Nice puzzle

Anything About Anything...
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Z-Man
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Post by Z-Man » Tue Mar 17, 2009 11:24 pm

No. Your answer is not even wrong. It doesn't make sense. Lacks definition for what bob and sue mean.

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rumpole
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Post by rumpole » Wed Mar 18, 2009 12:09 am

bob and sue are implied in the question but heres a little more detail

bob takes his first throw and has a 5 in 6 chance of not hitting a 6
sue takes her first throw and has a 5 in 6 chance of not hitting a 6
bob takes his second throw and has a 1 in 6 chance of hitting a 6

so the odds that bob will throw a 6 on his 2nd throw are

(5/6) * (5/6) * (1/6)

maybe thats wrong ? but it seems right to me
Writing code is easy. Finishing is hard.

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Z-Man
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Post by Z-Man » Wed Mar 18, 2009 12:20 am

rumpole wrote:bob and sue are implied in the question but heres a little more detail
Then just leave them out :) If you put them into your answer, they look like variables of unknown value.
rumpole wrote:so the odds that bob will throw a 6 on his 2nd throw are

(5/6) * (5/6) * (1/6)

maybe thats wrong ? but it seems right to me
Correct, but it's not the question that was asked.

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rumpole
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Post by rumpole » Wed Mar 18, 2009 1:02 am

Sorry guys... I read the question again and sue rolls 1st, originally I read it as bob rolls 1st some how ?
I have z-man to thank for forcing my eyes to open

so the answer is (5/6) * (5/6) * (5/6) * (1/6) = 125/1296

ie 9.645061728% or there abouts
Writing code is easy. Finishing is hard.

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Z-Man
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Post by Z-Man » Wed Mar 18, 2009 8:34 am

Oh, heh, I didn't even notice THAT mistake of yours. Anyway, you're still answering the wrong question :) You're answering 'In this game, what are the chances of bob winning on his second throw?', where the real question is 'Given that bob wins, what are the chances he did so on his second throw?'.

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rumpole
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Post by rumpole » Wed Mar 18, 2009 4:50 pm

Z-Man wrote:...the real question is 'Given that bob wins, what are the chances he did so on his second throw?'.
Is that really the question ? I dont interpret it in that way

Nurse, new brain please asap.
Writing code is easy. Finishing is hard.

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Jonathan
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Post by Jonathan » Wed Mar 18, 2009 5:21 pm

rumpole, "Bob rolls a 6 before Sue." isn't meant to be ignored, nor is "What is the probability Bob rolled the 6 on his second turn?"

---

I got bored and recorded a few (ahem) actual dice rolls, and made a program to automate interpretation and all that.

