Ask Graeme?

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Matt Morrison
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Re: Ask Graeme?

Post by Matt Morrison » Fri Mar 08, 2013 5:07 pm

I'll post something inside you.

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Re: Ask Graeme?

Post by JackHurst » Fri Mar 08, 2013 5:11 pm

I can confirm that the buzzers are activated once Nick presses the button to start the clock. This means you can buzz whenever the clock is going (so in any round), but not when the clock isnt going.

Whilst waiting to play our final, Conor and I asked the floor manager (Jay) about this, and he started the clock for us and let us mess around with the buzzers. It was great fun.

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Re: Ask Graeme?

Post by Dave Preece » Fri Mar 08, 2013 5:51 pm

JackHurst wrote:I can confirm that the buzzers are activated once Nick presses the button to start the clock. This means you can buzz whenever the clock is going (so in any round), but not when the clock isnt going.

Whilst waiting to play our final, Conor and I asked the floor manager (Jay) about this, and he started the clock for us and let us mess around with the buzzers. It was great fun.
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Graeme Cole
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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 09, 2013 1:13 am

Chris Marshall wrote:Is it possible to get a letter distribution frequency for each letter over the data you have?
The letter distribution has changed quite a few times over the years. To start with, let's look at series 66 only.

The frequency with which each letter appeared in that series is as follows.

Code: Select all

VOWELS
   A 1081
   E 1444
   I 943
   O 963
   U 506

CONSONANTS
   B 178
   C 272
   D 531
   F 183
   G 348
   H 186
   J  91
   K  98
   L 445
   M 351
   N 718
   P 359
   Q  86
   R 781
   S 795
   T 799
   V 175
   W 185
   X  91
   Y  90
   Z  82
We don't know exactly how many letters are in the vowel and consonant piles at the start of the game. However, if we can assume the distribution used for a game has exactly one of each of Q, X, Z and J, that helps us. They came out an average of 88.5 times, so let's say that for series 66, a letter that comes out 88.5 times in the series appears exactly once in the pack, and that's the baseline from which we can scale all the other frequencies. That gives us this:

Code: Select all

   B  2.0
   C  3.1
   D  6.0
   F  2.1
   G  3.9
   H  2.1
   J  1.0
   K  1.1
   L  5.0
   M  4.0
   N  8.1
   P  4.1
   Q  1.0
   R  8.8
   S  9.0
   T  9.0
   V  2.0
   W  2.1
   X  1.0
   Y  1.0
   Z  0.9
These all look to be near a whole number, which is a good sign. So our best guess at the consonant distribution used in series 66 is this:

Code: Select all

   B  2
   C  3
   D  6
   F  2
   G  4
   H  2
   J  1
   K  1
   L  5
   M  4
   N  8
   P  4
   Q  1
   R  9
   S  9
   T  9
   V  2
   W  2
   X  1
   Y  1
   Z  1
Applying this same method to all the other series since the introduction of the 15-round format, and assuming they've only ever had one Q, Z, X and J in the pack, the most likely distributions for each series are as follows:

Code: Select all

SERIES   B  C  D  F  G  H  J  K  L  M  N  P  Q  R  S  T  V  W  X  Y  Z
   46    2  4  8  3  6  3  1  1  7  4  7  4  1 10 10 10  2  1  1  2  1
   47    2  5  8  4  6  3  1  1  8  6  7  5  1 10 10 10  2  1  1  1  1
   48    1  5  7  3  6  2  1  1  7  6  7  5  1 10 10 10  2  1  1  1  1
   49    2  4  7  2  4  3  1  1  6  5  7  5  1  9  9  9  1  1  1  1  1
   50    2  5  7  2  4  2  1  1  7  6  7  5  1  9  9  9  1  1  1  1  1
   51    4  7 10  4  5  4  1  2 10  9 10  7  1 13 13 13  2  2  1  2  1
   52    3  6  9  3  5  3  1  2  9  7  9  6  1 12 12 12  2  2  1  2  1
   53    2  4  7  2  4  2  1  1  6  5  9  5  1 10 10 10  1  1  1  1  1
   54    2  3  6  2  3  2  1  1  5  4  8  4  1  9  9  9  1  1  1  1  1
   55    2  3  6  2  3  2  1  1  5  4  8  4  1  9  9  9  1  1  1  1  1
   56    2  3  6  2  3  2  1  1  5  4  8  4  1  9  9  9  1  1  1  1  1
   57    2  3  6  2  3  2  1  1  5  4  8  4  1  9  9  9  1  1  1  1  1
   58    2  3  6  2  3  2  1  1  5  4  8  4  1  9 10  9  1  1  1  1  1
   59    2  3  6  2  3  2  1  1  5  4  8  4  1  9  9  9  1  1  1  1  1
   60    2  3  6  2  3  2  1  1  5  4  8  4  1  9  9  9  1  1  1  1  1
   61    2  3  6  2  3  2  1  1  5  4  8  4  1  9  9  9  1  1  1  1  1
   62    2  4  7  2  4  2  1  1  6  4  9  4  1 10 10 10  2  2  1  2  1
   63    2  3  7  2  4  2  1  1  6  4  9  4  1 10 10 10  2  2  1  1  1
   64    2  3  7  2  4  2  1  1  6  5  9  5  1 10 10 10  2  2  1  1  1
   65    2  3  6  2  4  2  1  1  5  4  8  4  1  9  9  9  2  2  1  1  1
   66    2  3  6  2  4  2  1  1  5  4  8  4  1  9  9  9  2  2  1  1  1
   67    2  4  7  2  4  2  1  1  5  4  8  4  1 10 10 11  2  2  1  1  1
So it looks like a second V and W were added to the pile from series 62 onwards. It's possible they sneaked an extra Y into the pile for much/all of that series as well, but took it out afterwards.

The vowel pile is a bit more tricky, as we don't have any known data points to work with, only their frequencies relative to each other. We do know that there have to be at least 55 vowels in the pile at the start of the game (in case both contestants are Jonathan Rawlinson), but without an exact count it's difficult to reach details of the actual distribution. So it's much more finger-in-the-air.

My rough guess, based on trying numbers and seeing if they give counts roughly near whole numbers, are that as of series 66 there were about 15 As, 20 Es, 13 Is, 13 Os and 7 Us.

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Re: Ask Graeme?

