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# Tag Info

## Hot answers tagged dice

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
43 votes
Accepted

### How many tries to roll a 6?

The answer is indeed...             ...because the question is equivalent to...   Calculations:
• 21.9k
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 ...
• 21.9k
33 votes
Accepted

### How to simulate one die with three dice?

I believe this set of dice satisfies all your requirements:
• 147k
25 votes
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### A Short Dice Puzzle

The answer is Proof Alternative proof
• 136k
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 ...
• 6,964
23 votes
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### A Short Dice Puzzle II

Answer: Explanation:
• 7,282
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 +...
• 32.4k
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 ...
• 18.9k
19 votes

• 474
19 votes
Accepted

### A dice game, what is the optimal strategy?

Strategy: Expectated gain: Conclusion:
• 4,992
19 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 (...
• 77.5k
16 votes
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### Date Dice Dilemma

My answer: Numbers on each die: Reasoning: . Additional reasoning:
• 18.1k
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 ...
• 22k
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: ...
• 1,287
14 votes
Accepted

Easy:
• 35.6k
14 votes
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### 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, ...
• 14.6k
12 votes
Accepted

I make it
12 votes
Accepted

### Two dice with the same probability for each sum?

I think: Here's my proof:
• 17.9k
11 votes

### The Good, the Bad and the Ugly

I think the answer is Reasoning
• 136k
10 votes

### Three Dice minimum value

A lower bound is An upper bound is
• 496
10 votes
Accepted

### Generating Roman numerals with dice

UPDATE (after a pretty sturdy hint from OP): (Again, one more number can be constructed, if flipping the dice is allowed.) Original answer: I got all the way up to with these dice: Here's how to ...
• 77.5k
10 votes
Accepted

### A bet with your friend

Suppose we have $n$ dice. Then When $n=15$ Just for fun, here's a smartass combinatorial way to prove the identity I used above: Perhaps there's a smarter-ass way to do it a bit more briefly.
• 119k
9 votes
Accepted

### The Good, the Bad and the Ugly

Let $P$ be the probability that the player to start throws the first six. The probability that Tuco throws the first six is, per definition, $P$. If Tuco does not throw a six (chance $5/6$), ...
• 4,392
9 votes
Accepted

### Building the ideal Scrabble dice set

I chose to use a standard set of D&D dice, as you might get from a game shop, for ease of manufacturing and rolling. Incidentally, it contains seven dice, which is the number of tiles that form a ...
• 19.7k
9 votes

### How many tries to roll a 6?

I believe the answer is This is computational calculation, so it is not statistical answer. It is for the people who try to find it probabilistically. Here is the probabilistic solution: First of ...
• 30.3k
9 votes

### Putting the pips on a d6

I decided to solve this in the second hardest possible way myself, and created a 3D model of all the possibilities. Here it is: The sides that are not visible are fully determined by the visible ones,...
• 77.5k
8 votes

### The Good, the Bad and the Ugly

ANSWER: For Tuco to roll the first six, it must be the case that one of the following cases holds: Thus, the probability for Tuco to get the first six is Once Tuco has rolled his six, the game is ...
• 1,619
8 votes

### What is the 'best' way to tilt through a D20?

One should note that we may break this problem down into a number of subproblems: What is the path from $n$ to $n+1$ containing the least number of negative points? It is relatively clear that ...
• 7,881

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