Dice specs: wooden, painted red, shaped like the intersection of a sphere and a cube (so that the cube's edges are engulfed, but just barely), not heavy enough to influence results by hitting the keyboard.
Scroll down to see final stats wrote:6 | Sue1 | Win
2 | Sue1
2 | Bob1
6 | Sue2 | Win
5 | Sue1
6 | Bob1 | Win | Recording Bob: 1 | Bob2/Bob = 0/1 = 0
2 | Sue1
1 | Bob1
3 | Sue2
5 | Bob2
5 | Sue3
1 | Bob3
1 | Sue4
1 | Bob4
6 | Sue5 | Win
2 | Sue1
1 | Bob1
1 | Sue2
1 | Bob2
1 | Sue3
6 | Bob3 | Win | Recording Bob: 2 | Bob2/Bob = 0/2 = 0/1 = 0
1 | Sue1
3 | Bob1
6 | Sue2 | Win
6 | Sue1 | Win
4 | Sue1
3 | Bob1
3 | Sue2
1 | Bob2
2 | Sue3
2 | Bob3
3 | Sue4
5 | Bob4
5 | Sue5
6 | Bob5 | Win | Recording Bob: 3 | Bob2/Bob = 0/3 = 0/1 = 0
1 | Sue1
3 | Bob1
4 | Sue2
6 | Bob2 | Win | Recording Bob: 4 | Recording Bob2: 1 | Bob2/Bob = 1/4 = 0.25
3 | Sue1
2 | Bob1
3 | Sue2
4 | Bob2
6 | Sue3 | Win
1 | Sue1
6 | Bob1 | Win | Recording Bob: 5 | Bob2/Bob = 1/5 = 0.2
2 | Sue1
1 | Bob1
6 | Sue2 | Win
5 | Sue1
1 | Bob1
2 | Sue2
3 | Bob2
1 | Sue3
4 | Bob3
2 | Sue4
5 | Bob4
3 | Sue5
3 | Bob5
5 | Sue6
6 | Bob6 | Win | Recording Bob: 6 | Bob2/Bob = 1/6 = 0.1(6)
6 | Sue1 | Win
6 | Sue1 | Win
6 | Sue1 | Win
3 | Sue1
6 | Bob1 | Win | Recording Bob: 7 | Bob2/Bob = 1/7 = 0.(142857)
3 | Sue1
4 | Bob1
1 | Sue2
2 | Bob2
2 | Sue3
2 | Bob3
4 | Sue4
4 | Bob4
1 | Sue5
3 | Bob5
6 | Sue6 | Win
3 | Sue1
3 | Bob1
5 | Sue2
3 | Bob2
4 | Sue3
5 | Bob3
1 | Sue4
5 | Bob4
4 | Sue5
1 | Bob5
4 | Sue6
2 | Bob6
2 | Sue7
5 | Bob7
4 | Sue8
3 | Bob8
4 | Sue9
3 | Bob9
4 | Sue10
6 | Bob10 | Win | Recording Bob: 8 | Bob2/Bob = 1/8 = 0.125
2 | Sue1
4 | Bob1
4 | Sue2
2 | Bob2
4 | Sue3
6 | Bob3 | Win | Recording Bob: 9 | Bob2/Bob = 1/9 = 0.(1)
5 | Sue1
3 | Bob1
5 | Sue2
6 | Bob2 | Win | Recording Bob: 10 | Recording Bob2: 2 | Bob2/Bob = 2/10 = 1/5 = 0.2
1 | Sue1
4 | Bob1
2 | Sue2
4 | Bob2
5 | Sue3
2 | Bob3
1 | Sue4
4 | Bob4
6 | Sue5 | Win
4 | Sue1
1 | Bob1
5 | Sue2
2 | Bob2
3 | Sue3
2 | Bob3
6 | Sue4 | Win
6 | Sue1 | Win
2 | Sue1
4 | Bob1
5 | Sue2
1 | Bob2
6 | Sue3 | Win
2 | Sue1
4 | Bob1
5 | Sue2
6 | Bob2 | Win | Recording Bob: 11 | Recording Bob2: 3 | Bob2/Bob = 3/11 = 0.(27)
3 | Sue1
3 | Bob1
6 | Sue2 | Win
6 | Sue1 | Win
6 | Sue1 | Win
6 | Sue1 | Win
2 | Sue1
1 | Bob1
3 | Sue2
4 | Bob2
4 | Sue3
6 | Bob3 | Win | Recording Bob: 12 | Bob2/Bob = 3/12 = 1/4 = 0.25
6 | Sue1 | Win
6 | Sue1 | Win
4 | Sue1
1 | Bob1
4 | Sue2
4 | Bob2
4 | Sue3
3 | Bob3
2 | Sue4
4 | Bob4
6 | Sue5 | Win
5 | Sue1
5 | Bob1
5 | Sue2
6 | Bob2 | Win | Recording Bob: 13 | Recording Bob2: 4 | Bob2/Bob = 4/13 = 0.(307692)
2 | Sue1
1 | Bob1
1 | Sue2
2 | Bob2
5 | Sue3
5 | Bob3
1 | Sue4
4 | Bob4
6 | Sue5 | Win
4 | Sue1
1 | Bob1
2 | Sue2
4 | Bob2
1 | Sue3
2 | Bob3
4 | Sue4
5 | Bob4
3 | Sue5
1 | Bob5
3 | Sue6
1 | Bob6
5 | Sue7
6 | Bob7 | Win | Recording Bob: 14 | Bob2/Bob = 4/14 = 2/7 = 0.(285714)
2 | Sue1
4 | Bob1
3 | Sue2
6 | Bob2 | Win | Recording Bob: 15 | Recording Bob2: 5 | Bob2/Bob = 5/15 = 1/3 = 0.(3)
2 | Sue1
5 | Bob1
4 | Sue2
6 | Bob2 | Win | Recording Bob: 16 | Recording Bob2: 6 | Bob2/Bob = 6/16 = 3/8 = 0.375
4 | Sue1