Post by Mark Ivey » Sat Mar 09, 2013 2:58 am

JackHurst wrote:I can confirm that the buzzers are activated once Nick presses the button to start the clock. This means you can buzz whenever the clock is going (so in any round), but not when the clock isnt going.

Whilst waiting to play our final, Conor and I asked the floor manager (Jay) about this, and he started the clock for us and let us mess around with the buzzers. It was great fun.
Remember the Gotcha where 'Richard Max' buzzed in on one of later rounds claiming he thought it was the conundrum... I'm surprised to learn that could actually happen. What's to stop someone buzzing in half-way through for any reason ("I can only find four letter words, can we start again?" or "I'm going to be sick!" for instance)?

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Re: Ask Graeme?

Post by Clive Brooker » Sat Mar 09, 2013 6:55 am

As a cross-check, I tried finding the maximum number of times each letter was seen in a game in series 66. Gratifyingly, the answers for consonants were identical to Graeme's which suggests stability in the pack if nothing else.

For vowels I get answers that are slightly lower, which I think makes intuitive sense. Taken at face value, our numbers imply that there were never fewer than 3 As, 3 Es, 2 Is, plus a single O and U left in the pack at the end of a game.

The one concern I have with Graeme's numbers is the suggestion that there were 2 Ks in series 51 and 52. In the 15-round era we have only seen 2 Ks 8 times, 5 during a 2-week period in series 46, and the other 3 in a single week in series 49. If there were 2 Ks available for a prolonged period at any other time I think it's stretching credibility to suggest they wouldn't both have been seen in most of the games during that period.

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 09, 2013 11:57 am

Clive Brooker wrote:The one concern I have with Graeme's numbers is the suggestion that there were 2 Ks in series 51 and 52. In the 15-round era we have only seen 2 Ks 8 times, 5 during a 2-week period in series 46, and the other 3 in a single week in series 49. If there were 2 Ks available for a prolonged period at any other time I think it's stretching credibility to suggest they wouldn't both have been seen in most of the games during that period.
True. I've had a look at series 51 and 52 and I don't see any evidence that there was more than one K. However, the frequency of K for those two series was still significantly greater than the frequency of Q, X, Z and J.

Code: Select all

SERIES     A    E    I    O    U   B   C   D   F   G   H   J   K   L   M   N   P   Q   R   S   T   V   W   X   Y   Z
   49    876 1173  833  802  355 170 353 523 168 284 197  70  91 511 424 520 357  68 695 691 699  88  87  87  84  90
   50    880 1173  848  827  328 184 340 508 182 263 170  69  98 504 424 517 352  64 691 667 676  84  92  85  91  80
   51    964 1282  908  904  401 214 396 575 204 298 215  55 102 569 487 572 388  52 765 759 748  99 106  61 103  59
   52    961 1295  909  850  406 217 372 556 200 295 188  64 105 532 460 584 372  56 747 726 756 101 110  67  97  62
   53   1000 1476  926  877  354 195 295 575 195 300 193  92  99 492 406 776 395  80 862 861 869  99  98  83 103  80
Looking at the frequencies for nearby series, it seems that K doesn't appear much more frequently than usual, but Q, J, X and Z suffer a significant drop in frequency. So a more likely explanation is that there was still only one K, but for some games one or more of Q, J, X and Z were removed completely.

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Re: Ask Graeme?

Post by Dave Preece » Sat Mar 09, 2013 1:54 pm

Is there a link between some of the great players playing in final stages to the distribution of 'nice' letters for the production to ensure big scores for pulicity purposes?

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Re: Ask Graeme?

Post by Thomas Carey » Sat Mar 09, 2013 1:55 pm

Graeme wrote:
To start with, let's look at series 66 only.

Code: Select all

   B  2
   C  3
   D  6
   F  2
   G  4
   H  2
   J  1
   K  1
   L  5
   M  4
   N  8
   P  4
   Q  1
   R  9
   S  9
   T  9
   V  2
   W  2
   X  1
   Y  1
   Z  1
The Countdown board game I have (the new flashy blue Jeff and Rachel one which I think is the newest edition) uses that, but with an extra B and F (3 of each).
In that, the vowel distribution is:

A 15
E 21
I 13
O 13
U 8
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Re: Ask Graeme?

Post by Jack Worsley » Sat Mar 09, 2013 2:17 pm

Great work both but I really don't think there are that many U's. I'd say six at the most, possibly even five. How many games in Series 66 saw more than five U's appear?

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Re: Ask Graeme?

Post by David Williams » Sat Mar 09, 2013 2:52 pm

Maybe ten years ago there was a suggestion that for a couple of months one of the letters (possibly J) never appeared once, suggesting it had been mislaid. Is this true, and if so was the length of absence statistically significant?

What evidence is there that letters are manually sorted, rather than shuffled?

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Re: Ask Graeme?

Post by Gavin Chipper » Sat Mar 09, 2013 3:03 pm

I remember the thing about the Js. With the vowels you could look at how the probability of each vowel changes depending on what has come up already to work out actual numbers.

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Re: Ask Graeme?

Post by Johnny Canuck » Sat Mar 09, 2013 3:21 pm

How many times has the same target come up in two consecutive numbers rounds? And in any of those instances, has it been possible to solve the rounds with exactly the same solutions twice in a row? (e.g. 100 6 1 8 3 2 -> 801 and 100 50 75 25 1 8 -> 801 could both be solved with 100x8+1)
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Re: Ask Graeme?

Post by Clive Brooker » Sat Mar 09, 2013 10:56 pm

Jack Worsley wrote:Great work both but I really don't think there are that many U's. I'd say six at the most, possibly even five. How many games in Series 66 saw more than five U's appear?
By my reckoning the full picture is this, both for series 66 and all 15-rounders to the end of the 30th championship, but excluding S-prefix specials:

Series 66

0 0 (0%)
1 0 (0%)
2 3 (2.6%)
3 19 (16.5%)
4 50 (43.5%)
5 36 (31.3%)
6 7 (6.1%)
7 0 (0%)
8+ 0 (0%)

All 15-rounders

0 4 (0.2%)
1 68 (2.7%)
2 379 (14.8%)
3 920 (35.9%)
4 807 (31.5%)
5 301 (11.7%)
6 73 (2.8%)
7 10 (0.4%)
8+ 0 (0%)

Sorry I can't do pretty results tables like Graeme can.

