Roll a die, highest number wins
$begingroup$
My brothers and I (three of us) decided to roll a single die to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, thus ending the contest, I got the knife.
But I'm not comfortable with this. My brothers did not even get to roll the die! My question is: Was the way I won the knife statistically fair? If not, what is the fair way to do this with a single die?
dice
edited Feb 10 at 7:53
jvdhooft
5,68561641
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
$endgroup$
add a comment |
$begingroup$
My brothers and I (three of us) decided to roll a single die to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, thus ending the contest, I got the knife.
But I'm not comfortable with this. My brothers did not even get to roll the die! My question is: Was the way I won the knife statistically fair? If not, what is the fair way to do this with a single die?
dice
edited Feb 10 at 7:53
jvdhooft
5,68561641
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
$endgroup$
5
$begingroup$
You each roll. If more than one gets the highest number, then those individuals roll again to see who is highest, repeating if necessary
$endgroup$
– Henry
Sep 28 '15 at 13:45
$begingroup$
You say 'the guy who rolled the highest number would win' but if your brothers didn't roll the dice then how could you be the winner?
$endgroup$
– Mattos
Sep 28 '15 at 13:45
$begingroup$
@Mattos That's the thing, it's obviously not fair.
$endgroup$
– peter.petrov
Sep 28 '15 at 13:51
$begingroup$
@peter.petrov That was my point..
$endgroup$
– Mattos
Sep 28 '15 at 13:52
$begingroup$
I call for a re-roll!
$endgroup$
– Mark Watson
Sep 28 '15 at 14:10
add a comment |
$begingroup$
My brothers and I (three of us) decided to roll a single die to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, thus ending the contest, I got the knife.
But I'm not comfortable with this. My brothers did not even get to roll the die! My question is: Was the way I won the knife statistically fair? If not, what is the fair way to do this with a single die?
dice
edited Feb 10 at 7:53
jvdhooft
5,68561641
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
$endgroup$
My brothers and I (three of us) decided to roll a single die to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, thus ending the contest, I got the knife.
But I'm not comfortable with this. My brothers did not even get to roll the die! My question is: Was the way I won the knife statistically fair? If not, what is the fair way to do this with a single die?
dice
dice
edited Feb 10 at 7:53
jvdhooft
5,68561641
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
edited Feb 10 at 7:53
jvdhooft
5,68561641
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
edited Feb 10 at 7:53
jvdhooft
5,68561641
edited Feb 10 at 7:53
jvdhooft
5,68561641
edited Feb 10 at 7:53
jvdhooft
5,68561641
5,68561641
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
asked Sep 28 '15 at 13:41
John CampbellJohn Campbell
1
1
5
$begingroup$
You each roll. If more than one gets the highest number, then those individuals roll again to see who is highest, repeating if necessary
$endgroup$
– Henry
Sep 28 '15 at 13:45
$begingroup$
You say 'the guy who rolled the highest number would win' but if your brothers didn't roll the dice then how could you be the winner?
$endgroup$
– Mattos
Sep 28 '15 at 13:45
$begingroup$
@Mattos That's the thing, it's obviously not fair.
$endgroup$
– peter.petrov
Sep 28 '15 at 13:51
$begingroup$
@peter.petrov That was my point..
$endgroup$
– Mattos
Sep 28 '15 at 13:52
$begingroup$
I call for a re-roll!
$endgroup$
– Mark Watson
Sep 28 '15 at 14:10
add a comment |
5
$begingroup$
You each roll. If more than one gets the highest number, then those individuals roll again to see who is highest, repeating if necessary
$endgroup$
– Henry
Sep 28 '15 at 13:45
$begingroup$
You say 'the guy who rolled the highest number would win' but if your brothers didn't roll the dice then how could you be the winner?
$endgroup$
– Mattos
Sep 28 '15 at 13:45
$begingroup$
@Mattos That's the thing, it's obviously not fair.
$endgroup$
– peter.petrov
Sep 28 '15 at 13:51
$begingroup$
@peter.petrov That was my point..
$endgroup$
– Mattos
Sep 28 '15 at 13:52
$begingroup$
I call for a re-roll!
$endgroup$
– Mark Watson
Sep 28 '15 at 14:10
5
5
$begingroup$
You each roll. If more than one gets the highest number, then those individuals roll again to see who is highest, repeating if necessary
$endgroup$
– Henry
Sep 28 '15 at 13:45
$begingroup$
You each roll. If more than one gets the highest number, then those individuals roll again to see who is highest, repeating if necessary
$endgroup$
– Henry
Sep 28 '15 at 13:45
$begingroup$
You say 'the guy who rolled the highest number would win' but if your brothers didn't roll the dice then how could you be the winner?
$endgroup$
– Mattos
Sep 28 '15 at 13:45
$begingroup$
You say 'the guy who rolled the highest number would win' but if your brothers didn't roll the dice then how could you be the winner?
