54
votes
Accepted
Deceptive dice game
You can make arbitrarily large sets of dice with this property.
Start with Efron's dice:
A: 4, 4, 4, 4, 0, 0
B: 3, 3, 3, 3, 3, 3
C: 6, 6, 2, 2, 2, 2
D: 5, 5, 5, 1, 1, 1
A beats B, B beats C, C ...
- 33.6k
44
votes
Accepted
Aproximating 100 by 6
As xnor points out in his answer, this question is basically asking for the way to most evenly distribute $6^n$ results among $100$ bins, and gives a very brief description of the solution. I'll go ...
- 18.6k
42
votes
Accepted
How many tries to roll a 6?
The answer is indeed...
...because the question is equivalent to...
Calculations:
- 21.8k
40
votes
How many tries to roll a 6?
This surprisingly beguiling puzzle may also be solved
with a surprisingly unsophisticated approach.
Symmetry, by itself, predicts the average length of
evens-only sequences ending with 6 to ...
- 21.8k
33
votes
Accepted
How to simulate one die with three dice?
I believe this set of dice satisfies all your requirements:
- 145k
28
votes
Aproximating 100 by 6
Get 10 different d6 dices and describe them on paper. Next to each description, associate a unique number from 0 to 9.
Put all those dices in an opaque bag (you should have one to transport that near-...
- 603
27
votes
Accepted
Loaded Dice with Uniform Sum
To explain, here is a more formal way to state Ian's answer:
Let the probability of die A rolling $i$ be $a_i$ for $1\le i\le6$, and similarly for die B.
If every sum has the same probability, then ...
- 33.6k
25
votes
Accepted
24
votes
Accepted
A new six-sided die
As already mentioned, the smallest possible sum is 27, resulting from the numbers 1, 2, 4, 5, 7, 8 arranged like this:
1
4758
2
Optimality is a consequence of ...
- 13.4k
23
votes
How to simulate one die with three dice?
@Deusovi's answer is totally correct, but I want to add here the general approach for solving such problems as well. No need to upvote, since I did not invent the technique, and you can see it ...
- 6,944
23
votes
Accepted
22
votes
Accepted
Make 2 dice out of 3 dice
All addition is modulo 6 (e.g. 4 + 3 = 1, 3 + 3 = 6, 5 + 3 = 2, 6 + 1 = 1).
3 Dice Roll
Resulting 2 Dice Roll
Two same, one different: AAB
AB
135
14
246
25
All same: AAA
36
Three in a row: A, A +...
- 32k
20
votes
Aproximating 100 by 6
Figured i'd add my comment as an answer:
We roll 3 dice $(D1,D2,D3)$, which we seperate spatially or in some other way (we used to use 3 different colors). We reroll D1 and D2 if they land on 6, and ...
- 2,418
20
votes
Accepted
8 dice with a product being a square
The only prime factors of the numbers 1 through 6 are 2, 3, and 5. Therefore the factorization of the numbers on the paper will only consist of these primes, i.e. they will be of the form:
$$
2^a 3^b ...
- 18.6k
19
votes
19
votes
Accepted
18
votes
Fair d5 with as few faces as possible
Surely
will suffice for all n > 2.
Consider a symmetrical cone with an n-sided regular polygon as its base.
If we take a "stubby" one (of a shortish height) and a "pointy" one (...
- 74.1k
16
votes
Aproximating 100 by 6
As @MikeEarnest says, unless you put an upper limit on the number of rolls, you can always do better with more rolls. Since $6^n$ is never divisible by $100$, you can never be completely fair. With ...
- 7,346
16
votes
Accepted
15
votes
The Sphinx's Dice
The post linked in rand al'thor answer optimized the worst case pick the visitor of the sphinx can make. But the question asked for the best average case.
A better solution in that case is:
...
- 849
15
votes
How many tries to roll a 6?
Let $X_n$ be the event that the dice takes $n$ rolls to get the first 6, given all the rolls are even. Let $A_n$ be the event that it takes $n$ rolls to get the first 6, and let $B$ be the event that ...
- 21.9k
14
votes
Three Dice minimum value
The answer is
First I show that a lower number is not possible:
This establishes a lower bound. The upper bound is established by providing an actual solution.
First die:
Second die:
Third die:
...
- 1,267
14
votes
Accepted
14
votes
Accepted
Chain Puzzle: Tabletop Games #05 - It's Yahtzee, Jim, but not as we know it
I rotated the grid 90 degrees clockwise before solving the grid deductions, in order to reduce vertical space.
Let's solve Statue Park first.
Now to the Fillomino.
Now that the two grids are solved, ...
- 11.5k
13
votes
A new six-sided die
Can I use a barrel die? Then we could do an arrangement of
for a sum of
We can also do
which works even better, since opposing faces have the same sum.
- 459
12
votes
Accepted
Two Dice = Nine Cards
The cards are numbered:
Reasoning:
There are 36 possible ways to choose two cards out of nine, so the results must be $2,3,3,4,4,4,\ldots,11,11,12$. If we sum all of these, we find that the total is ...
- 33.6k
12
votes
Accepted
12
votes
Accepted
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