There is a large number of games with special dice. The best overview is available in various geeklists on http://www.boardgamegeek.com/:
Dice  A Dicey Love Affair currently the most extensive list
Games with specially numbered die/dice six sided dice
okay, I admit it: I love specialty dice
I am interested in numbered or pipped dice only, no symbols, and no stickers.
This section contains a list of dice from games as well as special dice sets (e.g. cheaters, trick dice, Sicherman dice and nontranstive dice)
To do: Include & check on Dice  A Dicey Love Affair
HalfTime Football
NinGonost
Break the safe
Phase 10
Real Math  A Sampler of Games

AirshipsBottom row shows same dice, rotated by 180° along the horizontal axis parallel to the screen. White die: 112233, Red die: 233445, Black die: 446688 
123 DiceBottom row shows same dice, rotated by 180° along the horizontal axis parallel to the screen.
From left to right: D6 81,72,54,36,18,9 D6 40,32,24,16,8,8 D6 40,30,25,20,15,10 D6 12,11,10,10,9,2 D6 10,9,7,6,5,3 D6 9,8,5,4,3,2 D6 8,7,6,5,4,3 D6 6,5,4,3,2,1 (opposite faces do not sum to 7) 
Bottom row shows same dice, rotated by 180° along the horizontal axis parallel to the screen. 16 dice, but some are identical.
Foggle, aka as Math Boggle 

18 dice of 6 different shapes and a down counter 

Formula DéBlue D30: 3 x (2130) Black D20: regular Purple D20: 2 x (1120) Green D12: 2 x (712) Red D8: 2 x (58) Orange D6: 4,4,4,3,3,2 Yellow D4: 2 x (12) 

FrameoGames5D6 dice frame with 3 axes 

Monopoly Express500,200,200,100,50,50 500,200,200,50,50,? 400,300,250,200,200,200 Type 1 400,300,250,200,200,200 Type 2 400,300,250,200,150,? 150,150,100,100,100,100 bulb 150,150,100,100,100,100 tap 2x policeman, 4x blank 

Monopoly: FA Premier LeagueD12, 2x16 

Rummikub Rummy Dice GameFrom left to right: Top row: 13,12,9,8,4,3 ; 13,12,8,7,4,3 ; 13,10,9,5,4,1 ; 13,9,8,5,4,face Bottom row: 12,11,7,6,3,2 ; 12,11,8,7,3,2 ; 11,10,6,5,2,1 ; 11,10,7,6,2,1 ; 10,9,6,5,1,face 

Heads Up, aka Mathe Mix14 wooden dice, numbers 115. Two dice with same numbers but different configuration (13,11,8,6,3,1). Two different wooden sets, set with red numbers is incomplete. Some dice have the same numbers, but different configurations (manual printing?) 15,14,9,8,4,2 15,12,10,7,5,2 15,12,9,7,5,2 15,11,10,6,5,1 14,13,10,9,5,4 14,13,9,8,4,3 14,12,9,7,4,2 13,12,9,8,4,3 13,11,8,6,3,1 12,11,7,6,2,1 13,12,8,6,4,3 (red only, 6 instead of 9, dot manually printed?)
Plastic set with 14 dice, numbers 115, but completely different numbers than wooden set: 15,12,10,7,4,2 15,12,8,6,4,1 15,9,5,3,2,1 15,6,5,4,3,1 14,12,11,10,2,1 14,11,7,6,5,2 14,11,6,5,3,2 14,8,5,4,2,1 13,10,9,6,4,1 13,10,8,4,3,1 13,9,8,6,3,2 12,10,8,5,4,3 12,10,7,4,3,2 12,9,8,7,3,1 

