L

14,12,9,7,4,2

14UR9.L2L12LR4R7R

14,11,7,6,5,2

14UL11U2U7UR6_U5U

14,11,6,5,3,2

14UL11U2U5UR3U6_U

14,8,5,4,2,1

14UR8U4U2UL1U5U

13,12,11,10,9,8

13UL12U10D8UR9_U11U

Opposite faces sum to 21

13,12,9,8,4,3

13LL12L3U9_UL8L4U

13,12,9,8,4,3

13LR8L3R12LL4R6.U

13,12,8,7,4,3

13LL12L3U8UL7L4U

13,12,8,6,4,3

13UR8L3L12LR6.R4R

13,11,8,6,3,1

13UR11L1L3LR6.R8R

13,11,8,6,3,1

13LR11U1R3LR6.R8R

13,11,8,6,3,1

13UR8L1L11LR3R6.R

13,11,8,6,3,1

13LR8D1R11LR3L6.R

13,10,9,6,4,1

13LR10D9_D4LL6_D1D

13,10,9,5,4,1

13LL10L1U9_UL5L4U

13,10,8,4,3,1

13UL8U4U10UR1U3U

13,9,8,6,3,2

13LR8D3D9_LL6_D2D

12,11,10,10,9,2

12LR10_D10_D11LL2U9_U

12,11,10,9,8,7

Opposite faces sum to 19

12UL11D10L7UL8U9.R

Educational die

12,11,10,9,8,7

Opposite faces sum to 19

12UR11D10U7UL8U9.U

Educational die

12,11,10,9,8,7

12UL11U9_D7UR8U10U

Opposite faces sum to 19

12,11,10,9,8,7

Opposite faces sum to 19

12LR11L9.U7UR10D8L

Educational die

12,11,10,9,8,7

Opposite faces sum to 19

12LR11L9.R7LL8L10L

Educational die

12,11,10,9,8,7

Opposite faces sum to 19

12LR11L8L7UR9.R10R

Educational die

12,11,10,9,8,7

Opposite faces sum to 19

12LR11R8R7UL9.R10L

Educational die

12,11,8,7,3,2

12LL11L2U8UL7L3U

12,11,7,6,3,2

12LL11L2U7UL6_L3U

12,11,7,6,2,1

12UR7U1R11LR2L6.R

12,10,8,5,4,3

12UL8U5U10UR3U4U

12,10,7,4,3,2

12UL7U4U10UR3U2U

12,9,8,7,3,1

12LR8D1D9_LL7D3D

11,10,9,8,7,6

11UL10U8D6_UR7U9_U

Opposite faces sum to 17

11,10,7,6,2,1

11LL10L1U7UL6_L2U

11,10,6,5,2,1

11LL10L1U6_UL5L2U

11,8,7,5,3,0

IIUL8D7L3LL0U5L

Break the Safe

10,9,8,7,6,5

Opposite faces sum to 15

10UL9.R8R5UL6.U7L

10,9,8,7,6,5

10UL9_U7D5UR6_U8U

Opposite faces sum to 15

Real Math - A Sampler of Games

10,9,8,7,6,5

Opposite faces sum to 15

10LL9_R7R5UL6_U8D

Phase 10 Dice

10,9,8,7,6,5

Opposite faces sum to 15

10LR9.R7L5UR6.D8D

10,9,8,7,6,5

Opposite faces do not sum to 15

I0LL9_D6_D5LR7U8U

Wooden, 25mm, TENS (left, yellow), 20mm (right, red, underlined)

