Mixing
Expected number of rounds in a game based on chance [closed]
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Suppose we have a game where we roll one die first. If the number is a one, then we reroll two dice in its place. We continue this until there are no more ones, and the score is all the numbers added together that weren't 1s. Ex. John rolls a dice, gets a 1, then he rerolls two more dice in its place. He gets a 3 and a 1. The 3 remains, but the 1 is replaced by two dice, which are a 5 and a 6. Then his score is 3+5+6 = 14.
If he gets any number besides a 1 on the first roll, game ends.
How would I find the expected number of rounds that will occur. (new round happens when a 1 occurs).
probability eigenvalues-eigenvectors expected-value
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
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closed as off-topic by Mark S., Leucippus, YiFan, Cesareo, quid♦ Feb 3 at 1:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Mark S., Leucippus, YiFan, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
locked by quid♦ Feb 3 at 1:12
This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.
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$begingroup$
Suppose we have a game where we roll one die first. If the number is a one, then we reroll two dice in its place. We continue this until there are no more ones, and the score is all the numbers added together that weren't 1s. Ex. John rolls a dice, gets a 1, then he rerolls two more dice in its place. He gets a 3 and a 1. The 3 remains, but the 1 is replaced by two dice, which are a 5 and a 6. Then his score is 3+5+6 = 14.
If he gets any number besides a 1 on the first roll, game ends.
How would I find the expected number of rounds that will occur. (new round happens when a 1 occurs).
probability eigenvalues-eigenvectors expected-value
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
$endgroup$
closed as off-topic by Mark S., Leucippus, YiFan, Cesareo, quid♦ Feb 3 at 1:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Mark S., Leucippus, YiFan, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
locked by quid♦ Feb 3 at 1:12
This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.
Read more about locked posts here.
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If he rolls double $1$'s one the second roll, does he roll four dice on the third roll?
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– saulspatz
Jan 27 at 14:53
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Yes, always replaces a one with two other dice rolls
$endgroup$
– johnhudgo
Jan 27 at 15:38
$begingroup$
This appears to be related to a question from the MathCamp application or similar, and has been asked without providing that key context, just like this user's other question (which was literally copied from a mathcamp document). See problem 2 at mathcamp.org/2019/…
$endgroup$
– Mark S.
Feb 2 at 20:26
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I'm voting to close this question as off-topic because it's from a contest
$endgroup$
– quid♦
Feb 3 at 1:13
comments disabled on deleted / locked posts / reviews |
$begingroup$
Suppose we have a game where we roll one die first. If the number is a one, then we reroll two dice in its place. We continue this until there are no more ones, and the score is all the numbers added together that weren't 1s. Ex. John rolls a dice, gets a 1, then he rerolls two more dice in its place. He gets a 3 and a 1. The 3 remains, but the 1 is replaced by two dice, which are a 5 and a 6. Then his score is 3+5+6 = 14.
If he gets any number besides a 1 on the first roll, game ends.
How would I find the expected number of rounds that will occur. (new round happens when a 1 occurs).
probability eigenvalues-eigenvectors expected-value
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
$endgroup$
Suppose we have a game where we roll one die first. If the number is a one, then we reroll two dice in its place. We continue this until there are no more ones, and the score is all the numbers added together that weren't 1s. Ex. John rolls a dice, gets a 1, then he rerolls two more dice in its place. He gets a 3 and a 1. The 3 remains, but the 1 is replaced by two dice, which are a 5 and a 6. Then his score is 3+5+6 = 14.
If he gets any number besides a 1 on the first roll, game ends.
How would I find the expected number of rounds that will occur. (new round happens when a 1 occurs).
probability eigenvalues-eigenvectors expected-value
probability eigenvalues-eigenvectors expected-value
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
asked Jan 27 at 14:42
johnhudgojohnhudgo
42
42
closed as off-topic by Mark S., Leucippus, YiFan, Cesareo, quid♦ Feb 3 at 1:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Mark S., Leucippus, YiFan, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
locked by quid♦ Feb 3 at 1:12
This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.