MEGADICE36,30,24,18,12,6 35,29,23,17,11,5 34,28,22,16,10,4 33,27,21,15,9,3 32,26,20,14,8,2 31,25,19,13,7,1 

GolfProfiD20 Beginner 15,14,14,13,13,12,12,11,11,11,10,10,10,9,9,9,8,8,7,6 D20 Advanced 19,18,18,17,17,16,16,15,15,15,14,14,14,13,13,13,12,12,11,10 D20 Driver 25,24,23,22,21,21,21,20,20,20,20,19,19,19,19,18,18,17,16,15 D12 Beginner 12,11,10,9,9,8,8,8,7,7,6,5 D12 Advanced 16,15,14,13,13,12,12,11,11,10,9,8 D10 Beginner 8,7,7,6,6,6,5,5,4,3 D10 Advanced 11,10,9,9,8,8,7,7,6,5 D8 Beginner 5,5,4,4,3,2,1,0 D8 Advanced 8,7,6,5,4,3,2,1 (regular D8) D6 Beginner 6,5,4,3,2,1 (regular D6) D6 Advanced 9,8,7,6,5,4 D6 2/2,3/4,2/3,2/3,2/3,2/4 D4 Beginner 4,3,2,1 D4 Advanced 6,5,4,3 

5,4,2 4,3,2 4,3,1 3,2,1 
Top view
Bottom view 
Tumble Numble11 wooden dice 1 Red: 1, 2, (3), 4, (5), 7 1 Blue: 1, 2, 3, 4, 7, 8 1 Green: 1, 2, 3, 7, 8, 9 1 Black: 0, 1, 2, 7, 8, 9 1 Black: blank, 0, 1, 7, 8, 9 6 Black:1, 2, 3, 4, 5, 6 (opposite faces do not sum to 7) 
In many games, two or three dice are used and their sum is used as a random number. If the individual dice yield a uniform distribution, the density function of their sum is no longer uniform. The example of dice with M=2, M=4 and M=6 random numbers is considered below.
Let us assume that there are three fair binary dice with numbers 0 and 1. A single die generates those numbers with probability 1/2 each. The sum of two dice has three possible outcomes: 0 (with probability 1/4), 1 (1/2), and 2 (1/4). For the sum of three dice, the possible outcomes are 0 (with probability 1/8), 1 (3/8), 2 (3/8), and 3 (1/8)
There is an interesting set of three dice representing these three cases, the socalled Ubiquity Dice by Exile Game Studio. They are all octahedra, the white one being a binary die, the red and the blue one generating the sum of two or three binary dice, respectively.



1,1,1,1,0,0,0,0 D2 (binary die) Exile Game Studio (Ubiquity Dice) 
2,2,1,1,1,1,0,0 2D2 (sum of 2 binary dice) Exile Game Studio (Ubiquity Dice) 
3,2,2,2,1,1,1,0 3D2 (sum of 3 binary dice) Exile Game Studio (Ubiquity Dice) 
A fair quaternary die generates numbers 0, 1, 2, and 3 with probability 1/4 each. The sum of two such dice has seven possible outcomes: 0 (with probability 1/16), 1 (1/8), 2 (3/8), 3 (1/2), 4 (3/8), 5 (1/8), and 6 (1/8).
The socalled Y2K die is a special die that generates exactly this type of random numbers. It consists of two halves, each with 0,1,2, or 3 dots. When the die is rolled, these halves can move (more or less) independently.

2D4: Y2K Die 
There are spinners and rollers that generates the same probability distribution as the sum of two D6: 2 (with probability 1/36), 3 (1/18), 4 (1/12), 5 (1/9), 6 (5/36), 7 (1/6), 8 (5/36), 9 (1/9), 10 (1/12), 11 (1/18), and 12 (1/36).
The two parts of that spinner move (more or less) independently:


2D6 Double spinner 
2D6 Double roller 
There is a unique roller that generates the same probability distribution as the sum of three D6. The three parts of that spinner move (more or less) independently:

3D6, triple roller 
There is a unique roller that generates the same probability distribution as the sum of five D6. The five parts of that spinner move (more or less) independently:

5D6, quintuple roller 

5D6, quintuple roller, Poker 

5D6 FrameoGames 
A fair “regular” cube generates numbers 1, 2, 3, 4, 5, and 6 with probability 1/6 each. The sum of two such dice has eleven possible outcomes: 2 (with probability 1/36), 3 (1/18), 4 (1/12), 5 (1/9), 6 (5/36), 7 (1/6), 8 (5/36), 9 (1/9), 10 (1/12), 11 (1/18), and 12 (1/36).
Sicherman dice are the only other pair of 6sided dice bearing only positive integers which have the same probability distribution as a pair of normal dice. These dice were discovered by Colonel George Sicherman, of Buffalo, New York and were originally reported by Martin Gardner in a 1978 article in Scientific American. The numbers can be arranged so that all pairs of numbers on opposing sides sum to equal numbers, 5 for the first and 9 for the second.
http://en.wikipedia.org/wiki/Sicherman_dice
http://mathworld.wolfram.com/SichermanDice.html