6 | Bob1 | Win | Recording Bob: 17 | Bob2/Bob = 6/17 = 0.(3529411764705882)
2 | Sue1
3 | Bob1
2 | Sue2
1 | Bob2
5 | Sue3
4 | Bob3
5 | Sue4
3 | Bob4
3 | Sue5
5 | Bob5
6 | Sue6 | Win
4 | Sue1
3 | Bob1
6 | Sue2 | Win
6 | Sue1 | Win
2 | Sue1
4 | Bob1
6 | Sue2 | Win
3 | Sue1
1 | Bob1
1 | Sue2
1 | Bob2
5 | Sue3
1 | Bob3
2 | Sue4
1 | Bob4
5 | Sue5
5 | Bob5
5 | Sue6
6 | Bob6 | Win | Recording Bob: 18 | Bob2/Bob = 6/18 = 1/3 = 0.(3)
1 | Sue1
5 | Bob1
6 | Sue2 | Win
6 | Sue1 | Win
5 | Sue1
2 | Bob1
3 | Sue2
6 | Bob2 | Win | Recording Bob: 19 | Recording Bob2: 7 | Bob2/Bob = 7/19 = 0.(368421052631578947)
4 | Sue1
4 | Bob1
1 | Sue2
5 | Bob2
4 | Sue3
5 | Bob3
1 | Sue4
3 | Bob4
3 | Sue5
1 | Bob5
1 | Sue6
3 | Bob6
1 | Sue7
3 | Bob7
6 | Sue8 | Win
5 | Sue1
1 | Bob1
3 | Sue2
3 | Bob2
4 | Sue3
3 | Bob3
6 | Sue4 | Win
1 | Sue1
5 | Bob1
6 | Sue2 | Win
1 | Sue1
6 | Bob1 | Win | Recording Bob: 20 | Bob2/Bob = 7/20 = 0.35
1 | Sue1
4 | Bob1
4 | Sue2
5 | Bob2
5 | Sue3
5 | Bob3
5 | Sue4
6 | Bob4 | Win | Recording Bob: 21 | Bob2/Bob = 7/21 = 1/3 = 0.(3)
6 | Sue1 | Win
1 | Sue1
2 | Bob1
2 | Sue2
4 | Bob2
5 | Sue3
6 | Bob3 | Win | Recording Bob: 22 | Bob2/Bob = 7/22 = 0.3(18)
2 | Sue1
4 | Bob1
6 | Sue2 | Win
3 | Sue1
1 | Bob1
5 | Sue2
6 | Bob2 | Win | Recording Bob: 23 | Recording Bob2: 8 | Bob2/Bob = 8/23 = 0.(3478260869565217391304)
4 | Sue1
4 | Bob1
4 | Sue2
3 | Bob2
2 | Sue3
5 | Bob3
2 | Sue4
3 | Bob4
6 | Sue5 | Win
3 | Sue1
1 | Bob1
6 | Sue2 | Win
3 | Sue1
2 | Bob1
1 | Sue2
4 | Bob2
5 | Sue3
5 | Bob3
6 | Sue4 | Win
5 | Sue1
5 | Bob1
1 | Sue2
5 | Bob2
4 | Sue3
1 | Bob3
1 | Sue4
4 | Bob4
1 | Sue5
3 | Bob5
1 | Sue6
3 | Bob6
1 | Sue7
2 | Bob7
3 | Sue8
2 | Bob8
1 | Sue9
4 | Bob9
6 | Sue10 | Win
3 | Sue1
4 | Bob1
1 | Sue2
4 | Bob2
1 | Sue3
1 | Bob3
6 | Sue4 | Win
3 | Sue1
2 | Bob1
6 | Sue2 | Win
5 | Sue1
2 | Bob1
2 | Sue2
6 | Bob2 | Win | Recording Bob: 24 | Recording Bob2: 9 | Bob2/Bob = 9/24 = 3/8 = 0.375
6 | Sue1 | Win
3 | Sue1
1 | Bob1
6 | Sue2 | Win
2 | Sue1
5 | Bob1
6 | Sue2 | Win
3 | Sue1
3 | Bob1
5 | Sue2
2 | Bob2
6 | Sue3 | Win
2 | Sue1
6 | Bob1 | Win | Recording Bob: 25 | Bob2/Bob = 9/25 = 0.36
2 | Sue1
1 | Bob1
4 | Sue2
5 | Bob2
3 | Sue3
6 | Bob3 | Win | Recording Bob: 26 | Bob2/Bob = 9/26 = 0.3(461538)
1 | Sue1
4 | Bob1
6 | Sue2 | Win
5 | Sue1
6 | Bob1 | Win | Recording Bob: 27 | Bob2/Bob = 9/27 = 1/3 = 0.(3)
2 | Sue1
6 | Bob1 | Win | Recording Bob: 28 | Bob2/Bob = 9/28 = 0.32(142857)
6 | Sue1 | Win
2 | Sue1
2 | Bob1
5 | Sue2
5 | Bob2
5 | Sue3
4 | Bob3
2 | Sue4
6 | Bob4 | Win | Recording Bob: 29 | Bob2/Bob = 9/29 = 0.(3103448275862068965517241379)
4 | Sue1
5 | Bob1
3 | Sue2
4 | Bob2
2 | Sue3
6 | Bob3 | Win | Recording Bob: 30 | Bob2/Bob = 9/30 = 3/10 = 0.3
3 | Sue1
1 | Bob1
1 | Sue2
6 | Bob2 | Win | Recording Bob: 31 | Recording Bob2: 10 | Bob2/Bob = 10/31 = 0.(322580645161290)
6 | Sue1 | Win
6 | Sue1 | Win
6 | Sue1 | Win
6 | Sue1 | Win
3 | Sue1
5 | Bob1
1 | Sue2
3 | Bob2
4 | Sue3
6 | Bob3 | Win | Recording Bob: 32 | Bob2/Bob = 10/32 = 5/16 = 0.3125
5 | Sue1
5 | Bob1
5 | Sue2
6 | Bob2 | Win | Recording Bob: 33 | Recording Bob2: 11 | Bob2/Bob = 11/33 = 1/3 = 0.(3)
1 | Sue1
2 | Bob1