I can't do probability either, but looking at the bulge at 3 and 4 in the "all series" numbers I think Jack is right; there must have been long periods where there were no more than 5 Us.

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Re: Ask Graeme?

Post by Clive Brooker » Sun Mar 10, 2013 11:00 am

David Williams wrote:What evidence is there that letters are manually sorted, rather than shuffled?
I know it's often been pointed out that we don't seem to get enough triple or quadruple vowels in individual rounds. No doubt that can be tested with the data now available. However, conclusive evidence is more easily found: between games 3636 in series 51 and 3780 in series 52 there seems to have been a policy whereby either the J and the Z or the Q and the X were excluded (or put at the bottom of the pack) on alternate days.

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Re: Ask Graeme?

Post by Chris Philpot » Sun Mar 10, 2013 11:12 pm

A quick question that occurred to me last night (I've only just rediscovered the Post-it note with it scribbled down on):

Susie Dent's contribution to Countdown history has been acknowledged via the conundrums SUSISDENT and SUSIEDANT. But given her nine letter name, made of up a valid selection of common letters, has a letters round ever produced a perfect scramble of SUSIEDENT?

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Re: Ask Graeme?

Post by James Robinson » Sun Mar 10, 2013 11:19 pm

Chris Philpot wrote:A quick question that occurred to me last night (I've only just rediscovered the Post-it note with it scribbled down on):

Susie Dent's contribution to Countdown history has been acknowledged via the conundrums SUSISDENT and SUSIEDANT. But given her nine letter name, made of up a valid selection of common letters, has a letters round ever produced a perfect scramble of SUSIEDENT?
Round 3 in this episode seems to be the only round I can find: http://wiki.apterous.org/Episode_5555
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Re: Ask Graeme?

Post by Chris Philpot » Sun Mar 10, 2013 11:30 pm

Who needs a database when you have James Robinson? :)

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Re: Ask Graeme?

Post by James Robinson » Sun Mar 10, 2013 11:38 pm

Chris Philpot wrote:Who needs a database when you have James Robinson? :)
:D I do realise that this is "Ask Graeme", so if it's me giving the answers, just think of me, but with Jools Holland's voice. :P :lol:
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Re: Ask Graeme?

Post by Ciaran Thompson » Tue Mar 12, 2013 10:03 pm

In relation to letter frequency's, the Spreading the Word book states that there are 66 consonants and 65 vowels. However, that is from 2001 and as we know, the amounts have changed, but not by that much it seems. Having 66 consonants makes sense as the maximum number of consonants that could be picked in a game is 66, if 6 consonants were picked in all 11 letters rounds. But seen as that never happens and they'll be 10 letters games from now on, there isn't a need for 66 consonants or 65 vowels, but I suppose if you have more than enough letters you have more letter variation from game to game and a greater variety of words to be found.

I'm sure there have been a few episodes with two K's as people above have said. I remember seeing it. I personally think there should be two K's, as there are words like: kayak, karaoke, khaki, knack, knapsack, knock, kook, knickers, knuckle, trekked, trekker, trekking, kick, kink, kiosk... that you can never get on Countdown with one K. I know it would be rare to get two K's in one round but at least there would be the possibility. The Gotcha episode appears to be the only episode with two K's in the same round, but admitedly the letters were put in a specific order for that episode.

I remember for a few weeks in around 2010, there were two Q's appearing per episode (thankfully not in the same round). I suppose this was to increase the likehood of getting a round with both a Q and U. The better way is having more U's, which is less daunting. It seems there are currently 6 U's, which is better than in a long period from around 2007 to 2009ish, when there seemed to be only four U's, one V, W and Y which decreased the amount of possible words. I remember that the only time there was more than one W per game was when the M was the wrong way around. As Graeme said, it seems from S62 (2010) onwards, they sneaked some of those letters back.

I also think there should be two Z's (as off-putting as that may be) because of the wealth of double Z words: blizzard, buzz, buzzard, dazzle, dizzy, drizzle, fizz, fizzle, fozzy, frazzle, frizzle, fuzz, gizzard, grizzly, huzzah, jazz, jazzy, lizzy, mezzo, muzzle, nozzle, palazzo, piazza, pizza, pizzicato, puzzle, quizzical, tizzy, twizzler... Such words are currently impossible to get. It is ironic that you can't get the words 'puzzle' and 'quizzical' on Countdown.

I know Scrabble and Words With Friends have only one K and one Z, but you can use a blank square to make an extra one. At least the 8 and 9-letter words which have either two K's or two Z's can be used as TTT's and Conundrums respectively.

There was an article on the BBC News wesbite recently saying that the letter values in Scrabble should be changed to reflect the changes of letter-use from the days when Scrabble was first invented, 80 years ago. http://www.bbc.co.uk/news/magazine-20984707

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Re: Ask Graeme?

Post by Andy Platt » Wed Mar 13, 2013 9:11 pm

How do you reckon previous octochamps' totals in the classic 15 rounder format convert into the new 10-letter, 4-number 15 rounder format? Much difference? Maybe a few points a game on average? This will be interesting to see over the next few series

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Re: Ask Graeme?

Post by Gavin Chipper » Wed Mar 13, 2013 9:40 pm

Andy Platt wrote:How do you reckon previous octochamps' totals in the classic 15 rounder format convert into the new 10-letter, 4-number 15 rounder format? Much difference? Maybe a few points a game on average? This will be interesting to see over the next few series
Although I'm not Graeme, I think when scores were converted from the 9-round games to the 15-round games, a score of about 61 was equivalent to 100. So proportionally more numbers (and conundrums for that matter) seemed to lead to higher scores, but not by much.

Knowing this would help.

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Re: Ask Graeme?

Post by Anthony Endsor » Wed Mar 13, 2013 9:50 pm

Now here's one to create a debate. :lol:
A numbers game replacing a letters game, which of course means a lot of the time, 10 points. This, as opposed to whatever you might get with the letters. Now considering MOST of the time you wouldn't get a nine letter word, you could say on that basis the score ratio would increase, but against a record score of 146, where nines are inevitable? This could run and run, but to me I think it could just increase some scores ever so slightly.

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Re: Ask Graeme?

Post by Gavin Chipper » Wed Mar 13, 2013 10:58 pm

Yeah, I'd say it would increase average scores, but decrease the chances of a 146 or 146-beater. However, 146 can be beaten with three 9s, so essentially there's only a 3/11 chance that by reducing the letters rounds to 10 you'd actually take away one of your nines. So the extra numbers could still boost your score even in this case.

