an interesting game The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Game of cards and GCDwhat is the probability of BOB winning the game?Alice and Bob are flipping coins…Competition between two geometric distributionsMaximize probability of hitting a square in a board game.Unbiased coin gameThrowing Poker Chips Close to Wall GameRandom Game Using Real NumbersCount conditional probability of winning a gameOptimal code for simple game
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an interesting game
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Game of cards and GCDwhat is the probability of BOB winning the game?Alice and Bob are flipping coins…Competition between two geometric distributionsMaximize probability of hitting a square in a board game.Unbiased coin gameThrowing Poker Chips Close to Wall GameRandom Game Using Real NumbersCount conditional probability of winning a gameOptimal code for simple game
$begingroup$
Alice, Bob and Cindy are playing a game of a circle. Firstly, Alice starts by drawing a point around the circle. Subsequently, being aware of Alice's decision Bob makes his move. Finally, Cindy puts a point around the circle being aware of Alice's and Bob's decisions. After all players fix their positions a point X drawn around the circle randomly. The winner of the game is the one whose position is the closest to the point X.
Question: How should Bob make his choice in order to maximize the probability of winning?
probability random
asked Mar 24 at 15:47
mathfunmathfun
263
$endgroup$
add a comment |
$begingroup$
Alice, Bob and Cindy are playing a game of a circle. Firstly, Alice starts by drawing a point around the circle. Subsequently, being aware of Alice's decision Bob makes his move. Finally, Cindy puts a point around the circle being aware of Alice's and Bob's decisions. After all players fix their positions a point X drawn around the circle randomly. The winner of the game is the one whose position is the closest to the point X.
Question: How should Bob make his choice in order to maximize the probability of winning?
probability random
asked Mar 24 at 15:47
mathfunmathfun
263
$endgroup$
1
$begingroup$
When you mean closest do you mean in a particular direction, that is, clockwise or anticlockwise? Or is it Euclidean distance?
$endgroup$
– Balakrishnan Rajan
Mar 24 at 15:49
$begingroup$
Sorry, when we draw a point around a circle, do that mean outside of the circle?
$endgroup$
– mathpadawan
Mar 24 at 16:02
$begingroup$
@BalakrishnanRajan, by closest I mean clockwise or anticlockwise direction
$endgroup$
– mathfun
Mar 24 at 16:11
$begingroup$
@nafhgood, I mean on the circle (neither inside or outside of it)
$endgroup$
– mathfun
Mar 24 at 16:12
$begingroup$
Please restore the original title. It' tells nothing about the contents now (especially because interesting is highly subjective), while the previous one contained three important details, related to the nature of the problem. Those details may help others to find for your problem and its solution if they ever have a similar one. See advices at Meta, thread How to ask a good question, section A good title.
$endgroup$
– CiaPan
Mar 25 at 6:47
add a comment |
$begingroup$
Alice, Bob and Cindy are playing a game of a circle. Firstly, Alice starts by drawing a point around the circle. Subsequently, being aware of Alice's decision Bob makes his move. Finally, Cindy puts a point around the circle being aware of Alice's and Bob's decisions. After all players fix their positions a point X drawn around the circle randomly. The winner of the game is the one whose position is the closest to the point X.
Question: How should Bob make his choice in order to maximize the probability of winning?
probability random
asked Mar 24 at 15:47
mathfunmathfun
263
$endgroup$
Alice, Bob and Cindy are playing a game of a circle. Firstly, Alice starts by drawing a point around the circle. Subsequently, being aware of Alice's decision Bob makes his move. Finally, Cindy puts a point around the circle being aware of Alice's and Bob's decisions. After all players fix their positions a point X drawn around the circle randomly. The winner of the game is the one whose position is the closest to the point X.
Question: How should Bob make his choice in order to maximize the probability of winning?
probability random
probability random
asked Mar 24 at 15:47
mathfunmathfun
263
asked Mar 24 at 15:47
mathfunmathfun
263
edited Mar 25 at 6:38
mathfun
asked Mar 24 at 15:47
mathfunmathfun
263
asked Mar 24 at 15:47
mathfunmathfun
263
asked Mar 24 at 15:47
mathfunmathfun
263
263
1
$begingroup$
When you mean closest do you mean in a particular direction, that is, clockwise or anticlockwise? Or is it Euclidean distance?