5 | Sue2
1 | Bob2
2 | Sue3
3 | Bob3
1 | Sue4
3 | Bob4
3 | Sue5
2 | Bob5
1 | Sue6
5 | Bob6
5 | Sue7
5 | Bob7
5 | Sue8
4 | Bob8
5 | Sue9
6 | Bob9 | Win | Recording Bob: 34 | Bob2/Bob = 11/34 = 0.3(2352941176470588)
1 | Sue1
1 | Bob1
2 | Sue2
1 | Bob2
4 | Sue3
4 | Bob3
4 | Sue4
1 | Bob4
2 | Sue5
6 | Bob5 | Win | Recording Bob: 35 | Bob2/Bob = 11/35 = 0.3(142857)
5 | Sue1
3 | Bob1
1 | Sue2
2 | Bob2
2 | Sue3
4 | Bob3
6 | Sue4 | Win
2 | Sue1
2 | Bob1
5 | Sue2
2 | Bob2
1 | Sue3
1 | Bob3
2 | Sue4
6 | Bob4 | Win | Recording Bob: 36 | Bob2/Bob = 11/36 = 0.30(5)
1 | Sue1
5 | Bob1
2 | Sue2
4 | Bob2
1 | Sue3
1 | Bob3
6 | Sue4 | Win
3 | Sue1
1 | Bob1
6 | Sue2 | Win
2 | Sue1
6 | Bob1 | Win | Recording Bob: 37 | Bob2/Bob = 11/37 = 0.(297)
1 | Sue1
2 | Bob1
2 | Sue2
5 | Bob2
4 | Sue3
1 | Bob3
6 | Sue4 | Win
3 | Sue1
6 | Bob1 | Win | Recording Bob: 38 | Bob2/Bob = 11/38 = 0.2(894736842105263157)
5 | Sue1
6 | Bob1 | Win | Recording Bob: 39 | Bob2/Bob = 11/39 = 0.(282051)
4 | Sue1
5 | Bob1
3 | Sue2
6 | Bob2 | Win | Recording Bob: 40 | Recording Bob2: 12 | Bob2/Bob = 12/40 = 3/10 = 0.3
5 | Sue1
3 | Bob1
1 | Sue2
2 | Bob2
4 | Sue3
2 | Bob3
1 | Sue4
4 | Bob4
1 | Sue5
2 | Bob5
4 | Sue6
6 | Bob6 | Win | Recording Bob: 41 | Bob2/Bob = 12/41 = 0.(29268)
5 | Sue1
5 | Bob1
5 | Sue2
2 | Bob2
5 | Sue3
5 | Bob3
6 | Sue4 | Win
6 | Sue1 | Win
1 | Sue1
6 | Bob1 | Win | Recording Bob: 42 | Bob2/Bob = 12/42 = 2/7 = 0.(285714)
6 | Sue1 | Win
6 | Sue1 | Win
4 | Sue1
1 | Bob1
2 | Sue2
3 | Bob2
2 | Sue3
5 | Bob3
3 | Sue4
5 | Bob4
5 | Sue5
4 | Bob5
4 | Sue6
2 | Bob6
1 | Sue7
2 | Bob7
4 | Sue8
6 | Bob8 | Win | Recording Bob: 43 | Bob2/Bob = 12/43 = 0.(279069767441860465116)
5 | Sue1
2 | Bob1
1 | Sue2
6 | Bob2 | Win | Recording Bob: 44 | Recording Bob2: 13 | Bob2/Bob = 13/44 = 0.29(54)
5 | Sue1
1 | Bob1
6 | Sue2 | Win
3 | Sue1
4 | Bob1
2 | Sue2
4 | Bob2
4 | Sue3
1 | Bob3
2 | Sue4
1 | Bob4
1 | Sue5
1 | Bob5
4 | Sue6
1 | Bob6
5 | Sue7
3 | Bob7
1 | Sue8
5 | Bob8
3 | Sue9
4 | Bob9
5 | Sue10
5 | Bob10
2 | Sue11
6 | Bob11 | Win | Recording Bob: 45 | Bob2/Bob = 13/45 = 0.2(8)
5 | Sue1
5 | Bob1
4 | Sue2
3 | Bob2
4 | Sue3
6 | Bob3 | Win | Recording Bob: 46 | Bob2/Bob = 13/46 = 0.2(8260869565217391304347)
3 | Sue1
3 | Bob1
3 | Sue2
2 | Bob2
5 | Sue3
6 | Bob3 | Win | Recording Bob: 47 | Bob2/Bob = 13/47 = 0.(2765957446808510638297872340425531914893617021)
6 | Sue1 | Win
4 | Sue1
3 | Bob1
3 | Sue2
1 | Bob2
2 | Sue3
1 | Bob3
1 | Sue4
3 | Bob4
5 | Sue5
4 | Bob5
6 | Sue6 | Win
4 | Sue1
1 | Bob1
1 | Sue2
5 | Bob2
5 | Sue3
2 | Bob3
4 | Sue4
4 | Bob4
5 | Sue5
4 | Bob5
2 | Sue6
2 | Bob6
5 | Sue7
3 | Bob7
6 | Sue8 | Win
1 | Sue1
6 | Bob1 | Win | Recording Bob: 48 | Bob2/Bob = 13/48 = 0.2708(3)
6 | Sue1 | Win
1 | Sue1
4 | Bob1
5 | Sue2
4 | Bob2
2 | Sue3
5 | Bob3
6 | Sue4 | Win
3 | Sue1
2 | Bob1
1 | Sue2
2 | Bob2
5 | Sue3
2 | Bob3
6 | Sue4 | Win
3 | Sue1
3 | Bob1
2 | Sue2
3 | Bob2
2 | Sue3
2 | Bob3
3 | Sue4
1 | Bob4
6 | Sue5 | Win
6 | Sue1 | Win
2 | Sue1
4 | Bob1
3 | Sue2
6 | Bob2 | Win | Recording Bob: 49 | Recording Bob2: 14 | Bob2/Bob = 14/49 = 2/7 = 0.(285714)
6 | Sue1 | Win
4 | Sue1
1 | Bob1
4 | Sue2
2 | Bob2
