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Questions tagged [dice]

For puzzles involving rolling numbered dice.

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26
votes
10answers
3k views

Make 2 dice out of 3 dice

This question was first posted by standupmaths on youtube: https://www.youtube.com/watch?v=xHh0ui5mi_E He already got some answers but I think this community can probably find a better answer. ...
8
votes
2answers
634 views

Four dice puzzle: 2,2,4,5

Damiano has thrown four dice and the numbers 2, 2, 4, 5 showed up on top. Damiano asks himself: What is the smallest positive integer that cannot be generated with these four numbers according to ...
43
votes
3answers
3k views

Relabeling two 20-sided dice without changing their total

Usually, 20-sided dice are labeled with the numbers 1 to 20. When you roll two of these, their sum is a random number between 2 and 40. The total 21 is most likely to occur, while 2 and 40 are the ...
14
votes
2answers
1k views

Crazy Dice - Unusual Dice with Usual Sum

Can you design two six-sided dice (different from the standard ones), where each face has a nonzero number of dots, so that the probability distribution of their total is the same as for two standard ...
44
votes
7answers
9k views

How many tries to roll a 6?

Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6. Now ...
23
votes
3answers
2k views

Gambling in a rigged casino

A well-known crooked casino is offering the following bet with a pair of (identically looking and indistinguishable) dice that both show the numbers $1,2,3,4,5,6$ on their faces. The first die ...
39
votes
22answers
8k views

Aproximating 100 by 6

You're a fan of pen & paper RPGs and have finally arranged a new playing group, recruited amongst your friends from the mathematical faculty. As a GameMaster (GM) you've assumed that all your ...
35
votes
2answers
4k views

A Boyfriend's Mysterious Message

Imogen was dog-tired, but excited! After 3 gruelling weeks of 16-hour work days imposed by an iron-willed boss, she was finally finished all her projects. She'd been processing (figurative) ...
17
votes
2answers
1k views

Rolling Dice puzzle

The answer is a six-letter word. Here's an attempt at a text version, but you're really better off looking at the picture. Rolling Dice To get a full tour, you must be a man of many faces and ...
13
votes
7answers
3k views

Fair n-sided dice

I have recently bought a fair $10$-sided dice for generating equally distributed random numbers from the range $1,2,\ldots,10$. Let me describe this dice in some more detail. Consider a regular 5-gon $...
9
votes
1answer
364 views

Four dice puzzle: What's the best throw?

This continues Damiano's puzzle "Four dice puzzle: 2,2,4,5" Damiano keeps throwing his four dice. After a lot of throwing and thinking and working, he has determined for every throw $a,b,c,d$ of his ...
8
votes
3answers
1k views

A first choice die

You and your friend have met to play a game of dice. This is a very simple game where both players roll a die at the same time, and the player with the lower score pays a coin to the other player. In ...
-9
votes
1answer
1k views

Coins, Dice, and Probability! [closed]

Background: It's time for a little bit of fun, your friends are playing a game and you decide to join them! Gamplay: You each sit down and play on a flat surface. You sit in a circle and each throw ...
0
votes
3answers
398 views

This Dice Blackjack game - is there Nash equilibrium?

This dice Blackjack is game for two - bettor and dealer. It is played with fair six-sided dice. Bettor: Bettor starts the game. Bettor can roll dice as many times he/she desires while the sum of ...
9
votes
4answers
1k views

Putting the pips on a d6

Using a blank cube and a bunch of circular stickers, an average person constructs a d6. A d6 is also known as a six-sided die, or sometimes, a dice. For the purpose of this puzzle, the average person ...