Is the target number completely random?!
- Dmitry Goretsky
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Is the target number completely random?!
Is the target number completely random?! Why do I ask this? Because I don't know the target that haven't a solution.
I'm a probability guru, so please PM or e-mail me if you need some help about probabilities.
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
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Re: Is the target number completely random?!
It is random. CECIL (the generator yoke) gives a random target. All Rachel has to do is push the button. (And work it out of course!)
It does give unsolvable (is that a word?) solutions, but that is quite rare and any that have eluded her are usually solved by the brains of our Countdown Forumites!
It does give unsolvable (is that a word?) solutions, but that is quite rare and any that have eluded her are usually solved by the brains of our Countdown Forumites!
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Re: Is the target number completely random?!
With alternative solutions provided by Mark K.Eoin Monaghan wrote:It is random. CECIL (the generator yoke) gives a random target. All Rachel has to do is push the button. (And work it out of course!)
It does give unsolvable (is that a word?) solutions, but that is quite rare and any that have eluded her are usually solved by the brains of our Countdown Forumites!
GR MSL GNDT MSS NGVWL SRND NNLYC NNCT
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Re: Is the target number completely random?!
My first game had these numbers for the third numbers game.Dmitry Goretsky wrote:Is the target number completely random?! Why do I ask this? Because I don't know the target that haven't a solution.
2, 2, 50, 75, 100, 25. Target: 720.
721 is as close as you can get, there are some six small solutions where it is impossible to get within a hundred of some solutions.
Re: Is the target number completely random?!
I fear the day when 1, 1, 2, 2, 3, 3 happens.David O'Donnell wrote:
...there are some six small solutions where it is impossible to get within a hundred of some solutions.
- Ray Folwell
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Re: Is the target number completely random?!
I estimate that if 6 small was chosen once per game, this would happen about once every 150 years on average.Jordan F wrote: I fear the day when 1, 1, 2, 2, 3, 3 happens.
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Re: Is the target number completely random?!
No, it's completely pseudo-random.
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Re: Is the target number completely random?!
The number of different combinations of 6 numbers from 20 is given by 20 ! / (14 ! x 6 !) or 38,760.Ray Folwell wrote:I estimate that if 6 small numbers were chosen once per game, this would happen about once every 150 years on average.Jordan F wrote: I fear the day when 1, 1, 2, 2, 3, 3 happens.
Combination 1, 1, 2, 2, 3, 3 is one of them, so the odds of this occurring are 38,759 to 1 against.
This means that if 6 small numbers were chosen once per show, the probability would be 1 in 7,752 in every week. This would work out as once int 172 years, assuming 45 weeks or 225 shows per year.
(Assuming 52 weeks or 260 episodes per year, we get a 'once in 149 years' result, like Ray's.)
The exclamation marks in 20 ! , 14 ! and 6 ! are not expressions of surprise. They are factorials, defined as follows:
1 ! = 1
2 ! = 2 x 1 = 2
3 ! = 3 x 2 x 1 = 6
4 ! = 4 x 3 x 2 x 1 = 24
and so on ....
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Re: Is the target number completely random?!
Just to add to Mark's post, the x isn't him offering his affection in the form of (several!) kisses, but in fact is a symbol meaning 'multiply'. It's a bit like a short-hand for lots of addition, rather than writing out (say) 3 + 3 + 3 + 3 + 3, you can instead just write 3 x 5.
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Re: Is the target number completely random?!
lol !Michael Wallace wrote:Just to add to Mark's post, the x isn't him offering his affection in the form of (several!) kisses, but in fact is a symbol meaning 'multiply'. It's a bit like a short-hand for lots of addition, rather than writing out (say) 3 + 3 + 3 + 3 + 3, you can instead just write 3 x 5.
Further to my first post on combinations, it must be remembered that 1, 1, 2, 2, 3, 3 can only be made in one way, so the probability of it occurring on a '6 small' game is 1 in 38760.
A group like 1, 1, 2, 2, 3, 4 is easier to achieve, as there are two 3s and two 4s in the small number pack.