1 | Sue3
2 | Bob3
3 | Sue4
1 | Bob4
4 | Sue5
2 | Bob5
1 | Sue6
3 | Bob6
4 | Sue7
2 | Bob7
6 | Sue8 | Win
1 | Sue1
6 | Bob1 | Win | Recording Bob: 50 | Bob2/Bob = 14/50 = 7/25 = 0.28
5 | Sue1
5 | Bob1
1 | Sue2
5 | Bob2
5 | Sue3
4 | Bob3
1 | Sue4
4 | Bob4
1 | Sue5
2 | Bob5
2 | Sue6
5 | Bob6
1 | Sue7
3 | Bob7
6 | Sue8 | Win
3 | Sue1
2 | Bob1
3 | Sue2
6 | Bob2 | Win | Recording Bob: 51 | Recording Bob2: 15 | Bob2/Bob = 15/51 = 5/17 = 0.(2941176470588235)
6 | Sue1 | Win
4 | Sue1
4 | Bob1
6 | Sue2 | Win
1 | Sue1
6 | Bob1 | Win | Recording Bob: 52 | Bob2/Bob = 15/52 = 0.28(846153)
2 | Sue1
6 | Bob1 | Win | Recording Bob: 53 | Bob2/Bob = 15/53 = 0.(2830188679245)
5 | Sue1
4 | Bob1
2 | Sue2
5 | Bob2
4 | Sue3
6 | Bob3 | Win | Recording Bob: 54 | Bob2/Bob = 15/54 = 5/18 = 0.2(7)
3 | Sue1
4 | Bob1
1 | Sue2
4 | Bob2
4 | Sue3
6 | Bob3 | Win | Recording Bob: 55 | Bob2/Bob = 15/55 = 3/11 = 0.(27)
2 | Sue1
2 | Bob1
4 | Sue2
2 | Bob2
3 | Sue3
4 | Bob3
2 | Sue4
2 | Bob4
5 | Sue5
2 | Bob5
1 | Sue6
3 | Bob6
3 | Sue7
5 | Bob7
4 | Sue8
3 | Bob8
3 | Sue9
4 | Bob9
2 | Sue10
6 | Bob10 | Win | Recording Bob: 56 | Bob2/Bob = 15/56 = 0.267(857142)
6 | Sue1 | Win
6 | Sue1 | Win
3 | Sue1
5 | Bob1
3 | Sue2
4 | Bob2
6 | Sue3 | Win
6 | Sue1 | Win
1 | Sue1
5 | Bob1
6 | Sue2 | Win
3 | Sue1
6 | Bob1 | Win | Recording Bob: 57 | Bob2/Bob = 15/57 = 5/19 = 0.(263157894736842105)
3 | Sue1
2 | Bob1
6 | Sue2 | Win
2 | Sue1
6 | Bob1 | Win | Recording Bob: 58 | Bob2/Bob = 15/58 = 0.2(5862068965517241379310344827)
5 | Sue1
1 | Bob1
6 | Sue2 | Win
6 | Sue1 | Win
5 | Sue1
5 | Bob1
1 | Sue2
1 | Bob2
3 | Sue3
4 | Bob3
6 | Sue4 | Win
4 | Sue1
2 | Bob1
6 | Sue2 | Win
5 | Sue1
3 | Bob1
4 | Sue2
1 | Bob2
6 | Sue3 | Win
3 | Sue1
3 | Bob1
3 | Sue2
5 | Bob2
3 | Sue3
4 | Bob3
4 | Sue4
3 | Bob4
6 | Sue5 | Win
5 | Sue1
3 | Bob1
5 | Sue2
4 | Bob2
2 | Sue3
6 | Bob3 | Win | Recording Bob: 59 | Bob2/Bob = 15/59 = 0.(2542372881355932203389830508474576271186440677966101694915)
4 | Sue1
6 | Bob1 | Win | Recording Bob: 60 | Bob2/Bob = 15/60 = 1/4 = 0.25
3 | Sue1
2 | Bob1
2 | Sue2
2 | Bob2
2 | Sue3
2 | Bob3
4 | Sue4
6 | Bob4 | Win | Recording Bob: 61 | Bob2/Bob = 15/61 = 0.(245901639344262295081967213114754098360655737704918032786885)
1 | Sue1
1 | Bob1
6 | Sue2 | Win
5 | Sue1
5 | Bob1
1 | Sue2
6 | Bob2 | Win | Recording Bob: 62 | Recording Bob2: 16 | Bob2/Bob = 16/62 = 8/31 = 0.(258064516129032)
4 | Sue1
6 | Bob1 | Win | Recording Bob: 63 | Bob2/Bob = 16/63 = 0.(253968)
1 | Sue1
1 | Bob1
3 | Sue2
6 | Bob2 | Win | Recording Bob: 64 | Recording Bob2: 17 | Bob2/Bob = 17/64 = 0.265625
5 | Sue1
1 | Bob1
6 | Sue2 | Win
4 | Sue1
2 | Bob1
4 | Sue2
1 | Bob2
1 | Sue3
5 | Bob3
4 | Sue4
5 | Bob4
2 | Sue5
4 | Bob5
4 | Sue6
3 | Bob6
1 | Sue7
6 | Bob7 | Win | Recording Bob: 65 | Bob2/Bob = 17/65 = 0.2(615384)
3 | Sue1
2 | Bob1
2 | Sue2
2 | Bob2
5 | Sue3
1 | Bob3
3 | Sue4
4 | Bob4
3 | Sue5
3 | Bob5
1 | Sue6
3 | Bob6
2 | Sue7
5 | Bob7
6 | Sue8 | Win
3 | Sue1
3 | Bob1
1 | Sue2
1 | Bob2
4 | Sue3
6 | Bob3 | Win | Recording Bob: 66 | Bob2/Bob = 17/66 = 0.2(57)
4 | Sue1
6 | Bob1 | Win | Recording Bob: 67 | Bob2/Bob = 17/67 = 0.(253731343283582089552238805970149)