10,9,8,7,6,5

Opposite faces do not sum to 15

10LL9.D6.D5LR7U8U

Wooden, 20mm

10,9,8,7,6,5

Opposite faces do not sum to 15

10LL8U7U9_LR6_D5D

10,9,8,7,6,5

Opposite faces do not sum to 15

10LR8L5L9_UR6_R7R

10,9,8,7,6,0

10UL9_R6_D0UL8L7D

wooden

10,9,7,6,5,3

10_UR9_U7U6_UL5D3D

9,9,8,7,6,6

9.UL9.U6.U8UR7U6.D

9,8,7,6,5,4

Opposite faces sum to 13

9.UL8D7R4LL5L6.U

9,8,7,6,5,4

Opposite faces do not sum to 13

9_UL8U6_U5UL4L7D

9,8,7,6,5,4

9_UL8U6_D4UR5U7U

Opposite faces sum to 13

9,8,7,6,5,4

9.UL8L6.U4LR5D7U

Opposite faces sum to 13

Beginner Die

9,8,7,6,5,4

Opposite faces sum to 13

9.UR8D6.U4LR5U7U

9,8,7,6,5,4

9_LL8D6_R5LR4U7D

9,8,7,6,5,4

Opposite faces sum to 13

9_LR7L4L8UR5R6_R

9,8,7,6,5,blank

9,8,7,3,2,1

9.UR8L3U2UL7L1U

9,8,7,2,1,0

9_LL8D1R7LR0R2L

9,8,7,2,1,0

9_UL8L0R7UL1R2R

9,8,7,2,1,0

Everlasting calendar,

matches with 5,4,3,2,1,0.

9 can also be read as 6.

9LR8D2L1LL7U0R

30mm, hollow plastic

9,8,7,2,1,0

9.LL8R7R0UL2L1

9,8,7,2,1,0

Everlasting calendar,

matches with 5,4,3,2,1,0

(missing in my collection).

9 can also be read as 6.

9UL7R2R8UR1L0U

9,8,7,2,1,0

Everlasting calendar,

matches with 5,4,3,2,1,0.

9 can also be read as 6.

9LR7D0U8LL1U2U

9,8,7,2,1,blank

9,8,5,4,3,2

9_UR5D2D8UL3U4U

9,4,3,2,1,0

9_LR4D2D1UR3R0U

8,8,6,6,4,4

8UR6.R4U8UL6.R4D

Airships

8,7,7,6,6,5

8UR7U6.R5UR7L6.R

Wood, 18mm

The Golf Rules Game

8,7,6,5,4,3

Opposite faces do not sum to 11

8LL7D6.D5LR3U4L

8,7,6,5,4,3

8UL7U5D3UR4U6_U

Opposite faces sum to 11

8,7,6,5,4,3

Opposite faces do not sum to 11

8UL6_L5U7LR4R3U

8,7,6,5,4,3

Opposite faces do not sum to 11

8LR6R5R7UL4R3R

8,7,6,5,4,3

Opposite faces do not sum to 11

8UR6_D3D7UL4U5U

8,7,6,5,4,3

Opposite faces do not sum to 11

8LR6_L3L7UR4R5R

8,7,6,5,4,3

Opposite faces do not sum to 11

8LL6_D3D7LL4U5U

8,7,6,2,1,0

Everlasting calendar

matches with 5,4,3,2,1,0.

6 can also be read as 9.

8UL7U2U6LL1D0U

8,7,6,2,1,0

Everlasting calendar

matches with 5,4,3,2,1,0

(missing in my collection).

6 can also be read as 9.

8UL7L0U6UR1R2

8,7,6,2,1,0

Everlasting calendar,

matches with 5,4,3,2,1,0.

6 can also be read as 9.