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Re: Ask Graeme?

Post by Andy Platt » Wed Mar 13, 2013 11:07 pm

Yeah probably consistently higher scores but less fluctuation/standard deviation so 146 maybe becomes slightly more elusive. I'll do a case study later maybe

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Re: Ask Graeme?

Post by Graeme Cole » Wed Mar 13, 2013 11:34 pm

Jack Worsley wrote:Is it possible to work out the most consecutive letters rounds an individual contestant has gone without having a nine available? I've gone 95 and counting and I was wondering if this was close to a record.
Not quite the record, but you're a close second.

Players with more than 70 consecutive letters rounds without a nine available:

Code: Select all

                     ROUNDS   FROM DATE   EP   RND
   Richard Heald         98   2005-06-03  3939   2
   Jack Worsley          95   2012-01-13  5403   6
   Darryl Francis        94   1985-01-21  245    1
   Andrew Tatham         86   2003-03-10  3435   3
   Joe Zubaidi           81   2002-11-25  3370   3
   Andrew McNamara       77   2011-03-30  5231   1
   Hilary Hopper         74   1987-07-08  607    5
   Richard Campbell      74   1994-03-02  1500   1
   Richard Priest        71   2008-03-26  4565   7
Where the max for a letters round isn't known, I've treated this the same as if a nine were available. It's worth noting that Darryl Francis's 94 starts from his first game in series 6, so if there were no nines available in his series 1 game he'd be top of this table with 100.

Incidentally, this and all future stats now include all of series 67 and the 30th birthday championship.

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Re: Ask Graeme?

Post by Thomas Carey » Thu Mar 14, 2013 12:34 am

Graeme, not sure how hard this would be to do but could you make a list of all players who've had at least one 13+ max game, and their amounts of 15, 14 and 13 max games?

So Conor and Kirk (I think) would be:

Code: Select all

                     GAMES   15s   14s   13s
   Conor Travers      20     3     2      2
   Kirk Bevins        15     2     0      3
   etc.
cheers maus

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Re: Ask Graeme?

Post by Matthew Tassier » Thu Mar 14, 2013 9:56 am

Gavin Chipper wrote:Yeah, I'd say it would increase average scores, but decrease the chances of a 146 or 146-beater. However, 146 can be beaten with three 9s, so essentially there's only a 3/11 chance that by reducing the letters rounds to 10 you'd actually take away one of your nines. So the extra numbers could still boost your score even in this case.
Surprisingly it appears that the change to 10/4/1 actually increases the chance of a 146+ max being available.
Using Graeme's letters round max distribution and assuming 1 large/2 large numbers picks (i.e. 98% chance 10 max, 2% chance 7 max) the chance of 146+ being available is increased from 2.14% to 2.89%

This can probably be explained by the increase in the chance that 2 available 9 letter words are enough to get you to a 146 max.

I'd also like to take the chance to thank Graeme for his great work on this thread, a delight to any stats-geek.

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Re: Ask Graeme?

Post by Graeme Cole » Thu Mar 14, 2013 11:40 pm

Conor wrote:
Graeme Cole wrote: Series 66 had the highest proportion of five-vowel picks of any series since 1985, because Jonathan Rawlinson was in it. (No, really - 43 of the 82 five-vowel letters rounds in that series were in his games.)
I suspect Series 68 might break the record. In the semifinal between Jack Hurst and Jonathan Rawlinson there were 5-vowel picks in 8 out of 11 letters rounds. Is this the most five-vowel-tastic game ever?
Yes. No game besides that one had eight or more five-vowel letters rounds, although this one had seven.

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Re: Ask Graeme?

Post by Graeme Cole » Fri Mar 15, 2013 12:05 am

Gavin Chipper wrote:In what proportion of games (separately for 9 and 15 rounders) are all the numbers games rendered "worthless", by both contestants maxing them all? Actually I know you can only go by points rather than true maxes so yo uwon't be able to get whether a 7 is the true max. So maybe two separate stats - one for all max scores (erring on the side of inclusivity), and one for all 10s (erring on the side of exclusivity).
In 15 rounders, both contestants scored the maximum numbers round points available in 170 out of 2596 games, which is about 6.5%. Both contestants scored 30/30 on numbers in 154 games, or 5.9%.

In 9 rounders, both contestants scored the maximum numbers round points available in 401 out of 2944 games, or 13.6%. Both contestants scored 20/20 on numbers in 387 games, which is 13.1%. Note that while the database knows about 3035 9-rounders, I've excluded those where we don't know the max.

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Re: Ask Graeme?

Post by Jon Corby » Fri Mar 15, 2013 10:17 am

Graeme Cole wrote:Yes. No game besides that one had eight or more five-vowel letters rounds, although this one had seven.
Speaking of numbers of vowels, has it always been an official rule that you had to pick between 3 and 5 vowels? Was it ever mentioned on-screen, as nobody (other than contestants) seemed to be aware of it. Also, are there any anomalies - I'm positive I remember a 2-vowel letters round slipping through in the last few years.

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Re: Ask Graeme?

Post by Conor » Fri Mar 15, 2013 11:26 am

Jon Corby wrote:Speaking of numbers of vowels, has it always been an official rule that you had to pick between 3 and 5 vowels? Was it ever mentioned on-screen, as nobody (other than contestants) seemed to be aware of it. Also, are there any anomalies - I'm positive I remember a 2-vowel letters round slipping through in the last few years.
Nope, wasn't always a rule. Not only did Andy Cusworth pick 6 vowels every time against Shacklady, in round 1 he picked the 6 vowels straight off the bat. Utterly shameless.

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Re: Ask Graeme?

Post by Andy Platt » Fri Mar 15, 2013 12:12 pm

In a related theme, in the guidelines I noticed that it said (and I wish I had the exact words in front of me, but I don't) that a failure to conform to these rules (and I remember they are official rules), would result in the round being scrapped and the contestant having to pick them all again.

Now seen as though I almost always go CCCC to start every round, what if I got the consonants QZJW, and decided "hey, you know what, I don't really fancy this" and just kept picking consonants? I never really asked Jay or Damian or anyone about it, nor did I consider doing it when I filmed, but the guidelines do leave the exploitation open and it would be interesting to see what the production team would do about it. Presumably they'd just stick the same bad consonants at the top again, rendering the exploitation fruitless, and give you a warning? Still probably worth a try!