Left 4,3,3,2,2,1 Right 8,6,5,4,3,1 Grand Illusions 
Left 8,6,5,4,3,1 Right 4,3,3,2,2,1 GameStation 
They are the only such alternate arrangement if face values are required to be positive. However, if faces are permitted to have zero value, then three additional possible equalodds pairs of dice are possible: Two are obtained by subtracting one from each face on either of the two dice and adding one to each face the other, yielding to 5,4,4,3,3,2 / 7,5,4,3,2,0 and 3,2,2,1,1,0 / 9,7,6,5,4,3. The third one is obtained by performing the same +1 / 1 operation with a regular pair of D6, yielding to 7,6,5,4,3,2 / 5,4,3,2,1,0, as used in Magic’s Double D6:

Inner die 7,6,5,4,3,2 Outer die (frame): 5,4,3,2,1,0 Right picture shows “12” (7+5) Magic / Shapeways 
If negative values are permitted, there are an infinite number of equalodds dice.
A set of nontransitive dice is a set of dice for which the relation "is more likely to roll a higher number" is not transitive. This situation is similar to that in the game Rock, Paper, Scissors, in which each element has an advantage over one choice and a disadvantage to the other.
Each die beats the one in clockwise direction


Red 4,4,4,4,4,1 Blue 6,3,3,3,3,3 Green 5,5,5,2,2,2 Red beats blue with probability 25/36, blue beats green with probability 21/36, and green beats red with probability 21/36. Grand Illusions 
Blue 9,7,6,5,2,1 Orange 9,8,5,4,3,1 Black 8,7,6,4,3,2 Miwin Dice. Each die beats the one in clockwise direction with probability 17/36 (lose 16/36, draw 3/36) Miwin 

Top 6,6,2,2,2,2 Right 5,5,5,1,1,1 Bottom 4,4,4,4,0,0,0 Left 3,3,3,3,3,3 Efron’s Dice. Each die beats the one in clockwise direction with probability 2/3 Grand Illusions 
Three dice:
3,3,5,5,7,7; 2,2,4,4,9,9; and 1,1,6,6,8,8 (Efron set. Uses all the numbers from 1 to 9, and the face value of each die sums to 30).
1,1,1,13,13,13; 0,3,3,12,12,12; and 2,2,2,11,11,14 (the face value of each die sums to 42).
1,4,4,4,4,4; 3,3,3,3,3,6; and 2,2,2,5,5,5 (no face has a number higher than 6, and each die has two different numbers. This is the red/blue/green pipped set shown above)
1,2,5,6,7,9; 1,3,4,5,8,9; 2,3,4,6,7,8 (this is the wooden pipped set shown above, blue/orange/black). Minwin dice, invented in 1975 by Michael Winkelmann. No number appears twice on the same die, the face value of each die sums to 30, and the average is 5.
1,1,1,13,13,13; 0,3,3,12,12,12; 2,2,2,11,11,14 (Schwenk's dice)
Four dice:
6,6,2,2,2,2; 5,5,5,1,1,1; 4,4,4,4,0,0; and 3,3,3,3,3,3 (Efron set. No number is greater than 6. This is the white numbered set shown above)
2,3,3,9,10,11; 0,1,7,8,8,8; 5,5,6,6,6,6; and 4,4,4,4,12,12 (Efron set).
1,2,3,9,10,11; 0,1,7,8,8,9; 5,5,6,6,7,7; and 3,4,4,5,11,12 (Efron set)
2,3,3,9,10,11; 0,1,7,8,8,8; 5,5,6,6,6,6; and 4,4,4,4,12,12;
References:
http://en.wikipedia.org/wiki/Nontransitive_dice
http://www.grandillusions.com/magicdice.htm
http://www.sciencenews.org/articles/20020420/mathtrek.asp
http://www.maa.org/mathland/mathtrek_04_15_02.html
http://plus.maths.org/issue41/features/hobbs/index.html
Cheater dice generate random numbers that differ from “fair” dice. Some dice generate on average higher numbers than fair dice, others lower numbers. Other sets generate only a few (down to a single) random numbers and are used to tweak results in games such as craps.