Combining these options means that 1, 1, 2, 2, 3, 4 is four times easier to obtain, i.e. a probability of 1 in 9690. This is because we aren't bothered as to which of the two 3s or 4s we're after.
An 'all-different' combination like 1, 2, 4, 5, 7, 8 is similarly 64 times easier, giving an 'easier' probability of 1 in 606.
Re: Is the target number completely random?!
There are only two of each small number in the pack. Don't know if you knew that, but I think it might require a rejig of the calculations.
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Re: Is the target number completely random?!
I think the calculations are correct - 2 of each number 1-10 = 20 in total.JackHurst wrote:There are only two of each small number in the pack. Don't know if you knew that, but I think it might require a rejig of the calculations.
It easier to think about if you imagine that one set of small numbers is blue and the other red - then there is only one way to get 1,1,2,2,3,3 i.e. 1R,1B,2R,2B,3R,3B but 4 ways to get 1,1,2,2,3,4 (3R,4R; 3R,4B; 3B,4R; 3B,4B).
Do we have any statistics on how often contestants choose 6 small or any of the other combinations ?
- Dmitry Goretsky
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Re: Is the target number completely random?!
That's ABSOLUTELY RIGHT! I just recognized it when I read a "colored tile' message.Mark Kudlowski wrote:The number of different combinations of 6 numbers from 20 is given by 20 ! / (14 ! x 6 !) or 38,760.
Combination 1, 1, 2, 2, 3, 3 is one of them, so the odds of this occurring are 38,759 to 1 against.
Last edited by Dmitry Goretsky on Fri Jul 02, 2010 8:11 pm, edited 2 times in total.
I'm a probability guru, so please PM or e-mail me if you need some help about probabilities.
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Re: Is the target number completely random?!
Probability genius my hairy pods.Dmitry Goretsky wrote:You forgot to divide this by (2!)^3! This is because there are two 1s, two 2s and two 3s. So the probability of THIS occuring is 1/(C(20,6)/((2!)^3))=1/4,845Mark Kudlowski wrote:The number of different combinations of 6 numbers from 20 is given by 20 ! / (14 ! x 6 !) or 38,760.
Combination 1, 1, 2, 2, 3, 3 is one of them, so the odds of this occurring are 38,759 to 1 against.
Last edited by Jon Corby on Fri Jul 02, 2010 8:04 pm, edited 1 time in total.
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Re: Is the target number completely random?!
I think you are probability not a probably genius.Dmitry Goretsky wrote:You forgot to divide this by (2!)^3! This is because there are two 1s, two 2s and two 3s. So the probability of THIS occuring is 1/(C(20,6)/((2!)^3))=1/4,845Mark Kudlowski wrote:The number of different combinations of 6 numbers from 20 is given by 20 ! / (14 ! x 6 !) or 38,760.
Combination 1, 1, 2, 2, 3, 3 is one of them, so the odds of this occurring are 38,759 to 1 against.
- Dmitry Goretsky
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Re: Is the target number completely random?!
Sorry, I was wrong!Michael Wallace wrote:I think you are probability not a probably genius.Dmitry Goretsky wrote:You forgot to divide this by (2!)^3! This is because there are two 1s, two 2s and two 3s. So the probability of THIS occuring is 1/(C(20,6)/((2!)^3))=1/4,845Mark Kudlowski wrote:The number of different combinations of 6 numbers from 20 is given by 20 ! / (14 ! x 6 !) or 38,760.
Combination 1, 1, 2, 2, 3, 3 is one of them, so the odds of this occurring are 38,759 to 1 against.
I'm a probability guru, so please PM or e-mail me if you need some help about probabilities.
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
- Dmitry Goretsky
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Re: Is the target number completely random?!
Sorry, I was wrong!Jon Corby wrote:Probability genius my hairy pods.Dmitry Goretsky wrote:You forgot to divide this by (2!)^3! This is because there are two 1s, two 2s and two 3s. So the probability of THIS occuring is 1/(C(20,6)/((2!)^3))=1/4,845Mark Kudlowski wrote:The number of different combinations of 6 numbers from 20 is given by 20 ! / (14 ! x 6 !) or 38,760.