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Re: Ask Graeme?

Post by Jon Corby » Fri Mar 15, 2013 12:15 pm

Conor wrote:
Jon Corby wrote:Speaking of numbers of vowels, has it always been an official rule that you had to pick between 3 and 5 vowels? Was it ever mentioned on-screen, as nobody (other than contestants) seemed to be aware of it. Also, are there any anomalies - I'm positive I remember a 2-vowel letters round slipping through in the last few years.
Nope, wasn't always a rule. Not only did Andy Cusworth pick 6 vowels every time against Shacklady, in round 1 he picked the 6 vowels straight off the bat. Utterly shameless.
Ha, mental stuff. Are there any other anomalous rounds other than the 2-vowel round I mentioned (anyone find that?) since the rule was introduced? I'm sure it was brought up and Damian said they spotted it, but allowed the round to continue because it was a decent selection anyway.

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Re: Ask Graeme?

Post by Countdown Team » Fri Mar 15, 2013 12:50 pm

Andy Platt wrote:Presumably they'd just stick the same bad consonants at the top again, rendering the exploitation fruitless, and give you a warning? Still probably worth a try!
Likely that once you'd got CCCCCC and asked for another C, Rachel would tell you that you need 3 vowels now, so the first 6 letters, however bad, wouldn't change. We'd just resume the recording with you picking your 7th letter as a vowel.

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Re: Ask Graeme?

Post by Graeme Cole » Fri Mar 15, 2013 12:56 pm

Andy Platt wrote:In a related theme, in the guidelines I noticed that it said (and I wish I had the exact words in front of me, but I don't) that a failure to conform to these rules (and I remember they are official rules), would result in the round being scrapped and the contestant having to pick them all again.

Now seen as though I almost always go CCCC to start every round, what if I got the consonants QZJW, and decided "hey, you know what, I don't really fancy this" and just kept picking consonants? I never really asked Jay or Damian or anyone about it, nor did I consider doing it when I filmed, but the guidelines do leave the exploitation open and it would be interesting to see what the production team would do about it. Presumably they'd just stick the same bad consonants at the top again, rendering the exploitation fruitless, and give you a warning? Still probably worth a try!
I don't think they necessarily always do a retake. Multiple times I've seen a contestant pick a seventh consonant as their ninth letter, and Rachel just reminds them they need three vowels and gives them a vowel.

Edit: ignore me, listen to Mr Team.

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Re: Ask Graeme?

Post by Andy Platt » Fri Mar 15, 2013 1:31 pm

Countdown Team wrote:
Andy Platt wrote:Presumably they'd just stick the same bad consonants at the top again, rendering the exploitation fruitless, and give you a warning? Still probably worth a try!
Likely that once you'd got CCCCCC and asked for another C, Rachel would tell you that you need 3 vowels now, so the first 6 letters, however bad, wouldn't change. We'd just resume the recording with you picking your 7th letter as a vowel.
Yeah nice one that makes more sense - thought I remembered reading the words 'round would be scrapped' somewhere along the way

Graeme wrote:I don't think they necessarily always do a retake. Multiple times I've seen a contestant pick a seventh consonant as their ninth letter, and Rachel just reminds them they need three vowels and gives them a vowel.
Sometimes you ask Rachel for a consonant and she gives you an E even though she chose it from the correct pile.
Wonder if that stays in the final cut :mrgreen:

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 16, 2013 12:17 am

Gavin Chipper wrote:Can we do - what's the lowest highest number that's come out in a selection? So in 1, 1, 2, 2, 3, 3, the highest is 3, and that would be the lowest possible.
The always-unsolvable selection 1 1 2 2 3 3 has never happened, but 1 2 3 3 4 4 has happened once.
Gavin Chipper wrote:Or, how often has no number been higher than 5?
Six numbers between 1 and 5 last happened in round 5 of this recent championship game, when I pre-emptively answered this question. :-)

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 16, 2013 12:24 am

Mark Ivey wrote:Great thread, very interesting to see all these facts and figures. Ok, here's a question:

What is the highest winning score posted by a challenger who's gone on to lose in their second game?
113 by Bernie Corrigan.

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 16, 2013 1:56 am

Dave Preece wrote:Is there a link between some of the great players playing in final stages to the distribution of 'nice' letters for the production to ensure big scores for pulicity purposes?
The short answer is "no".

Here's a table of average max letters scores by episode type, for all 15-rounders. Only letters rounds are counted, in order to eliminate any variation caused by finalists opting for more challenging numbers picks.

Code: Select all

   EP TYPE   MEAN LETTERS MAX   COUNT
   ----------------------------------
   30BGF            109.0000        1 
   CQF               89.4167       12
   30B1              87.4375       16
   S                 87.3235       34
   P                 87.2962     2323
   CSF               86.8333        6 
   CP                86.6667       24  
   SF                86.4091       44
   QF                86.0000       88
   30B2              84.1250        8 
   30BP              83.7778        9 
   30BSF             83.0000        2 
   30BQF             82.0000        4 
   GF                81.9545       22 
   CGF               79.0000        3
As you can see, "big" matches do not, in general, have favourable letters compared with ordinary series games (episode type P). So I see no evidence that the letters are, or have ever been, deliberately arranged to give high maxes. If anything, with the exception of CQF (CoC quarter-finals), the average max for the higher-profile games is lower than in ordinary series games. Not sure why. Also not sure if the difference is even statistically significant. I'm sure there are equations that can help with this, but I'm not Michael Wallace so I don't really know what I'm doing.

A note on the limitations of what this analysis can tell us: if the production team were to deliberately arrange the letters for a high max in just one or two games ever (and I should stress that I've never seen any evidence to suggest this has happened), this table wouldn't show it up. Short of catching someone in the act of messing about with the letters, I don't think you could ever know, as it could be explainable by chance. However, if they routinely did it for certain classes of game as the question suggests, it would show up, and it doesn't.

The one outlier in all this is the final of the 30th birthday championship, with its three nines and letters max of 109. Since the sample size is 1, this isn't evidence of anything untoward. Of the 2,596 15-round games in the database, 69 of them had 109 or more points available from letters. This is about 1 in 38. So if anyone thinks the 30th birthday championship final is evidence of deliberate manipulation of the pack, that's roughly equivalent to rolling two dice once, getting two sixes, then claiming that's evidence the dice are loaded.