$endgroup$
– Mattos
Sep 28 '15 at 13:45
$begingroup$
@Mattos That's the thing, it's obviously not fair.
$endgroup$
– peter.petrov
Sep 28 '15 at 13:51
$begingroup$
@Mattos That's the thing, it's obviously not fair.
$endgroup$
– peter.petrov
Sep 28 '15 at 13:51
$begingroup$
@peter.petrov That was my point..
$endgroup$
– Mattos
Sep 28 '15 at 13:52
$begingroup$
@peter.petrov That was my point..
$endgroup$
– Mattos
Sep 28 '15 at 13:52
$begingroup$
I call for a re-roll!
$endgroup$
– Mark Watson
Sep 28 '15 at 14:10
$begingroup$
I call for a re-roll!
$endgroup$
– Mark Watson
Sep 28 '15 at 14:10
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The way you did it was unfair. Why? Firstly, the aim of the game was to get the highest number, not the highest number first and this goes to the heart of the reason as to why the way you did it was unfair.
Had you said "the one to roll the highest number first wins" yes this would have been a fair win, as you had rolled a six (highest number you can roll on a normal, fair six-sided die), but you didn't say first, which means that had they both rolled a six after you had rolled your six (i.e you all roll a six), based on the rules of the game, there would have been no winners or losers. Or had one of your brothers also rolled a six and the other hadn't, still none of you could have claimed they had rolled a higher number than the other (i.e 6 is not greater than or less than six. 6 = 6).
So based by your rules, in order for this to have been a fair win you must have had your brothers each take their turn at rolling the same dice once, even after you had rolled the six, and had still rolled the highest number between the three of you. Since this was not the case, no; the way you won was not statistically fair.
How should you have done it for it to have been statistically fair? Ensure everyone gets the same number of rolls with the same exact dice. If the rules are to simply roll the highest number, count a case where at least two people both roll the same number, and that number happens to be the highest number for that round, as a tie and have only the people who rolled that number to roll again until only one person rolls the highest number in that round.
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
$endgroup$
add a comment |
$begingroup$
Your brothers had a 1 in 6 chance of also rolling a six. Meaning they could have tied with you and in such a case a reroll would be in order, eliminating whoever didn't tie for highest and repeat until only one rolls highest. The way you determined the winner of the knife was not fair at all.
With a single die, you could each roll it one at a time.
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
$endgroup$
add a comment |
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2 Answers
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active
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votes
2 Answers
2
active
oldest
votes
active
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active
oldest
votes
$begingroup$
The way you did it was unfair. Why? Firstly, the aim of the game was to get the highest number, not the highest number first and this goes to the heart of the reason as to why the way you did it was unfair.
Had you said "the one to roll the highest number first wins" yes this would have been a fair win, as you had rolled a six (highest number you can roll on a normal, fair six-sided die), but you didn't say first, which means that had they both rolled a six after you had rolled your six (i.e you all roll a six), based on the rules of the game, there would have been no winners or losers. Or had one of your brothers also rolled a six and the other hadn't, still none of you could have claimed they had rolled a higher number than the other (i.e 6 is not greater than or less than six. 6 = 6).
So based by your rules, in order for this to have been a fair win you must have had your brothers each take their turn at rolling the same dice once, even after you had rolled the six, and had still rolled the highest number between the three of you. Since this was not the case, no; the way you won was not statistically fair.
How should you have done it for it to have been statistically fair? Ensure everyone gets the same number of rolls with the same exact dice. If the rules are to simply roll the highest number, count a case where at least two people both roll the same number, and that number happens to be the highest number for that round, as a tie and have only the people who rolled that number to roll again until only one person rolls the highest number in that round.
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
$endgroup$
add a comment |
$begingroup$
The way you did it was unfair. Why? Firstly, the aim of the game was to get the highest number, not the highest number first and this goes to the heart of the reason as to why the way you did it was unfair.
Had you said "the one to roll the highest number first wins" yes this would have been a fair win, as you had rolled a six (highest number you can roll on a normal, fair six-sided die), but you didn't say first, which means that had they both rolled a six after you had rolled your six (i.e you all roll a six), based on the rules of the game, there would have been no winners or losers. Or had one of your brothers also rolled a six and the other hadn't, still none of you could have claimed they had rolled a higher number than the other (i.e 6 is not greater than or less than six. 6 = 6).
So based by your rules, in order for this to have been a fair win you must have had your brothers each take their turn at rolling the same dice once, even after you had rolled the six, and had still rolled the highest number between the three of you. Since this was not the case, no; the way you won was not statistically fair.
How should you have done it for it to have been statistically fair? Ensure everyone gets the same number of rolls with the same exact dice. If the rules are to simply roll the highest number, count a case where at least two people both roll the same number, and that number happens to be the highest number for that round, as a tie and have only the people who rolled that number to roll again until only one person rolls the highest number in that round.