$endgroup$
– Balakrishnan Rajan
Mar 24 at 15:49
$begingroup$
Sorry, when we draw a point around a circle, do that mean outside of the circle?
$endgroup$
– mathpadawan
Mar 24 at 16:02
$begingroup$
@BalakrishnanRajan, by closest I mean clockwise or anticlockwise direction
$endgroup$
– mathfun
Mar 24 at 16:11
$begingroup$
@nafhgood, I mean on the circle (neither inside or outside of it)
$endgroup$
– mathfun
Mar 24 at 16:12
$begingroup$
Please restore the original title. It' tells nothing about the contents now (especially because interesting is highly subjective), while the previous one contained three important details, related to the nature of the problem. Those details may help others to find for your problem and its solution if they ever have a similar one. See advices at Meta, thread How to ask a good question, section A good title.
$endgroup$
– CiaPan
Mar 25 at 6:47
add a comment |
1
$begingroup$
When you mean closest do you mean in a particular direction, that is, clockwise or anticlockwise? Or is it Euclidean distance?
$endgroup$
– Balakrishnan Rajan
Mar 24 at 15:49
$begingroup$
Sorry, when we draw a point around a circle, do that mean outside of the circle?
$endgroup$
– mathpadawan
Mar 24 at 16:02
$begingroup$
@BalakrishnanRajan, by closest I mean clockwise or anticlockwise direction
$endgroup$
– mathfun
Mar 24 at 16:11
$begingroup$
@nafhgood, I mean on the circle (neither inside or outside of it)
$endgroup$
– mathfun
Mar 24 at 16:12
$begingroup$
Please restore the original title. It' tells nothing about the contents now (especially because interesting is highly subjective), while the previous one contained three important details, related to the nature of the problem. Those details may help others to find for your problem and its solution if they ever have a similar one. See advices at Meta, thread How to ask a good question, section A good title.
$endgroup$
– CiaPan
Mar 25 at 6:47
1
1
$begingroup$
When you mean closest do you mean in a particular direction, that is, clockwise or anticlockwise? Or is it Euclidean distance?
$endgroup$
– Balakrishnan Rajan
Mar 24 at 15:49
$begingroup$
When you mean closest do you mean in a particular direction, that is, clockwise or anticlockwise? Or is it Euclidean distance?
$endgroup$
– Balakrishnan Rajan
Mar 24 at 15:49
$begingroup$
Sorry, when we draw a point around a circle, do that mean outside of the circle?
$endgroup$
– mathpadawan
Mar 24 at 16:02
$begingroup$
Sorry, when we draw a point around a circle, do that mean outside of the circle?
$endgroup$
– mathpadawan
Mar 24 at 16:02
$begingroup$
@BalakrishnanRajan, by closest I mean clockwise or anticlockwise direction
$endgroup$
– mathfun
Mar 24 at 16:11
$begingroup$
@BalakrishnanRajan, by closest I mean clockwise or anticlockwise direction
$endgroup$
– mathfun
Mar 24 at 16:11
$begingroup$
@nafhgood, I mean on the circle (neither inside or outside of it)
$endgroup$
– mathfun
Mar 24 at 16:12
$begingroup$
@nafhgood, I mean on the circle (neither inside or outside of it)
$endgroup$
– mathfun
Mar 24 at 16:12
$begingroup$
Please restore the original title. It' tells nothing about the contents now (especially because interesting is highly subjective), while the previous one contained three important details, related to the nature of the problem. Those details may help others to find for your problem and its solution if they ever have a similar one. See advices at Meta, thread How to ask a good question, section A good title.
$endgroup$
– CiaPan
Mar 25 at 6:47
$begingroup$
Please restore the original title. It' tells nothing about the contents now (especially because interesting is highly subjective), while the previous one contained three important details, related to the nature of the problem. Those details may help others to find for your problem and its solution if they ever have a similar one. See advices at Meta, thread How to ask a good question, section A good title.