So there'll be no need for the tinfoil hats today.

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 16, 2013 1:40 pm

David Williams wrote:Maybe ten years ago there was a suggestion that for a couple of months one of the letters (possibly J) never appeared once, suggesting it had been mislaid. Is this true, and if so was the length of absence statistically significant?
No letter has been unseen for more consecutive rounds than J. It appeared in the series 46 final on Christmas Day 2001. Two months, 44 games and 480 rounds then passed with no J before it was seen again on 25th February 2002.

Other notable lengths of absence:

In series 61 on 30th October 2009, a V was selected in round 1. That was the last time we saw the V until the start of series 62 in January 2010. It had been unseen for 396 letters rounds.

The next appearance of the X after round 5 on 23rd May 1988 was in round 6 on 24th August of the same year, an absence of 398 letters rounds.

In all 2596 15 rounders, the J has been unseen in 711 of those games, the X in 617, and the V in 367. So if we take this as an indicator of how probable the absence of a letter is, the probability of a given 44 consecutive games in those 2596 having no J is (711/2596)^44, which is about 1 in 5.6 * 10^24. There were 2596 - 44 + 1 = 2553 opportunities for it to happen in that time, but that doesn't even make a dent in that number. It's the same story with the absences of the X and the V, so we can safely say that, whether it was by accident or design, those letters were removed from the pack.

Incidentally, this game surprisingly had no Ls in it, and is the only such 15-rounder.
David Williams wrote:What evidence is there that letters are manually sorted, rather than shuffled?
We've seen that there's no evidence that the letters are deliberately arranged to produce longer words or higher scores. However, it's a certainty that the order of the vowel pile is not entirely random. It gets tinkered with to remove consecutive occurrences of the same letter.

I've run a simulation of 10,000 random shuffles of the vowel pile, using the distribution I guessed at earlier, and then truncated the length of each shuffle at 40, because that's the average number of vowels we see in a 15-round game. I've used this as the basis for estimating probabilities.

In these 10,000 shuffles, a run of three consecutive Es happened 5,611 times, which means you'd expect this to happen roughly every other game. On the show, it hasn't happened since 2010. Three consecutive As should happen approximately once every four games, and that hasn't happened since 2011.

According to the simulation, two consecutive As should appear in 84% of 15 rounders, but the same figure on the show is only 14%. Two consecutive Es should appear in 98% of 15 rounders, but on the show it's only happened in 28% of games.

Presumably, the reason they make an effort to remove clusters of identical letters is that if five vowels in a row turn out to be E, which is not as unlikely as you might expect (it should happen in about 1 in 20 games), the production team would get letters from people who don't understand probability complaining that "you're not shuffling the letters properly".

I'm told apterous does the same thing. This is perhaps why we're surprised at CO-events when the Countdown board game turns up selections like TPGLEEEEE - that's just what true randomness sometimes looks like.

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Re: Ask Graeme?

Post by Dave Preece » Sat Mar 16, 2013 2:08 pm

Graeme Cole wrote:
Dave Preece wrote:Is there a link between some of the great players playing in final stages to the distribution of 'nice' letters for the production to ensure big scores for pulicity purposes?
The short answer is "no".

Here's a table of average max letters scores by episode type, for all 15-rounders. Only letters rounds are counted, in order to eliminate any variation caused by finalists opting for more challenging numbers picks.

Code: Select all

   EP TYPE   MEAN LETTERS MAX   COUNT
   ----------------------------------
   30BGF            109.0000        1 
   CQF               89.4167       12
   30B1              87.4375       16
   S                 87.3235       34
   P                 87.2962     2323
   CSF               86.8333        6 
   CP                86.6667       24  
   SF                86.4091       44
   QF                86.0000       88
   30B2              84.1250        8 
   30BP              83.7778        9 
   30BSF             83.0000        2 
   30BQF             82.0000        4 
   GF                81.9545       22 
   CGF               79.0000        3
As you can see, "big" matches do not, in general, have favourable letters compared with ordinary series games (episode type P). So I see no evidence that the letters are, or have ever been, deliberately arranged to give high maxes. If anything, with the exception of CQF (CoC quarter-finals), the average max for the higher-profile games is lower than in ordinary series games. Not sure why. Also not sure if the difference is even statistically significant. I'm sure there are equations that can help with this, but I'm not Michael Wallace so I don't really know what I'm doing.

A note on the limitations of what this analysis can tell us: if the production team were to deliberately arrange the letters for a high max in just one or two games ever (and I should stress that I've never seen any evidence to suggest this has happened), this table wouldn't show it up. Short of catching someone in the act of messing about with the letters, I don't think you could ever know, as it could be explainable by chance. However, if they routinely did it for certain classes of game as the question suggests, it would show up, and it doesn't.

The one outlier in all this is the final of the 30th birthday championship, with its three nines and letters max of 109. Since the sample size is 1, this isn't evidence of anything untoward. Of the 2,596 15-round games in the database, 69 of them had 109 or more points available from letters. This is about 1 in 38. So if anyone thinks the 30th birthday championship final is evidence of deliberate manipulation of the pack, that's roughly equivalent to rolling two dice once, getting two sixes, then claiming that's evidence the dice are loaded.

So there'll be no need for the tinfoil hats today.

What are the top – say – 100, mean letter max games, and at what stage in what comp were they please?

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 16, 2013 2:23 pm

Dave Preece wrote:What are the top – say – 100, mean letter max games, and at what stage in what comp were they please?
If we list all the games in order of their letters max, quite a few games are on joint 99th with 103. So we'll include all 15 rounders with a letters max of 103 or more, which is 136 games.

The breakdown is as follows:

Preliminaries: 126
Series quarter-finals: 3
Series semi-finals: 2
Series finals: 1
CoC quarter-finals: 1
Specials: 1
30th birthday championship last 32: 1
30th birthday championship final: 1

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 16, 2013 2:55 pm

Jon Corby wrote:Are there any other anomalous rounds other than the 2-vowel round I mentioned (anyone find that?) since the rule was introduced? I'm sure it was brought up and Damian said they spotted it, but allowed the round to continue because it was a decent selection anyway.
http://wiki.apterous.org/Episode_4287

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Re: Ask Graeme?