8UL6D0U7LL1U2U

30mm, hollow plastic

8,7,4,3,2,1

8UR4L1L7LR2R3R

8,7,4,2,1,0

8UL7R2U4LL1R0R

8,6,5,4,3,1

8UR5L4L6.LR3L1R

Sicherman die

Grand Illusions

7,6,5,4,3,2

7UL6_U4D2UR3U5U

Opposite faces sum to 9

7,6,5,4,3,2

Opposite faces do not sum to 9

7LL6_L3R5UL4L2R

7,6,5,4,3,2

Opposite faces do not sum to 9

7LR5D3R6.UR2D4R

7,6,5,4,3,2

Opposite faces do not sum to 9

7LR5L2L6_UR3R4R

7,5,4,3,2,1

7UR5L4U2UL3L1U

6,6,5,4,3,2

6.LR5R4D6.UR2R3R

Cheater, 1 replaced by 6

6,6,2,2,2,2

6.UL2R2D6.LL2U2D

Non-transitive die

Grand Illusions

6,5,4,4,3,3

6.UR4D3U5LR4D3L

6,5,4,3,2,1

Regular D6

More types see here

5,5,5,1,1,1

5UL5D1U5UR1D1D

Non-transitive die

Grand Illusions

5,5,4,4,3,2

5LL4L3U5UL4L2D

Wood, 16mm

The Golf Rules Game

5,5,2,2,0,0

5UL2U0U5UR2D0U

Opposite faces are identical

Mission Command Air

Screaming Eagles Game

5,4,4,3,3,2

Opposite faces sum to 7

Averaging die

5UL4U4U2LR3D3D

5,4,4,3,3,2

Opposite faces sum to 7

Averaging die

5UR4U4U2LR3D3D

Airships

5,4,4,3,3,2

Opposite faces sum to 7

Averaging die

5LL4R4R2UL3L3L

13 Dead End Drive

5,4,4,3,3,2

Opposite faces sum to 7

Averaging die

5LL4R4L2UR3D3U

5,4,4,3,3,2

Opposite faces sum to 7

Averaging die

5LL4L4L2UR3U3U

5,4,4,3,3,2

Opposite faces do not

sum to 7

Averaging die

5UL4U3D2LR4R3D

5,4,3,3,2,2

5UL4U3D2LR2U3R

Outburst

5,4,3,3,2,2

5UL4U3D2UR2U3U

5,4,3,3,2,2

5UL4U3D2LR2U3U

5,4,3,3,2,2

5UL4U3D2LL2L3R

5,4,3,2,1,1

5UL4U2D1UR1U3U

Opposite faces sum to 9

5,4,3,2,1,1

5UL4R1U2LL3D1D

Cheater, 6 replaced by 1

5,4,3,2,1,0

Opposite faces sum to 5

5UR4R3D0UL1R2D

5,4,3,2,1,0

Opposite faces sum to 5

5LR4U3U0UL1D2D

5,4,3,2,1,0

Opposite faces sum to 5

5LL4R3D0UR1R2D

South Korea

5,4,3,2,1,0

5UL4U2D0UR1U3U

Opposite faces sum to 5

Real Math - A Sampler of Games

5,4,3,2,1,0

Opposite faces

do not sum to 5

5LR4U1U2LL3D0U

5,4,3,2,1,0

Opposite faces

do not sum to 5

5LL4DIU0UL2U3U

5,4,3,2,1,0

Opposite faces

do not sum to 5

5LL4D1D0UL2U3U

Wooden, 20mm (left), 14mm (right)

5,4,3,2,1,0

Opposite faces

do not sum to 5

5LL4U0U2UL3D1D

5,4,3,2,1,0

Opposite faces

do not sum to 5

5UR3L2L4LR1R0R

wooden

5,4,3,2,1,0

Opposite faces

do not sum to 5

5LL3D2D4LR0U1U

5,4,3,2,1,0

Everlasting calendar,

matches with 9,8,7,2,1,0.

5UL3D0U4LL1U2U

30mm, hollow plastic

5,4,3,2,1,0

Everlasting calendar,

matches with 9,8,7,2,1,0.