Read more about locked posts here.
closed as off-topic by Mark S., Leucippus, YiFan, Cesareo, quid♦ Feb 3 at 1:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Mark S., Leucippus, YiFan, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
locked by quid♦ Feb 3 at 1:12
This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.
Read more about locked posts here.
$begingroup$
If he rolls double $1$'s one the second roll, does he roll four dice on the third roll?
$endgroup$
– saulspatz
Jan 27 at 14:53
$begingroup$
Yes, always replaces a one with two other dice rolls
$endgroup$
– johnhudgo
Jan 27 at 15:38
$begingroup$
This appears to be related to a question from the MathCamp application or similar, and has been asked without providing that key context, just like this user's other question (which was literally copied from a mathcamp document). See problem 2 at mathcamp.org/2019/…
$endgroup$
– Mark S.
Feb 2 at 20:26
$begingroup$
I'm voting to close this question as off-topic because it's from a contest
$endgroup$
– quid♦
Feb 3 at 1:13
comments disabled on deleted / locked posts / reviews |
$begingroup$
If he rolls double $1$'s one the second roll, does he roll four dice on the third roll?
$endgroup$
– saulspatz
Jan 27 at 14:53
$begingroup$
Yes, always replaces a one with two other dice rolls
$endgroup$
– johnhudgo
Jan 27 at 15:38
$begingroup$
This appears to be related to a question from the MathCamp application or similar, and has been asked without providing that key context, just like this user's other question (which was literally copied from a mathcamp document). See problem 2 at mathcamp.org/2019/…
$endgroup$
– Mark S.
Feb 2 at 20:26
$begingroup$
I'm voting to close this question as off-topic because it's from a contest
$endgroup$
– quid♦
Feb 3 at 1:13
$begingroup$
If he rolls double $1$'s one the second roll, does he roll four dice on the third roll?
$endgroup$
– saulspatz
Jan 27 at 14:53
$begingroup$
If he rolls double $1$'s one the second roll, does he roll four dice on the third roll?
$endgroup$
– saulspatz
Jan 27 at 14:53
$begingroup$
Yes, always replaces a one with two other dice rolls
$endgroup$
– johnhudgo
Jan 27 at 15:38
$begingroup$
Yes, always replaces a one with two other dice rolls
$endgroup$
– johnhudgo
Jan 27 at 15:38
$begingroup$
This appears to be related to a question from the MathCamp application or similar, and has been asked without providing that key context, just like this user's other question (which was literally copied from a mathcamp document). See problem 2 at mathcamp.org/2019/…
$endgroup$
– Mark S.
Feb 2 at 20:26
$begingroup$
This appears to be related to a question from the MathCamp application or similar, and has been asked without providing that key context, just like this user's other question (which was literally copied from a mathcamp document). See problem 2 at mathcamp.org/2019/…
$endgroup$
– Mark S.
Feb 2 at 20:26
$begingroup$
I'm voting to close this question as off-topic because it's from a contest
$endgroup$
– quid♦
Feb 3 at 1:13
$begingroup$
I'm voting to close this question as off-topic because it's from a contest
$endgroup$
– quid♦
Feb 3 at 1:13
comments disabled on deleted / locked posts / reviews |
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$begingroup$
If he rolls double $1$'s one the second roll, does he roll four dice on the third roll?
$endgroup$
– saulspatz
Jan 27 at 14:53
$begingroup$
Yes, always replaces a one with two other dice rolls
$endgroup$
– johnhudgo
Jan 27 at 15:38
$begingroup$
This appears to be related to a question from the MathCamp application or similar, and has been asked without providing that key context, just like this user's other question (which was literally copied from a mathcamp document). See problem 2 at mathcamp.org/2019/…
$endgroup$
– Mark S.
Feb 2 at 20:26
$begingroup$
I'm voting to close this question as off-topic because it's from a contest
$endgroup$
– quid♦
Feb 3 at 1:13