82
votes
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63
votes
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100 pieces 1 opportunity, choose wisely!
What you're missing here is the chance of playing at all, given that the game ends when someone finds the prize. (or, chance of finding a prize goes to 0, which is the same thing)
...
- 7,734
57
votes
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54
votes
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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
52
votes
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45
votes
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2 Monkeys on a computer
(a) I claim that the expected typing length are the same for both monkeys. I guess something in my argument will be incorrect, as jafe's answer has 9 approvals, but finding that incorrectness would be ...
- 566
44
votes
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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
43
votes
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Monty Hall Revisited: Winning Both Goats!
Leaving aside the dubious assumption that Monty is entirely on the up-and-up...
- 2,752
42
votes
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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
38
votes
Accepted
37
votes
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37
votes
36
votes
Accepted
33
votes
Accepted
How to simulate one die with three dice?
I believe this set of dice satisfies all your requirements:
- 145k
32
votes
32
votes
Accepted
Simulating an unbiased coin with a biased one
One possibility:
This works because:
EDIT: Inspired by @trolley813's answer here is a way to recycle the rejected entropy:
- 19.1k
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
28
votes
Coin Game with infinite paradox
OK, let's actually take this seriously. As others have said, this is the so-called St Petersburg paradox, and the reason it isn't really much of a paradox is that (1) an extra dollar matters much less ...
- 117k
28
votes
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27
votes
26
votes
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Unfair coins at South Park Elementary
Wendy wins on the first flip with probability $1/100$. Otherwise, the game keeps going and Sally has probability $p$ to win on the next flip, which has overall probability $99/100 \times p$. If not, ...
- 26.3k
26
votes
Accepted
Unfair coins at South Park Elementary v2
As Timmy has a "head" on his shoulders with probability of 1, he always wins at his turn. Then
- 9,870
26
votes
2 Monkeys on a computer
Monkey problem
To settle down which monkey is faster on average, I'll use Markov chains and Mathematica. Define a state $i$, for $i = 0..6$, as that the monkey 1 has currently written $i$ correct ...
- 361
25
votes
Accepted
25
votes
Accepted
24
votes
Three horse race
It is
The following scenarios are compatible with the information given:
Scenario 1:
Scenario 2:
Scenario 3:
- 19.1k
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 ...
- 6,954
23
votes
Accepted
Only top scored, non community-wiki answers of a minimum length are eligible