5LR3D0U4LL1U2U

5,4,3,2,1,blank

5,3,2,1,1,0

5UL2L1U3LR0U1U

Babylon 5

4,4,4,4,0,0

4UL4R0R4LL4R0R

Non-transitive die

Grand Illusions

4,4,4,3,3,2

4UR4U4L3LR2U3R

4,3,3,2,2,1

4UR3U1U3UL2R2R

Sicherman die

Grand Illusions

3,3,3,3,3,3

3UL3U3U3LL3D3D

Non-transitive die

Grand Illusions

3,3,2,2,2,1

3UL2D2D3LL2R1L

3,3,2,2,2,1

3LR2U2U3UR1D2D

3,3,2,2,1,1

3UL3R2L1LL1L2L

Opposite faces sum to 4

3,3,2,2,1,1

3UL3L2L1LL1L2L

Opposite faces sum to 4

Push Over

3,3,2,2,1,1

3UL3L2LIURIL2L

Opposite faces sum to 4

Mission Command Air

Screaming Eagles Game

3,3,2,2,1,1

3UL2U1U3LL2D1

Opposite faces are identical

3,3,2,2,1,1

3UL2U1L3LL2R1L

Opposite faces are identical

Airships

3,3,2,2,1,1

3UL2U1R3UR2R1R

Opposite faces are identical

3,3,2,2,1,1

3UL2D1R3UL2R1D

Opposite faces are identical

3,3,2,2,1,1

3UL2D1L3UR2L1L

Opposite faces are identical

3,3,2,2,1,1

3UR2U1U3UL2D1U

Opposite faces are identical

3,3,2,2,1,1

3UR2U1U3LR2D1D

Opposite faces are identical

3,3,2,2,1,1

D3, foam

3UR2R1U3UL2L1D

Opposite faces are identical

3,3,2,2,1,1

3UR2R1U3LR2R1D

Opposite faces are identical

3,3,2,2,1,1

3UR2R1R3LR2L1L

Opposite faces are identical

Wood, serifs (left), plastic, sans serifs (right)