2 | Sue1
4 | Bob1
3 | Sue2
6 | Bob2 | Win | Recording Bob: 68 | Recording Bob2: 18 | Bob2/Bob = 18/68 = 9/34 = 0.2(6470588235294117)
1 | Sue1
6 | Bob1 | Win | Recording Bob: 69 | Bob2/Bob = 18/69 = 6/23 = 0.(2608695652173913043478)
3 | Sue1
5 | Bob1
1 | Sue2
2 | Bob2
3 | Sue3
3 | Bob3
5 | Sue4
3 | Bob4
2 | Sue5
3 | Bob5
5 | Sue6
2 | Bob6
5 | Sue7
1 | Bob7
5 | Sue8
3 | Bob8
2 | Sue9
1 | Bob9
4 | Sue10
4 | Bob10
3 | Sue11
1 | Bob11
2 | Sue12
1 | Bob12
4 | Sue13
1 | Bob13
2 | Sue14
2 | Bob14
4 | Sue15
6 | Bob15 | Win | Recording Bob: 70 | Bob2/Bob = 18/70 = 9/35 = 0.2(571428)
1 | Sue1
4 | Bob1
5 | Sue2
6 | Bob2 | Win | Recording Bob: 71 | Recording Bob2: 19 | Bob2/Bob = 19/71 = 0.(26760563380281690140845070422535211)
5 | Sue1
6 | Bob1 | Win | Recording Bob: 72 | Bob2/Bob = 19/72 = 0.263(8)
3 | Sue1
6 | Bob1 | Win | Recording Bob: 73 | Bob2/Bob = 19/73 = 0.(26027397)
3 | Sue1
3 | Bob1
1 | Sue2
3 | Bob2
2 | Sue3
5 | Bob3
3 | Sue4
4 | Bob4
4 | Sue5
5 | Bob5
4 | Sue6
6 | Bob6 | Win | Recording Bob: 74 | Bob2/Bob = 19/74 = 0.2(567)
4 | Sue1
1 | Bob1
4 | Sue2
4 | Bob2
1 | Sue3
5 | Bob3
5 | Sue4
5 | Bob4
6 | Sue5 | Win
6 | Sue1 | Win
2 | Sue1
2 | Bob1
5 | Sue2
4 | Bob2
3 | Sue3
3 | Bob3
5 | Sue4
3 | Bob4
5 | Sue5
5 | Bob5
5 | Sue6
3 | Bob6
4 | Sue7
2 | Bob7
3 | Sue8
6 | Bob8 | Win | Recording Bob: 75 | Bob2/Bob = 19/75 = 0.25(3)
5 | Sue1
5 | Bob1
2 | Sue2
2 | Bob2
4 | Sue3
5 | Bob3
3 | Sue4
2 | Bob4
2 | Sue5
5 | Bob5
3 | Sue6
4 | Bob6
6 | Sue7 | Win
2 | Sue1
4 | Bob1
6 | Sue2 | Win
2 | Sue1
4 | Bob1
6 | Sue2 | Win
5 | Sue1
2 | Bob1
5 | Sue2
1 | Bob2
1 | Sue3
4 | Bob3
3 | Sue4
5 | Bob4
3 | Sue5
3 | Bob5
1 | Sue6
4 | Bob6
5 | Sue7
6 | Bob7 | Win | Recording Bob: 76 | Bob2/Bob = 19/76 = 1/4 = 0.25
4 | Sue1
3 | Bob1
2 | Sue2
1 | Bob2
2 | Sue3
5 | Bob3
3 | Sue4
4 | Bob4
6 | Sue5 | Win
5 | Sue1
1 | Bob1
1 | Sue2
5 | Bob2
6 | Sue3 | Win
4 | Sue1
5 | Bob1
5 | Sue2
1 | Bob2
1 | Sue3
4 | Bob3
1 | Sue4
6 | Bob4 | Win | Recording Bob: 77 | Bob2/Bob = 19/77 = 0.(246753)
5 | Sue1
1 | Bob1
5 | Sue2
3 | Bob2
5 | Sue3
6 | Bob3 | Win | Recording Bob: 78 | Bob2/Bob = 19/78 = 0.2(435897)
6 | Sue1 | Win
5 | Sue1
6 | Bob1 | Win | Recording Bob: 79 | Bob2/Bob = 19/79 = 0.(2405063291139)
6 | Sue1 | Win
2 | Sue1
5 | Bob1
5 | Sue2
6 | Bob2 | Win | Recording Bob: 80 | Recording Bob2: 20 | Bob2/Bob = 20/80 = 1/4 = 0.25
4 | Sue1
6 | Bob1 | Win | Recording Bob: 81 | Bob2/Bob = 20/81 = 0.(246913580)
5 | Sue1
1 | Bob1
6 | Sue2 | Win
5 | Sue1
3 | Bob1
1 | Sue2
5 | Bob2
3 | Sue3
6 | Bob3 | Win | Recording Bob: 82 | Bob2/Bob = 20/82 = 10/41 = 0.(24390)
3 | Sue1
5 | Bob1
4 | Sue2
4 | Bob2
5 | Sue3
2 | Bob3
1 | Sue4
1 | Bob4
2 | Sue5
1 | Bob5
6 | Sue6 | Win
6 | Sue1 | Win
4 | Sue1
1 | Bob1
2 | Sue2
1 | Bob2
2 | Sue3
4 | Bob3
4 | Sue4
4 | Bob4
1 | Sue5
2 | Bob5
5 | Sue6
2 | Bob6
2 | Sue7
5 | Bob7
5 | Sue8
1 | Bob8
6 | Sue9 | Win
1 | Sue1
5 | Bob1
2 | Sue2
3 | Bob2
6 | Sue3 | Win
3 | Sue1
5 | Bob1
5 | Sue2
1 | Bob2
4 | Sue3
5 | Bob3
2 | Sue4
4 | Bob4
3 | Sue5
4 | Bob5
3 | Sue6
Final Bob2/Bob = 20/82 = 10/41 = 0.(24390)
Pretty close to expected (by some of us).
ˌɑrməˈɡɛˌtrɑn

