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Guess ball colors
Hat 'trick': Can one of them guess right?How many strategies are there for this puzzle where one of n logicians must call his own hat's color among n?Hat guessing gameGuess the color of the capGuess the color of the cap - extendedprobability of occcuring alternative colorsColor of Last Ball?Probability of drawing at least 1 red, 1 blue, 1 green, 1 white, 1 black, and 1 grey when drawing 8 balls from a pool of 30?Nim Sum Game VariantColoring the ballsPermutation and combination ball selectionHat guessing gameWhat are the two possible solutions to this round of Mastermind?Guess the color of the capGuess the color of the cap - extended
$begingroup$
7 people receive either a black or a white ball. They can only see the color of the others balls, but not their own. Both of the colors are equally likely. They play as a team a game of guessing their own ball color.
With which strategy all of the 7 people answer correctly; and which probability of success does this strategy have?
(Sidenotes: The strategy should be made before they received the balls. And: The 7 people cannot communicate anything once they received the balls.)
combinatorics combinations puzzle coding-theory combinatorial-game-theory
asked 16 hours ago
JohnDJohnD
19312
$endgroup$
add a comment |
$begingroup$
7 people receive either a black or a white ball. They can only see the color of the others balls, but not their own. Both of the colors are equally likely. They play as a team a game of guessing their own ball color.
With which strategy all of the 7 people answer correctly; and which probability of success does this strategy have?
(Sidenotes: The strategy should be made before they received the balls. And: The 7 people cannot communicate anything once they received the balls.)
combinatorics combinations puzzle coding-theory combinatorial-game-theory
asked 16 hours ago
JohnDJohnD
19312
$endgroup$
$begingroup$
Similar questions: math.stackexchange.com/questions/2405283/hat-guessing-game and math.stackexchange.com/questions/3131078/… and math.stackexchange.com/questions/3139513/… and math.stackexchange.com/questions/79333/… and math.stackexchange.com/questions/2867979/… and surely many more.
$endgroup$
– Gerry Myerson
16 hours ago
$begingroup$
In the beginning, can they receive all black or all white?
$endgroup$
– nafhgood
16 hours ago
$begingroup$
@nafhgood All colors are equally likely...
$endgroup$
– JohnD
14 hours ago
add a comment |
$begingroup$
7 people receive either a black or a white ball. They can only see the color of the others balls, but not their own. Both of the colors are equally likely. They play as a team a game of guessing their own ball color.
With which strategy all of the 7 people answer correctly; and which probability of success does this strategy have?
(Sidenotes: The strategy should be made before they received the balls. And: The 7 people cannot communicate anything once they received the balls.)
combinatorics combinations puzzle coding-theory combinatorial-game-theory
asked 16 hours ago
JohnDJohnD
19312
$endgroup$
7 people receive either a black or a white ball. They can only see the color of the others balls, but not their own. Both of the colors are equally likely. They play as a team a game of guessing their own ball color.
With which strategy all of the 7 people answer correctly; and which probability of success does this strategy have?
(Sidenotes: The strategy should be made before they received the balls. And: The 7 people cannot communicate anything once they received the balls.)
combinatorics combinations puzzle coding-theory combinatorial-game-theory
combinatorics combinations puzzle coding-theory combinatorial-game-theory
asked 16 hours ago
JohnDJohnD
19312
asked 16 hours ago
JohnDJohnD
19312
asked 16 hours ago
JohnDJohnD
19312
asked 16 hours ago
JohnDJohnD
19312
asked 16 hours ago
JohnDJohnD
19312
19312
$begingroup$
Similar questions: math.stackexchange.com/questions/2405283/hat-guessing-game and math.stackexchange.com/questions/3131078/… and math.stackexchange.com/questions/3139513/… and math.stackexchange.com/questions/79333/… and math.stackexchange.com/questions/2867979/… and surely many more.
$endgroup$
– Gerry Myerson
16 hours ago
$begingroup$
In the beginning, can they receive all black or all white?
$endgroup$
– nafhgood
16 hours ago
$begingroup$
@nafhgood All colors are equally likely...
$endgroup$
– JohnD
14 hours ago
add a comment |
$begingroup$
Similar questions: math.stackexchange.com/questions/2405283/hat-guessing-game and math.stackexchange.com/questions/3131078/… and math.stackexchange.com/questions/3139513/… and math.stackexchange.com/questions/79333/… and math.stackexchange.com/questions/2867979/… and surely many more.
$endgroup$
– Gerry Myerson
16 hours ago
$begingroup$
In the beginning, can they receive all black or all white?