3,3,2,1,1,0

3LL2D1U3LR1R0R

3,2,2,1,1,0

3UR2D1D0UR2L1R

Wood, 14mm

The Golf Rules Game

3,2,1,1,1,0

3UL2R1U1UL1U0R

Babylon 5

Defense Grid Die

3,2,1,1,1,0

3UL1D1D2UR0U1U

3,2,1,1,1,0

3LR1D1D2UL0U1U

2,2,2,1,1,1

2UL2D2UIULIUIR

2,2,2,1,1,1

2UR2R1R1UR2D1R

2,2,2,1,1,1, EVEN, ODD

2,1,1,0,0,0

2UR1U0U1UR0U0U

1,1,1,0,0,0

Binary die

1LR1U1U0UL0U0U

1,1,1,0,0,0

Binary die

1LR1U1R0UR0U0R

D6, Pos Neg Math

+6.,+5,+4,+3,+2,+1

Addition, 6 dotted

+6_,+5,+4,+3,+2,+1

Addition, 6 underlined

6,4,2,-1,-3,-5

Odd Negative

+5,+4,+3,+2-1,-2

5,3,1,-2,-4,-6

Even Negative

3,2,1,0,-1,-2

3,2,1,-1,-2,-3

-6,-5,-4,-3,-2,-1

6 dotted

-6,-5,-4,-3,-2,-1

6 underlined

x6.,x5,x4,x3,x2,x1

Multiplication

D6, Fractions

1,5/6,2/3,1/2,1/3,1/6

1/1,1/2,1/3,1/4,1/5,1/6

1/1UL1/3U1/5U1/2UR1/4R

1/6D

1/1,1/2,1/3,1/4,1/5,1/6

1/1UL1/3U1/5L1/2UR1/4L

1/6R

2/2,3/4,2/3,2/3,2/3,2/4

11/12,7/8,5/6,3/4,2/3,1/2

3/4,2/3,2/4,1/2,1/3,1/4

1/2,1/2,1/3,1/3,1/4,1/6

Opposite faces are

identical

1/2,1/3,1/4,1/4,1/6,1/6

1/2,1/3,1/4,1/5,1/6,1/8

1/2,1/3,1/4,1/6,1/8,1/12

1/2LR1/3D1/6D1/12LL1/8D

1/4U

1/2,1/3,1/4,1/6,1/8,1/12

I/I2ULI/3RI/8RI/4URI/6U

I/I2R

1/2,1/4,1/4,1/8,1/8,1/8


1/3,1/6,1/6,1/12,1/12,1/12	1/6,1/6,1/8,1/8,1/9,1/9

D6, Decimal Fractions


1,.75,.67,.50.,33,.25	1.00,0.75,0.67,0.50,0.33,0.25	1.00,0.50,0.25,0.10,0.05,0.01

D6, Circle Fractions

1,2/2,3/3,4/4,5/5,6/6

Design by Jen Asperheim

D8


128,64,32,16,8,4,2,1 128U64U32U16U1U2U4U8U Product of opposite faces is 128 Doubling die	47,40,34,31,20,17,11,4 47UIIU3IUI7U20U4U40U34U blunt vertices Roll to Riches Lotto Dice	46,37,32,28,25,22,12,1 46UI2U37U28U32UIU22U25U blunt vertices Roll to Riches Lotto Dice


45,36,27,16,13,9,6 45UI3U9_UI6U36U2IU6_U27U blunt vertices Roll to Riches Lotto Dice	43,42,38,18,15,8,7,5 43U5UI8U8U42U7U35UI5U blunt vertices Roll to Riches Lotto Dice	35,30,29,26,23,14,10,3 35U26U23U30UI0U14U29U3U blunt vertices Roll to Riches Lotto Dice

9,8,7,6,5,4,3,2

8,8,7,7,6,6,5,4

8U6-U7U5U4U7U6.U8U

2x(8,7,6,5,4)

5,5,4,4,3,2,1,0

5U4U3UIU0U2U4U5U

Beginner Die

4,4,3,3,2,2,1,1

4U2U3UIUIU3U2U4U

Opposite faces sum to 5

4,4,3,3,2,2,1,1

4U1U3U2U1U4U3U2U

Opposite faces sum to 5

D4, blunt vertices

GameScience

4,4,3,3,2,2,1,1

4U1U3U2U1U4U3U2U

Opposite faces sum to 5

3,2,2,2,1,1,1,0

3UIU2UIU0U2UIU2U

3D2 (sum of 3 binary dice)

Exile Game Studio

(Ubiquity Dice)

2,2,1,1,1,1,0,0

2UIU0UIU0UIU2UIU

2D2 (sum of 2 binary dice)

Exile Game Studio

(Ubiquity Dice)

1,1,1,1,0,0,0,0

IU0UIU0U0UIU0UIU

D2 (binary die)

Exile Game Studio

(Ubiquity Dice)

1,7/8,3/4,5/8,1/2,3/8,1/4,1/8

Fractional D8, n/8, n=1..8

D10

900000,…,100000,000000

900000R100000R500000R

700000R300000R200000R

000000R600000R

400000R

800000R

Koplow

90000,…,10000,00000

900000R100000R500000R

700000R300000R200000R

00000R600000R

400000R800000R

Koplow

9000,…,1000,0000, Type 1

9000U1000U5000U7000U

3000U2000U0000U6000U

4000U8000U

Koplow

9000,…,1000,0000, Type 2

Opposite sides sum to 9000

9000U5000U6000U7000U

8000U0000U4000U3000U

2000U1000U

Dice & Games Ltd, UK

(Jumbo)

900,…,100,000, Type 1

900U100U500U700U300U

200U000U600U400U800U

Koplow

900,…,100,000, Type 2

900U100U700U300U500U

000U800U200U600U400U

Opposite sides sum to 900

Dice & Games Ltd, UK

(Jumbo)