Post by Gavin Chipper » Sat Mar 16, 2013 5:41 pm

Graeme Cole wrote:We've seen that there's no evidence that the letters are deliberately arranged to produce longer words or higher scores.
Isn't it that there is evidence, but no evidence that it's done for particular games over others?

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Re: Ask Graeme?

Post by Graeme Cole » Sat Mar 16, 2013 6:11 pm

Gavin Chipper wrote:
Graeme Cole wrote:We've seen that there's no evidence that the letters are deliberately arranged to produce longer words or higher scores.
Isn't it that there is evidence, but no evidence that it's done for particular games over others?
How do you mean? The only thing I can see evidence for is that clusters of identical letters in the pile are redistributed, not that the letters are deliberately arranged to make longer words available. Or are you saying that doing this increases the max?

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Re: Ask Graeme?

Post by Gavin Chipper » Sat Mar 16, 2013 6:29 pm

Graeme Cole wrote:
Gavin Chipper wrote:
Graeme Cole wrote:We've seen that there's no evidence that the letters are deliberately arranged to produce longer words or higher scores.
Isn't it that there is evidence, but no evidence that it's done for particular games over others?
How do you mean? The only thing I can see evidence for is that clusters of identical letters in the pile are redistributed, not that the letters are deliberately arranged to make longer words available. Or are you saying that doing this increases the max?
Yeah, I mean I doubt they plant words or anything, but reducing loads of consecutive letters presumably increases the average max.

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Re: Ask Graeme?

Post by Countdown Team » Sat Mar 16, 2013 9:44 pm

Okay, we once 'lost' the J and V for a few months. This was , i think, because we had conundrums with J and V in, so we needed 2 of each letter, one for the reveal, one for the solution. I seem to recall that there was a shortage of such letters, so we pinched J and V from the normal letters piles to compile the conundrums, and they were not put back afterwards.

Beyond that, everything is shuffled like a pack of cards, nothing is ever messed with, we get what we get.

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Re: Ask Graeme?

Post by James Robinson » Sat Mar 16, 2013 10:08 pm

Countdown Team wrote:Okay, we once 'lost' the J and V for a few months. This was , i think, because we had conundrums with J and V in, so we needed 2 of each letter, one for the reveal, one for the solution. I seem to recall that there was a shortage of such letters, so we pinched J and V from the normal letters piles to compile the conundrums, and they were not put back afterwards.

Beyond that, everything is shuffled like a pack of cards, nothing is ever messed with, we get what we get.
There is certainly a precedent, because in my very first game 10 years ago, me and my opponent were informed before the game started that the J and Q had been removed, and lo and behold, they didn't turn up. :)
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Re: Ask Graeme?

Post by Andy Platt » Sat Mar 16, 2013 10:12 pm

I have an interesting question. Why is the Y very very slightly darker than the rest of the letters?

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Re: Ask Graeme?

Post by Giles » Sat Mar 16, 2013 11:40 pm

In how many series has the number 1 seed lost the quarter-final against the number 8 seed?

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Re: Ask Graeme?

Post by James Robinson » Sat Mar 16, 2013 11:58 pm

Giles wrote:In how many series has the number 1 seed lost the quarter-final against the number 8 seed?
The answer is 6: Series 5 (John Wallace), Series 21 (Lew Schwarz), Series 24 (Norman Christian), Series 30 (Graham Cross), Series 44 (Kevin McMahon) & Series 55 (Steven Briers).
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Re: Ask Graeme?

Post by Johnny Canuck » Sun Mar 17, 2013 1:55 am

James Robinson wrote:
Giles wrote:In how many series has the number 1 seed lost the quarter-final against the number 8 seed?
The answer is 6: Series 5 (John Wallace), Series 21 (Lew Schwarz), Series 24 (Norman Christian), Series 30 (Graham Cross), Series 44 (Kevin McMahon) & Series 55 (Steven Briers).
On a semi-related note, what are the average margins of victory in each individual finals match? (i.e.: On average, by how many points does the #1 seed beat the #8 seed in the first quarter final? For series in which the #8 seed won the first QF, this value would be negative; for instance, Phil Watson beat Steve Briers 83 - 73, so you'd use -10.)
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Re: Ask Graeme?

Post by Clive Brooker » Sun Mar 17, 2013 10:25 am

James Robinson wrote:
Countdown Team wrote:Beyond that, everything is shuffled like a pack of cards, nothing is ever messed with, we get what we get.
There is certainly a precedent, because in my very first game 10 years ago, me and my opponent were informed before the game started that the J and Q had been removed, and lo and behold, they didn't turn up. :)
As I said a bit further up, there was a run of almost 150 games not so long ago when either the Q and the X or the J and the Z turned up on alternate days (occasionally one of the pair would fail to reach the top of the pile). That didn't happen by chance.

Does anyone remember that during COC13 (the first games with Jeff and Rachel) we all noticed immediately that the "shuffling" seemed different. This was swiftly confirmed by Kate Horton (and denied by Mr Team). Would that set of games (165 letters rounds) provide enough data to test whether the observed letters sequence corresponded more closely to random selection than it has in the rest of Countdown history?

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Re: Ask Graeme?

Post by Matthew Tassier » Sun Mar 17, 2013 11:53 am

Clive Brooker wrote:
Does anyone remember that during COC13 (the first games with Jeff and Rachel) we all noticed immediately that the "shuffling" seemed different. This was swiftly confirmed by Kate Horton (and denied by Mr Team). Would that set of games (165 letters rounds) provide enough data to test whether the observed letters sequence corresponded more closely to random selection than it has in the rest of Countdown history?
Yes, it was quite striking at the time how often we got pairs (or triples) of the same vowel coming out. I liked it and theoretically it opened up some new areas of the dictionary. I seem to remember that most of the top players disliked it as it would tend to bring down maxes.

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Re: Ask Graeme?

Post by Graeme Cole » Sun Mar 17, 2013 1:25 pm

Thomas Carey wrote:Graeme, not sure how hard this would be to do but could you make a list of all players who've had at least one 13+ max game, and their amounts of 15, 14 and 13 max games?