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
$endgroup$
add a comment |
$begingroup$
The way you did it was unfair. Why? Firstly, the aim of the game was to get the highest number, not the highest number first and this goes to the heart of the reason as to why the way you did it was unfair.
Had you said "the one to roll the highest number first wins" yes this would have been a fair win, as you had rolled a six (highest number you can roll on a normal, fair six-sided die), but you didn't say first, which means that had they both rolled a six after you had rolled your six (i.e you all roll a six), based on the rules of the game, there would have been no winners or losers. Or had one of your brothers also rolled a six and the other hadn't, still none of you could have claimed they had rolled a higher number than the other (i.e 6 is not greater than or less than six. 6 = 6).
So based by your rules, in order for this to have been a fair win you must have had your brothers each take their turn at rolling the same dice once, even after you had rolled the six, and had still rolled the highest number between the three of you. Since this was not the case, no; the way you won was not statistically fair.
How should you have done it for it to have been statistically fair? Ensure everyone gets the same number of rolls with the same exact dice. If the rules are to simply roll the highest number, count a case where at least two people both roll the same number, and that number happens to be the highest number for that round, as a tie and have only the people who rolled that number to roll again until only one person rolls the highest number in that round.
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
$endgroup$
The way you did it was unfair. Why? Firstly, the aim of the game was to get the highest number, not the highest number first and this goes to the heart of the reason as to why the way you did it was unfair.
Had you said "the one to roll the highest number first wins" yes this would have been a fair win, as you had rolled a six (highest number you can roll on a normal, fair six-sided die), but you didn't say first, which means that had they both rolled a six after you had rolled your six (i.e you all roll a six), based on the rules of the game, there would have been no winners or losers. Or had one of your brothers also rolled a six and the other hadn't, still none of you could have claimed they had rolled a higher number than the other (i.e 6 is not greater than or less than six. 6 = 6).
So based by your rules, in order for this to have been a fair win you must have had your brothers each take their turn at rolling the same dice once, even after you had rolled the six, and had still rolled the highest number between the three of you. Since this was not the case, no; the way you won was not statistically fair.
How should you have done it for it to have been statistically fair? Ensure everyone gets the same number of rolls with the same exact dice. If the rules are to simply roll the highest number, count a case where at least two people both roll the same number, and that number happens to be the highest number for that round, as a tie and have only the people who rolled that number to roll again until only one person rolls the highest number in that round.
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
answered Oct 9 '15 at 9:42
Brett ZonkeBrett Zonke
1
1
add a comment |
add a comment |
$begingroup$
Your brothers had a 1 in 6 chance of also rolling a six. Meaning they could have tied with you and in such a case a reroll would be in order, eliminating whoever didn't tie for highest and repeat until only one rolls highest. The way you determined the winner of the knife was not fair at all.
With a single die, you could each roll it one at a time.
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
$endgroup$
add a comment |
$begingroup$
Your brothers had a 1 in 6 chance of also rolling a six. Meaning they could have tied with you and in such a case a reroll would be in order, eliminating whoever didn't tie for highest and repeat until only one rolls highest. The way you determined the winner of the knife was not fair at all.
With a single die, you could each roll it one at a time.
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
$endgroup$
add a comment |
$begingroup$
Your brothers had a 1 in 6 chance of also rolling a six. Meaning they could have tied with you and in such a case a reroll would be in order, eliminating whoever didn't tie for highest and repeat until only one rolls highest. The way you determined the winner of the knife was not fair at all.
With a single die, you could each roll it one at a time.
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
$endgroup$
Your brothers had a 1 in 6 chance of also rolling a six. Meaning they could have tied with you and in such a case a reroll would be in order, eliminating whoever didn't tie for highest and repeat until only one rolls highest. The way you determined the winner of the knife was not fair at all.
With a single die, you could each roll it one at a time.
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
answered Feb 10 at 8:16
Tristan AlexanderTristan Alexander
43
43
add a comment |
add a comment |
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5
$begingroup$
You each roll. If more than one gets the highest number, then those individuals roll again to see who is highest, repeating if necessary
$endgroup$
– Henry
Sep 28 '15 at 13:45
$begingroup$
You say 'the guy who rolled the highest number would win' but if your brothers didn't roll the dice then how could you be the winner?
$endgroup$
– Mattos
Sep 28 '15 at 13:45
$begingroup$
@Mattos That's the thing, it's obviously not fair.
$endgroup$
– peter.petrov
Sep 28 '15 at 13:51
$begingroup$
@peter.petrov That was my point..
$endgroup$
– Mattos
Sep 28 '15 at 13:52
$begingroup$
I call for a re-roll!
$endgroup$
– Mark Watson
Sep 28 '15 at 14:10