90,80,…,10,00

90L50L60L70L80L

30L20L10L00L40L

World of Warcraft (WoW)

90,80,…,10,00

90U30U70UI0U60U

20U80U40U00U50U

GameScience

90,80,…,10,00

90U30U50UI0U70U

80U20U60U00U40U

GameScience

90,80,…,10,00

90U30U50UI0U50U

00U60U40U80U20U

Opposite sides sum to 90

90,80,…,10,00

90U10U70U30U50U

00U80U20U60U40U

Opposite sides sum to 90

Dice & Games Ltd, UK (Jumbo, left), Q-Workshop (right)

90,80,…,10,00

90UI0U50U70U30U

20U00U60U40U80U

Koplow

90,80,…,10,00

90U10U30U50U70U

20U00U80U60U40U

Q-Workshop Skull

90,80,…,10,00

90L10L70L30L50L

00L80L20L60L40L

Numbers shifted by 90°

90,80,…,10,00

Crystal Caste

90,80,…,10,00

GridIron Master

50,50,40,40,30,

30,20,20,10,10

50U20U30U40UI0U
I0U40U30U20U50U

50,40,30,20,10 x 2

Opposite sides sum to 60

Sumator

GameScience

45,44,35,34,30,

29,25,25,21,20

45U21U29U35U25U

34U20U30U44U25U

Bomb Die

Football Fever

40,40,30,30,20,20,10,10,00,00

40UI0U30U00U20U40UI0U30U00U20U

40,30,20,10,00 x 2

Opposite sides are equal

GameScience

11,10,9,9,8,8,7,7,6,5

IIU6.U9.U7U8U5U10U7U9.U8U

Advanced Die

10,9,8,7,6,5,4,3,2,1

10U2U8U4U6.U1U9.U3U7U5U

Numbers 1-10

Koplow

9,8,7,6,5,4,3,2,1,0

Numbers from 0-9

More types see here

8,7,7,6,6,6,5,5,4,3

8U4U7U5U6.U3U7U5U6.U6.U

Beginner Die

9,8,7,6,5,4,3,2,1,0

Numbers from 0-9

Crystal Caste

9,8,7,6,5,4,3,2,1,0

GridIron Master

9,8,7,6,5,4,3,2,0,0

9.U0U6.U2U5U

0U8U3U7U4U0U

Cheater, 1 replaced by 0

5,5,4,4,3,3,2,2,1,1

5U2U3UIU4UIU4U3U5U2U

Opposite faces sum to 6

GameScience

5,5,4,4,3,3,2,2,1,1

5U2U3U4U1U

1U4U3U2U5U

Opposite faces sum to 6

4,4,3,3,2,2,1,1,0,0

4UIU0U2U3U

3U2UIU0U4U

Opposite faces

do not sum to 5

0.9,0.8,…,0.1,0.0

Koplow

10/10,9/10,…,1/10

Opposite sides sum to 11/10

Fractional D10, n/10, n=1..10

0.09,0.08,…,0.01,0.00

Koplow

0.009,0.008,…,0.001,0.000

Koplow

D12

55,50,…5,0

55U40U30U35U45U50U0LR15U25U20U10U5U

16,15,14,13,13,12,12,11,11,10,9,8

I6UI2UI3UI4UI5UI3U8LLEI2UIIUI0U9.UIIU

Advanced Die

12,12,11,11,10,10,9,9,8,8,7,7

I2U9.U7U8UI0UIIU7ULIODI2DIID9.D8D

2x(12..7)