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rumpole
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Post by rumpole » Wed Mar 18, 2009 6:33 pm

I obviously cannot understand the question even when jonathan tried to explain it.
Writing code is easy. Finishing is hard.

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ed
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Post by ed » Wed Mar 18, 2009 8:37 pm

rumpole wrote:I obviously cannot understand the question even when jonathan tried to explain it.
It's worth reading through the comments on the original link
My favourite explaination of the question was this one
Another restatement of the problem for those who don’t get it:

“Bob and Sue played exactly one game with a fair in a closed room (but with a video camera to verify the result). They come out and report that Bob won the game (he rolled a 6 before Sue). Now Alice (who did not see the game) pipes up: “I will bet $10 against your $50 that won it on his 2nd turn! Any takers?” (This means if Bob won on his 2nd turn, then you pays $40, otherwise she pays you $10).

Please assume that there is no cheating, and Alice has no information that you do not have.

Is it a good bet to take? At exactly what payout is it an even bet?

If you believe the probability is 1/6 or 5/36 or 125/1296, you will think this is a good bet, because although you wager 5 times as much, you are at least 5 times as likely to win. If the probability is 1/6, then you win 5 times out of 6, while Alice wins 1 time out of 6, so 10:50 is an even bet. If the odds are 125/1296, they you are more than 9 times as likely to win as Alice, but you are wagering only 5 times as much!

Alice must have miscalculated! What a rube! Take the bet!