Code: Select all

                           15s  14s  13s
   Conor Travers             3    2    2
   Kirk Bevins               2    0    3
   Jon O'Neill               1    0    2
   Jonathan Rawlinson        0    3    0
   Paul Gallen               0    2    3
   Edward McCullagh          0    2    2
   Craig Beevers             0    2    1
   Jack Hurst                0    2    1
   Grace Page                0    1    0
   Chris Davies              0    0    3
   Jack Worsley              0    0    3
   Innis Carson              0    0    2
   Julian Fell               0    0    2
   Adam Gillard              0    0    1
   Adam Laws                 0    0    1
   Chris Wills               0    0    1
   Daniel Pati               0    0    1
   David O'Donnell           0    0    1
   Eoin Monaghan             0    0    1
   Graeme Cole               0    0    1
   Harshan Lamabadusuriya    0    0    1
   John Mayhew               0    0    1
   Mark Tournoff             0    0    1
   Matthew Shore             0    0    1
   Oliver Garner             0    0    1
   Paul Howe                 0    0    1
   Stewart Holden            0    0    1
As always, a "maxed round" is a sovereign state recognised by the UN. Or something.

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Re: Ask Graeme?

Post by Graeme Cole » Sun Mar 17, 2013 7:49 pm

Clive Brooker wrote:
James Robinson wrote:
Countdown Team wrote:Beyond that, everything is shuffled like a pack of cards, nothing is ever messed with, we get what we get.
There is certainly a precedent, because in my very first game 10 years ago, me and my opponent were informed before the game started that the J and Q had been removed, and lo and behold, they didn't turn up. :)
As I said a bit further up, there was a run of almost 150 games not so long ago when either the Q and the X or the J and the Z turned up on alternate days (occasionally one of the pair would fail to reach the top of the pile). That didn't happen by chance.
The distribution of letters has been tweaked over the years. If someone decided that even one Q in the pack over-represents its frequency in the language and there should effectively be "half a Q" in the pack, that's how you'd do it. The only alternative would be to double the frequencies of all the other letters, and then you'd find they don't all fit in the consonant box.
Clive Brooker wrote:Does anyone remember that during COC13 (the first games with Jeff and Rachel) we all noticed immediately that the "shuffling" seemed different. This was swiftly confirmed by Kate Horton (and denied by Mr Team). Would that set of games (165 letters rounds) provide enough data to test whether the observed letters sequence corresponded more closely to random selection than it has in the rest of Countdown history?
We can infer what the vowel and consonant piles looked like at the start of every game for which we have round details, as far into the pile as the number of each category we see. This isn't 100% infallible, as very occasionally they have reason to give up halfway through a round and throw the letters away, but this sort of thing is rare enough that it shouldn't matter. Anyway, the point is that having inferred what the vowel pile looked like at the start of the game (or at least the first N letters, where N is the number of vowels that came out in that game), we can look through it for clusters of identical letters.

The shuffling system does indeed appear to have been different during COC13. Here's a table of how often the vowel pile has been known to contain a cluster of three of the same letter in all 2,596 15-round games, and how many of those were in the 15 games of CoC13. (The vowel pile has never contained UUU in a 15 rounder.)

Code: Select all

         All 15R   CoC13
   AAA        10       4
   EEE        30       5
   III         5       4
   OOO         7       3
Countdown Team wrote:Okay, we once 'lost' the J and V for a few months. This was , i think, because we had conundrums with J and V in, so we needed 2 of each letter, one for the reveal, one for the solution. I seem to recall that there was a shortage of such letters, so we pinched J and V from the normal letters piles to compile the conundrums, and they were not put back afterwards.

Beyond that, everything is shuffled like a pack of cards, nothing is ever messed with, we get what we get.
I'm sure you know this anyway, but for the avoidance of doubt, if anything I'm coming up with in this thread sounds like a dig at you or the show, it isn't. I'll repeat that I'm not suggesting any impropriety or any deliberate attempt to manipulate what words come out - in fact we've already seen that any suggestion of that kind is rubbish.

Nevertheless, if someone asks what evidence there is that the ordering of the letter tiles has a non-random element to it, and I have a look and find that three consecutive Es has only happened 30 times over the past eleven years when truly random shuffling should make it happen every other game, it's interesting. That's why I assumed that the vowel pile, after shuffling, is manually examined and re-sorted to remove consecutive occurrences of the same letter. I'm not saying there's necessarily anything wrong with that, or even that it really matters at all, and if I'm wrong in assuming this happens then accept my apologies for suggesting it. Even so, it's indisputable that there's something about the shuffling process, conscious or otherwise, that makes clusters of identical letters much, much less likely than would be expected by chance. (Whether anyone should care is more open to debate.) If the letters are shuffled face up, that could explain it. Humans can't consciously generate truly random sequences, mainly because repeated occurrences of the same thing don't look "random" enough to us.

Dave Preece
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Re: Ask Graeme?

Post by Dave Preece » Sun Mar 17, 2013 11:14 pm

On the subject of shuffling face-up - What - Statistically are the chances of getting THREE available nine letter max rounds in a row?

How often has this happened and has there ever been more?

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Graeme Cole
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Re: Ask Graeme?

Post by Graeme Cole » Sun Mar 17, 2013 11:56 pm

Dave Preece wrote:On the subject of shuffling face-up - What - Statistically are the chances of getting THREE available nine letter max rounds in a row?

How often has this happened and has there ever been more?
I couldn't even begin to work out what the exact probability is, but three consecutive letters rounds in the same game having a nine available has happened six times. There have never been four or more consecutive rounds with nines available.

Rounds 2-4 in episode 3967
Rounds 9, 11 and 12 in episode 4607
Rounds 1-3 in episode 4842
Rounds 7-9 in episode 5227
Rounds 3, 4 and 6 in episode 5434
Rounds 3, 4 and 6 in the 30th birthday championship final - this was the first time all three nines were spotted.

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Re: Ask Graeme?

Post by JackHurst » Mon Mar 18, 2013 1:20 am

Graeme Cole wrote: Incidentally, this game surprisingly had no Ls in it, and is the only such 15-rounder.
Countdown Team wrote:Okay, we once 'lost' the J and V for a few months. This was , i think, because we had conundrums with J and V in, so we needed 2 of each letter, one for the reveal, one for the solution. I seem to recall that there was a shortage of such letters, so we pinched J and V from the normal letters piles to compile the conundrums, and they were not put back afterwards.

Beyond that, everything is shuffled like a pack of cards, nothing is ever messed with, we get what we get.
Putting these two together makes me wonder if they couldn't find the Ls for the conundrum letters in this episode, so they had to pinch 4 of them from the letters pack.

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