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# Hitting 137

Best Answer Prime, 14 January 2013 - 09:32 PM

It seems to stand the reason...

Spoiler for just a guess

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19 replies to this topic

### #1 bonanova

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Posted 14 January 2013 - 08:35 PM

If I repeatedly throw a fair 6-sided die, what is the probability that the running total will at one point equal 137?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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### #2 bushindo

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Posted 14 January 2013 - 09:25 PM

If I repeatedly throw a fair 6-sided die, what is the probability that the running total will at one point equal 137?

With some recursive code, I get

Spoiler for

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### #3 CaptainEd

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Posted 14 January 2013 - 09:32 PM

Spoiler for Bushindo's surprising value of

Edited by CaptainEd, 14 January 2013 - 09:32 PM.

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### #4 Prime

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Posted 14 January 2013 - 09:32 PM   Best Answer

It seems to stand the reason...

Spoiler for just a guess

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Past prime, actually.

### #5 BobbyGo

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Posted 14 January 2013 - 10:21 PM

Spoiler for I must be way off

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### #6 bonanova

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Posted 15 January 2013 - 01:22 AM

Bushindo has seven decimal places; the Captain has it exactly, if surprisingly; and Prime has the insight.
A triple tag team solution! Good job all. So who gets the "solved" tag .... ?

The nod goes to Prime's explanation.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #7 Prime

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Posted 15 January 2013 - 11:31 AM

Thanks Bonanova. My explanation does look sound. But now, after I have taken some time to reflect, I must disprove and disown my solution.

Sure, the fraction that we found here is good for everyday gambling needs, but it is not the exact probability.

I suspect, Bushindo’s method would have produced the exact answer, had it not succumbed to rounding error.

Spoiler for Proof of falsehood, but not the answer.

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Past prime, actually.

### #8 CaptainEd

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Posted 15 January 2013 - 03:54 PM

Prime, your "disproof" notwithstanding, we should congratulate you on your insight that has identified the limit towards which any experiment to 137 should tend (IMH and Naive Opinion). I'm interested to understand about Bushindo's recursive code. My contribution was only to respond to Bushindo's numeric result, as it matches the cyclic stream of digits I learned in childhood.

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### #9 BobbyGo

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Posted 15 January 2013 - 05:01 PM

Thanks Bonanova. My explanation does look sound. But now, after I have taken some time to reflect, I must disprove and disown my solution.

Sure, the fraction that we found here is good for everyday gambling needs, but it is not the exact probability.

I suspect, Bushindo’s method would have produced the exact answer, had it not succumbed to rounding error.

Spoiler for Proof of falsehood, but not the answer.

I'm glad I wasn't too far off in my thinking.  I had a similar approach, but only considered 131 - 136 when trying to calculate the odds for 137.  I had wrongly assumed each number 131 - 136 would have an equal likelyhood of being hit irrespective of of the likelyhood of any of the previous numbers.

Spoiler for Question

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### #10 bushindo

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Posted 15 January 2013 - 06:06 PM

Prime, your "disproof" notwithstanding, we should congratulate you on your insight that has identified the limit towards which any experiment to 137 should tend (IMH and Naive Opinion). I'm interested to understand about Bushindo's recursive code. My contribution was only to respond to Bushindo's numeric result, as it matches the cyclic stream of digits I learned in childhood.

Here is the recursive code I used. The logic behind it is already described by Prime's excellent and insightful analysis.

Spoiler for

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