Alice, however, has calculated the probability as 275/1296, approximately 21%. Alice thus that you are slightly less than 4 times as likely to win (you win about 79% of the time, and Alice wins about 21% of the time), but you would be risking 5 times as much money.

Alice is trolling for suckers! Are you going to bite?

So, with money on the line, what is the true probability?

Hint: If you want to take the bet at $10 to $50, I will be happy to oblige you!
The trouble for me was that once I fully understood the question it became clear I didn't have the maths skills to get to the solution.

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Lackadaisical
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Post by Lackadaisical » Wed Mar 18, 2009 11:49 pm

I suppose this is overkill, but it is said pictures say OVER 9000 words
Image
question: how much of the dark grey part is striped green

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Re: Nice puzzle

Post by writingsama » Fri Apr 03, 2009 8:59 am

I had to register her just to post this. Sigh.

You're all wrong, because the puzzle is flawed, or intentionally much more deceptive than anyone anywhere seems to get.

Even the people who head down the clever, but incorrect road to arrive at 21.21% haven't taken into account the fact that there are an infinite number of cases in which neither one ever, ever rolls a 6, for all of eternity. Nowhere in the rules was it stated that eventually someone HAS to roll a 6 in general play and end the game. It didn't even state that the 6-sided die had a side denoting '6', nor did it state if it could move through an infinite number of iterations before one finally rolls a 6, but that's just getting into set theory pedantry that's unnecessary. Games can be infinite and never resolve, or infinite AND resolve, and you didn't search "all possible games" since you didn't search infinity. Except that in this SPECIFIC instance, it was stated that Bob *DID* eventually roll a 6. Sue did not, her odds of ever doing so are 0 over the whole of the game space, and his are 1, even over an infinitely large game space. The odds that it was on his second roll are uncomputable because of this basic fact: we don't know how long the game was. The odds are either 0 or 1, but we don't know. This problem is not possible to solve. You could say the odds it happened on the 2nd roll are infinitely small, I suppose. I.e. 0. This presents a paradox, since the puzzle explicitly stated that he did in fact roll a 6, eventually. This means the puzzle is actually a paradox with no resolution.

Or is it? Let’s look at it another way. The only question we *can* answer is what is the probability that he rolled *a* 6 on his second turn. That probability is 1/6. This is equivalent to asking *the* 6, because it is game-ending; in an infinite number of games which Sue does not roll a 6 before him, in which he does eventually roll a 6 and the game terminates, he will roll a 6 on his second turn with a probability of 1/6. No more rolls are made, and the sequence is made non-infinite, and thus computable. Thus, the probability that he rolled *the* 6 on his second roll is 1/6, because that’s the probability he will roll *a* 6 on *any* roll. This is seriously basic computability and probability, messed up by attempts to be clever that just aren’t clever enough, because of the deceptive nature of the puzzle. Sorry guys.

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Lackadaisical
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Re: Nice puzzle

Post by Lackadaisical » Fri Apr 03, 2009 9:45 am

But isn't the sum of all odds that the game lasts infinitively:

lim n-> ∞ (5/6)^n = 0

I'm not much of a mathematician, but I don't think having an infinite large game space necessarily means there is also an infinitely large probability space.

Total prob = 1/6 * sum(n=0 -> ∞) (5/6)^n = 1/6 * 1/(1-5/6) = 1

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Re: Nice puzzle

Post by Z-Man » Fri Apr 03, 2009 11:02 am

Lackadaisical wrote:But isn't the sum of all odds that the game lasts infinitively:

lim n-> ∞ (5/6)^n = 0
Yes. It's possible that the game lasts forever, but infinitely improbable. It's a NULL-event that has no influence on the answer.

writingsama: Just... no. You are right that the question needs interpretation, but wrong claiming our interpretation does not make sense. It is perfectly possible to work with experiments that possibly last forever, and it's perfectly possible to calculate probabilities of a) bob winning b) sue winning c) the game lasting forever d) bob winning on his second throw e) combining a) and b) to get the answer.

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Re: Nice puzzle

Post by Word » Fri Apr 03, 2009 12:52 pm

I have never seen dice that look like this:

Image

If we are talking about dice I think everyone thinks of a cube that has the numbers 1, 2, 3, 4 , 5 and 6 on its side. If it isn't a normal die although it belongs to the puzzle it should be part of the given information.
You can solve an exercise like "1+1=2" but this is more like "1+?=?..., oh and the + stands for - "!

alea iacta est.

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Jonathan
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Re: Nice puzzle

Post by Jonathan » Fri Apr 03, 2009 6:05 pm

Convergence wins. See it like this. On the first roll, there's a 1/6 prob of winning, 5/6 of continuing. You can visualize that 5/6 as containing the next roll, which in turn contains the third and so on. Note how it never grows out of the original space. Now you can add all the 1/6 parts you like (as seen in the 'global' space), and get arbitrarily close to 1. That puts strong bounds on the influence of later turns. Even if you don't see how we did take it into account, you should get this.
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