$endgroup$
– nafhgood
16 hours ago
$begingroup$
@nafhgood All colors are equally likely...
$endgroup$
– JohnD
14 hours ago
$begingroup$
Similar questions: math.stackexchange.com/questions/2405283/hat-guessing-game and math.stackexchange.com/questions/3131078/… and math.stackexchange.com/questions/3139513/… and math.stackexchange.com/questions/79333/… and math.stackexchange.com/questions/2867979/… and surely many more.
$endgroup$
– Gerry Myerson
16 hours ago
$begingroup$
Similar questions: math.stackexchange.com/questions/2405283/hat-guessing-game and math.stackexchange.com/questions/3131078/… and math.stackexchange.com/questions/3139513/… and math.stackexchange.com/questions/79333/… and math.stackexchange.com/questions/2867979/… and surely many more.
$endgroup$
– Gerry Myerson
16 hours ago
$begingroup$
In the beginning, can they receive all black or all white?
$endgroup$
– nafhgood
16 hours ago
$begingroup$
In the beginning, can they receive all black or all white?
$endgroup$
– nafhgood
16 hours ago
$begingroup$
@nafhgood All colors are equally likely...
$endgroup$
– JohnD
14 hours ago
$begingroup$
@nafhgood All colors are equally likely...
$endgroup$
– JohnD
14 hours ago
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Here is an optimal strategy:
If you see an odd number of black hats, guess black.
If you see an even number of black hats, guess white.
As long as the total number of black hats is even, everyone will guess correctly. This occurs with probability 50%.
You cannot do any better, because no matter what strategy people use, each person will be wrong half the time on average. This is because each person’s hat is independent of their guess, as the guess depends on the other hats only, and all hats are independent. No matter what they guess, the probability their hat is the same as their guess is 50%.
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
$endgroup$
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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active
oldest
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votes
$begingroup$
Here is an optimal strategy:
If you see an odd number of black hats, guess black.
If you see an even number of black hats, guess white.
As long as the total number of black hats is even, everyone will guess correctly. This occurs with probability 50%.
You cannot do any better, because no matter what strategy people use, each person will be wrong half the time on average. This is because each person’s hat is independent of their guess, as the guess depends on the other hats only, and all hats are independent. No matter what they guess, the probability their hat is the same as their guess is 50%.
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
$endgroup$
add a comment |
$begingroup$
Here is an optimal strategy:
If you see an odd number of black hats, guess black.
If you see an even number of black hats, guess white.
As long as the total number of black hats is even, everyone will guess correctly. This occurs with probability 50%.
You cannot do any better, because no matter what strategy people use, each person will be wrong half the time on average. This is because each person’s hat is independent of their guess, as the guess depends on the other hats only, and all hats are independent. No matter what they guess, the probability their hat is the same as their guess is 50%.
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
$endgroup$
add a comment |
$begingroup$
Here is an optimal strategy:
If you see an odd number of black hats, guess black.
If you see an even number of black hats, guess white.
As long as the total number of black hats is even, everyone will guess correctly. This occurs with probability 50%.
You cannot do any better, because no matter what strategy people use, each person will be wrong half the time on average. This is because each person’s hat is independent of their guess, as the guess depends on the other hats only, and all hats are independent. No matter what they guess, the probability their hat is the same as their guess is 50%.
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
$endgroup$
Here is an optimal strategy:
If you see an odd number of black hats, guess black.
If you see an even number of black hats, guess white.
As long as the total number of black hats is even, everyone will guess correctly. This occurs with probability 50%.
You cannot do any better, because no matter what strategy people use, each person will be wrong half the time on average. This is because each person’s hat is independent of their guess, as the guess depends on the other hats only, and all hats are independent. No matter what they guess, the probability their hat is the same as their guess is 50%.
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
answered 6 hours ago
Mike EarnestMike Earnest
24.3k22151
24.3k22151
add a comment |
add a comment |
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$begingroup$
Similar questions: math.stackexchange.com/questions/2405283/hat-guessing-game and math.stackexchange.com/questions/3131078/… and math.stackexchange.com/questions/3139513/… and math.stackexchange.com/questions/79333/… and math.stackexchange.com/questions/2867979/… and surely many more.
$endgroup$
– Gerry Myerson
16 hours ago
$begingroup$
In the beginning, can they receive all black or all white?
$endgroup$
– nafhgood
16 hours ago
$begingroup$
@nafhgood All colors are equally likely...
$endgroup$
– JohnD
14 hours ago