Combination 1, 1, 2, 2, 3, 3 is one of them, so the odds of this occurring are 38,759 to 1 against.
I'm a probability guru, so please PM or e-mail me if you need some help about probabilities.
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Re: Is the target number completely random?!
About being a probability genius? Yeah, we guessedDmitry Goretsky wrote: Sorry, I was wrong!
- Dmitry Goretsky
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Re: Is the target number completely random?!
No, only about THIS probability! I just recognized it when I read a "colored tile' message. So PM me if you have any problems with probabilities. Genius never makes an error twiceJon Corby wrote:About being a probability genius? Yeah, we guessedDmitry Goretsky wrote: Sorry, I was wrong!
I'm a probability guru, so please PM or e-mail me if you need some help about probabilities.
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
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Re: Is the target number completely random?!
Dmitry Goretsky wrote:Sorry, I was wrong!
I like the double post. I presume it's some sort of reference to getting tails in the Sleeping Beauty Problem.Dmitry Goretsky wrote:Sorry, I was wrong!
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Re: Is the target number completely random?!
Maybe the second "I was wrong" was referring to the first one. So maybe he's saying he wasn't wrong in the first place.Gavin Chipper wrote:Dmitry Goretsky wrote:Sorry, I was wrong!I like the double post. I presume it's some sort of reference to getting tails in the Sleeping Beauty Problem.Dmitry Goretsky wrote:Sorry, I was wrong!
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Re: Is the target number completely random?!
No, I said "Sorry, I was wrong!" to each of the two usersHoward Somerset wrote:Maybe the second "I was wrong" was referring to the first one. So maybe he's saying he wasn't wrong in the first place.Gavin Chipper wrote:Dmitry Goretsky wrote:Sorry, I was wrong!I like the double post. I presume it's some sort of reference to getting tails in the Sleeping Beauty Problem.Dmitry Goretsky wrote:Sorry, I was wrong!
I'm a probability guru, so please PM or e-mail me if you need some help about probabilities.
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
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Re: Is the target number completely random?!
Since it's very rare for things such as this to have a probability of exactly 0 or exactly 1, what do you rate is the probability that you really are a probability genius, in view of the fact that you've admitted to getting things wrong earlier in this thread?Dmitry Goretsky wrote:I'm a probability genius
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Re: Is the target number completely random?!
0.9Howard Somerset wrote:Since it's very rare for things such as this to have a probability of exactly 0 or exactly 1, what do you rate is the probability that you really are a probability genius, in view of the fact that you've admitted to getting things wrong earlier in this thread?Dmitry Goretsky wrote:I'm a probability genius
I'm a probability guru, so please PM or e-mail me if you need some help about probabilities.
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
Truly yours,
Dmitry Goretsky <0668964628@mail.ru>
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Re: Is the target number completely random?!
So do I take it that you think that there's a 10% chance that you're wrong when you give an answer of 0.9?Dmitry Goretsky wrote:0.9Howard Somerset wrote:Since it's very rare for things such as this to have a probability of exactly 0 or exactly 1, what do you rate is the probability that you really are a probability genius, in view of the fact that you've admitted to getting things wrong earlier in this thread?Dmitry Goretsky wrote:I'm a probability genius
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Re: Is the target number completely random?!
Meh, I'd've given the probability of that claim being shot down in flames as 1...Howard Somerset wrote:Since it's very rare for things such as this to have a probability of exactly 0 or exactly 1,
Lowering the averages since 2009
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Re: Is the target number completely random?!
You bastard! I thought I'd pulled Wait, did I just inadvertently multiply your insult?Michael Wallace wrote:Just to add to Mark's post, the x isn't him offering his affection in the form of (several!) kisses, but in fact is a symbol meaning 'multiply'. It's a bit like a short-hand for lots of addition, rather than writing out (say) 3 + 3 + 3 + 3 + 3, you can instead just write 3 x 5.
xxx < Kisses for you Raccoon just for putting me straight, and don't tell CF
Lowering the averages since 2009