12,11,10,9,9,8,8,8,7,7,6,5

I2U9.U8U9.UI0UIIU5ULE7U8U8U7U6.U

Beginner Die

Monopoly: FA Premier League

10,8,8,8,7,7,6,6,5,5,5,3

3 in a star, 5s in a square

GOLO Golf Par 5 Die

9,8,8,8,7,7,6,6,5,5,5,4

4 in a circle, 5s in a square

GOLO Golf Par 5 Die

8,7,7,7,6,6,5,5,4,4,4,3

3 in a circle, 4s in a square

GOLO Golf Par 4 Die

8,6,6,6,5,5,4,4,3,3,3,1

1 in a star, 3s in a square

GOLO Golf Par 3 Die

7,6,6,6,5,5,4,4,3,3,3,2

2 in a circle, 3s in a square

GOLO Golf Par 3 Die

6,6,5,5,4,4,3,3,2,2,1,1

2 x 1-6

D12 pipped

4,4,4,3,3,3,2,2,2,1,1,1

pipped

Koplow

D20

57,51,50,46,45,43,38,35,32,29,24,20,19,16,13,11,07,04,02,00

57U19U28U02U24U45U13U07U50U32U00U51U35U16U04U20U29U11U43U46U

49,47,46,44,39,37,36,32,28,27,24,19,18,16,15,14,13,9,5,1

49U36LR47UI5LR37LR27LL32LLI6LL5LRI4UI9U9.LL24U44LLI8LLILRI3LR39LR28LL46U

Pic-6 Lotto Dice

49,46,43,40,37,34,31,28,25,22,21,19,16,13,10,7,4,3,2,1

49UI0LRIU40LL7LL25U22U2U43U46LRI9U34LL3IUI3LR37LR3U4U28UI6U2ILL

Pic-6 Lotto Dice

48,47,46,43,42,41,39,38,35,34,33,31,30,29,26,20,17,8,4,2

48U39LR47U26LR4ILR34LL38LL29LL4LR20U3IU8LL33U43LL30LL2LRI7LR42LR35LL46U

Pic-6 Lotto Dice

48,44,42,38,37,36,34,33,32,31,29,28,27,26,24,23,22,12,6,3

48U34LR44U24LR36LR3ILL33LL26LL6.LR23U28UI2LL29U38LL27LL3LR22LR37LR32LL42U

Pic-6 Lotto Dice

47,45,44,41,38,35,32,29,26,23,22,21,20,17,14,11,8,7,6,5

47U32LR45UI4LR35LR23LL29LLI7LL6.LRIIU2IU7LL22U4ILL20LL5LR8LR38LR26LL44U

Pic-6 Lotto Dice

45,43,42,41,40,39,36,33,30,27,25,24,23,21,18,15,12,11,10,9

45U36LR43UI8LR39LR27LL33LL2ILLI0LRI5U24UIILL25U4ILL23LL9.LRI2LR40LR30LL42U

Pic-6 Lotto Dice

25,24,23,22,21,21,21,20,20,20,20,19,19,19,19,18,18,17,16,15

25UI9U2IUI6U20U2IUI9UI8U23U20UI5LL20UI9U24U20UI8U2IU22UI7UI9U

Driver Die

20,20,19,19,...,11,11

2x(20…11)

Formula Dé (left), Truant (right)

20,20,19,18,…3,2

Cheater, 1 replaced by 20

Chessex/Koplow (left), Truant (right)

20,19,…,2,1

Regular D20

More types see here

19,18,18,17,17,16,16,15,15,15,14,14,14,13,13,13,12,12,11,10

I9UI4UI6UIIU14UI7UI3UI2UI8UI5UI0LLI5UI3UI8UI5U13UI6UI7UI2UI4U

Advanced Die

19,18,…3,2,1,1

Cheater, 20 replaced by 1

Truant

15,14,14,13,13,12,12,11,11,11,10,10,10,9,9,9,8,8,7,6

I5UI0UI2U7UI0UI3U9.U8UI4UIIU6.LLIIU9.UI4UIIU9.UI2UI3U8UI0U

Beginner Die

9,9,8,8,…,1,1,0,0

Twice 0..9

More types see here

D26

All prime numbers below 100

Design by my daughter

D30

30,30,30,29,29,29,…,21,21,21

3x(30…21)