$endgroup$
– CiaPan
Mar 25 at 6:47
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No matter how distance is measured (among those possibilities mentioned in a comment), he should put it opposite to that of Alice. The notion of 'probability' only makes sense though if Cindy is using a mathematically well-defined strategy.
Let the circle circumference go from $0$ to $1$. Say wlog. that Alice chooses $0$.
Also wlog. say that Bob chooses some $ain[0,0.5]$. Then the optimal place for Cindy is $(a+1)/2$.
The range of Bob winning is $[a/2,((a+1)/2+a)/2]$ the length of which is $(a+1)/4$ which is maximized by $a=1/2$.
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
$endgroup$
add a comment |
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$begingroup$
No matter how distance is measured (among those possibilities mentioned in a comment), he should put it opposite to that of Alice. The notion of 'probability' only makes sense though if Cindy is using a mathematically well-defined strategy.
Let the circle circumference go from $0$ to $1$. Say wlog. that Alice chooses $0$.
Also wlog. say that Bob chooses some $ain[0,0.5]$. Then the optimal place for Cindy is $(a+1)/2$.
The range of Bob winning is $[a/2,((a+1)/2+a)/2]$ the length of which is $(a+1)/4$ which is maximized by $a=1/2$.
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
$endgroup$
add a comment |
$begingroup$
No matter how distance is measured (among those possibilities mentioned in a comment), he should put it opposite to that of Alice. The notion of 'probability' only makes sense though if Cindy is using a mathematically well-defined strategy.
Let the circle circumference go from $0$ to $1$. Say wlog. that Alice chooses $0$.
Also wlog. say that Bob chooses some $ain[0,0.5]$. Then the optimal place for Cindy is $(a+1)/2$.
The range of Bob winning is $[a/2,((a+1)/2+a)/2]$ the length of which is $(a+1)/4$ which is maximized by $a=1/2$.
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
$endgroup$
add a comment |
$begingroup$
No matter how distance is measured (among those possibilities mentioned in a comment), he should put it opposite to that of Alice. The notion of 'probability' only makes sense though if Cindy is using a mathematically well-defined strategy.
Let the circle circumference go from $0$ to $1$. Say wlog. that Alice chooses $0$.
Also wlog. say that Bob chooses some $ain[0,0.5]$. Then the optimal place for Cindy is $(a+1)/2$.
The range of Bob winning is $[a/2,((a+1)/2+a)/2]$ the length of which is $(a+1)/4$ which is maximized by $a=1/2$.
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
$endgroup$
No matter how distance is measured (among those possibilities mentioned in a comment), he should put it opposite to that of Alice. The notion of 'probability' only makes sense though if Cindy is using a mathematically well-defined strategy.
Let the circle circumference go from $0$ to $1$. Say wlog. that Alice chooses $0$.
Also wlog. say that Bob chooses some $ain[0,0.5]$. Then the optimal place for Cindy is $(a+1)/2$.
The range of Bob winning is $[a/2,((a+1)/2+a)/2]$ the length of which is $(a+1)/4$ which is maximized by $a=1/2$.
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
edited Mar 24 at 16:18
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
answered Mar 24 at 15:53
CoolwaterCoolwater
806721
806721
add a comment |
add a comment |
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1
$begingroup$
When you mean closest do you mean in a particular direction, that is, clockwise or anticlockwise? Or is it Euclidean distance?
$endgroup$
– Balakrishnan Rajan
Mar 24 at 15:49
$begingroup$
Sorry, when we draw a point around a circle, do that mean outside of the circle?
$endgroup$
– mathpadawan
Mar 24 at 16:02
$begingroup$
@BalakrishnanRajan, by closest I mean clockwise or anticlockwise direction
$endgroup$
– mathfun
Mar 24 at 16:11
$begingroup$
@nafhgood, I mean on the circle (neither inside or outside of it)
$endgroup$
– mathfun
Mar 24 at 16:12
$begingroup$
Please restore the original title. It' tells nothing about the contents now (especially because interesting is highly subjective), while the previous one contained three important details, related to the nature of the problem. Those details may help others to find for your problem and its solution if they ever have a similar one. See advices at Meta, thread How to ask a good question, section A good title.
$endgroup$
– CiaPan
Mar 25 at 6:47