Center 6,5,4,3,2,1 (regular D6), average 21/6=3.50 Left 5,4,3,2,1,1 (6 replaced by 1), average 16/6=2.67 Right 6,6,5,4,3,2 (1 replaced by 6) , average 26/6=4.33 Chessex / Koplow 

Right 9,8,7,6,5,4,3,2,1,0 (regular D10) , average 45/10=4.50 Left 9,8,7,6,5,4,3,2,0,0 (1 replaced by 0), average 44/10=4.40 Chessex / Koplow 

Left regular D20 , average 220/20=11.0 Right 1 replaced by 20, average 239/20=11.95 Chessex / Koplow 

From left to right (top and bottom pictures show the same die from front and back) 2 x 1120, average = 310/20=16.5 1 replaced by 20, average 239/20=11.95 regular D20 , average 220/20=11.0 20 replaced by 1, average 201/20=10.05 2 x 09, average 90/20=4.5 Truant 

Loaded Dice, throw 7 or 11 Left: 6,6,6,2,2,2 Right 5,5,5,5,5,5 

Loaded Dice Left: 6,6,5,5,4,4 Right 5,5,3,3,1,1 Both dice: Best bet is 7 followed by 5 or 9 2 x 5,5,3,3,1,1 dice  Best bet is the 6 followed by 4 Koplow 

Loaded Dice, Left: 6,6,5,5,1,1 Right 5,5,4,4,3,3 Will
roll only points  4,5,6,8,9,10,11, best bets are 9 & 10 

Loaded Dice Left: 6,6,3,3,2,2 Right 5,5,4,4,1,1 Both
dice: Best bet is 7 



6,6,6,6,6,6 Loaded die 
5,5,5,5,5,5 Loaded die 
4,4,4,4,4,4 Loaded die 



3,3,3,3,3,3 Loaded die 
3,3,3,3,3,3 Loaded die 
0,0 Loaded die 
These dice are physically loaded, such that a particular number is rolled with very high probability

wanted 


wanted 

Loaded die “1” 
Loaded die “2” 
Loaded die “3” 
Loaded die “4” 
Loaded die “5” 
Loaded die “6” 

Loaded die “6” (left), regular die (right) Both dice are hollow 

Loaded die, filled with liquid. Can be “loaded” within seconds to roll any number with high probability 

Trick Dice Yellow: 971,872,773,377,278,179 Green: 960,762,663,564,366,168 Blue: 954,855,756,657,558,459 Black: 840,741,642,543,345,147 Red: 780,681,483,384,285,186 
Trick: A magician can add the numbers of the five dice within seconds – the result will be different each time the dice are rolled.
Solution: The answer will be a four digit number. Sum the final digits of the dice to get the final two digits of the answer; subtract this from 50 to get the first two digits.
Explanation: http://www.mathpuzzle.com/dicetrick.txt

Trick Dice 971,872,773,377,278,179 (same as black die above) 960,762,663,564,366,168 (similar to green die, but 267 instead of 762) 954,855,756,657,558,459 (same as black die above) 913,814,616,517,418,319 902,803,704,605,506,209 840,741,642,543,345,147 (same as black die above) 780,681,483,384,285,186 (same as red die above) 690,591,492,393,294,195 Creative Crafthouse, Sprig Hill, FL 
The original set of 5 dice, invented by Royal V. Heath in 1927, was extended to 8 dice by Stephen Bradd of Clinton, IL. The rule is the same as above, but subtract the sum from 80 instead.

Set of 9 D10 dice Can throw any number from 0 to 999’999.999 in steps of 0.001 
7 dice, numbers 135. All red numbers appear twice.



35,32,25,18,11,4 
35,28,21,17,14,7 
34,27,26,20,13,6 



33,31,24,17,10,3 
33,28,26,19,12,5 
30,23,18,16,9,2 

29,22,15,8,5,1 