Ask Graeme?

[Steve Hyde]

Has any player ever scored more than Alex Robertson (115/92% of max) while winning only one match?

[Thomas Carey]

Has any player ever scored more than Alex Robertson (115/92% of max) while winning only one match?

My boy https://wiki.apterous.org/Jamie_Ilett-Jones

Anyone heard from him recently? He's not been to events in a while

[Tom S]

There was reference to the fact that yesterday's game featured two players born in the 21st century. My quarter-final game was the 1st finals game to feature two players born after the millennium. I'd also wager that it is the game with the smallest age difference between two players (5 days), but obviously this is very hard to verify, unless anyone can remember anything being mentioned on previous shows?

[Steve Hyde]

There was reference to the fact that yesterday's game featured two players born in the 21st century. My quarter-final game was the 1st finals game to feature two players born after the millennium. I'd also wager that it is the game with the smallest age difference between two players (5 days), but obviously this is very hard to verify, unless anyone can remember anything being mentioned on previous shows?

Graeme Cole is one day younger than me and we played eachother at Colin 2024 if that counts?

[JackHurst]

.

[JackHurst]

Just realized that's crap. Why would roughly one in 23 games based on the birthday problem? Dingus.

[Gavin Chipper]

I'd say it's not unlikely there are closer ones based on the number of games there have been.

[Gavin Chipper]

There have been over 8000 games of Countdown. It's difficult to get a distribution of ages - but 20,000 days covers nearly 55 years and while not all contestants are within 55 years of each other, a uniform distribution over 55 years doesn't take into account peaks in the distribution and would likely underestimate the number of close birthdays.

And with those numbers - 8000 and 20,000 we're looking at 5 days probably not being the closest without needing to do any real maths.

Edit - But to do a bit more maths, if one contestant is born on a specific day, then there are 9 days the other contestant can be born on to be +/- 4 days (i.e. closer than the 5 days suggested as a potential record). Using the 20,000 days thing, it would be a 9 in 20,000 chance. So the chances of this not happening over 8000 games would be (19,991/20000)^8000 = 0.0273. So a greater than 97% chance of there being two players born 4 days or less apart. And I think that's an underestimate. And probably quite a big underestimate.

[Jamie Weisenberg]

Does Graeme work on the TV show ? If not, what's this thread about ?

[Graeme Cole]

Does Graeme work on the TV show ?

No.

If not, what's this thread about ?

A very long time ago, I wrote a loose collection of Python scripts to scrape all the results and rounds we have on the wiki into a database. Over the years I've refreshed and updated it, usually after each series, and I use it to answer questions like "what valid word has been disallowed most often for not being in the selection?" to which the answer is EXILED (7 times).

[Graeme Cole]

Hi Graeme, I was wondering how many octochamps in the fifteen round format have scored less than 100 each game? (I originally posted this a couple of weeks ago, but there have been no replies. Sorry if my original wording was a bit abrupt.)

15.

Here are all the 15-round octochamps whose maximum heat game score was less than 100:

https://wiki.apterous.org/Chris_McHenry (99)
https://wiki.apterous.org/Nick_Wainwright (99)
https://wiki.apterous.org/Adam_Rolston (99)
https://wiki.apterous.org/David_Von_Geyer (98)
https://wiki.apterous.org/Chris_Marshall (98)
https://wiki.apterous.org/David_Law (97)
https://wiki.apterous.org/Danny_Pledger (96)
https://wiki.apterous.org/Steven_Turnbull (96)
https://wiki.apterous.org/Jeffrey_Burgin (95)
https://wiki.apterous.org/Joe_McGonigle (95)
https://wiki.apterous.org/James_Slater (95)
https://wiki.apterous.org/Joe_Zubaidi (93)
https://wiki.apterous.org/Alan_Duval (93)
https://wiki.apterous.org/Steve_Wood_(Series_61) (92)
https://wiki.apterous.org/Ned_Pendleton (92)

[Jamie Weisenberg]

A very long time ago, I wrote a loose collection of Python scripts to scrape all the results and rounds we have on the wiki into a database. Over the years I've refreshed and updated it, usually after each series, and I use it to answer questions like "what valid word has been disallowed most often for not being in the selection?" to which the answer is EXILED (7 times).

Ah, makes sense now.

[Peter Thomas]

Hi Graeme, I was wondering how many octochamps in the fifteen round format have scored less than 100 each game? (I originally posted this a couple of weeks ago, but there have been no replies. Sorry if my original wording was a bit abrupt.)

15.

Here are all the 15-round octochamps whose maximum heat game score was less than 100:

https://wiki.apterous.org/Chris_McHenry (99)
https://wiki.apterous.org/Nick_Wainwright (99)
https://wiki.apterous.org/Adam_Rolston (99)
https://wiki.apterous.org/David_Von_Geyer (98)
https://wiki.apterous.org/Chris_Marshall (98)
https://wiki.apterous.org/David_Law (97)
https://wiki.apterous.org/Danny_Pledger (96)
https://wiki.apterous.org/Steven_Turnbull (96)
https://wiki.apterous.org/Jeffrey_Burgin (95)
https://wiki.apterous.org/Joe_McGonigle (95)
https://wiki.apterous.org/James_Slater (95)
https://wiki.apterous.org/Joe_Zubaidi (93)
https://wiki.apterous.org/Alan_Duval (93)
https://wiki.apterous.org/Steve_Wood_(Series_61) (92)
https://wiki.apterous.org/Ned_Pendleton (92)

There was also Isabelle Heward from earlier this year.

[Jamie Weisenberg]

Ask Graeme:- Has anyone above the age of 40 ever won a series ? Who is the oldest winner ?

[Graeme Cole]

There was also Isabelle Heward from earlier this year.

Forgot to mention that this only counts games up to the most recently-completed series.

[A Sivaramani]

Is it possible for the results database to be available publically? Thanks

[Martin Hurst]

For each of the last 3 completed series (or more if the data is easy to obtain), how many points were scored in letters games by the picker compared to the non-picker? Am trying to establish the advantage (if any) that there is between picking and not picking in letters games on TV. Would also be interesting to know if there is any difference between the results comparing "normal" episodes between mere mortals, and episodes between top players (e.g grand finals, CoCs, etc). Cheers

[David Williams]

For each of the last 3 completed series (or more if the data is easy to obtain), how many points were scored in letters games by the picker compared to the non-picker? Am trying to establish the advantage (if any) that there is between picking and not picking in letters games on TV. Would also be interesting to know if there is any difference between the results comparing "normal" episodes between mere mortals, and episodes between top players (e.g grand finals, CoCs, etc). Cheers

There will be the occasional time when you see you have eight letters of a non-trivial nine, but if there is a difference, it's surely more about who declares first. If you've got a dodgy eight and a safe seven, it's a very easy decision if your opponent has already declared nine or six, and it's a big help if he declares seven or eight.

[James Laverty]

Carol Vorderman appeared as a guest on HIGNFY on Friday, with former contestant Little Alex Horne as host. Is this the first time a former contestant has hosted a TV show with a former/current Countdown team member as a participant? (excluding Catsdown)

[Gavin Chipper]

Vorderman was still on the show when Horne was a contestant as well - her last series!

[Steve Hyde]

Carol Vorderman appeared as a guest on HIGNFY on Friday, with former contestant Little Alex Horne as host. Is this the first time a former contestant has hosted a TV show with a former/current Countdown team member as a participant? (excluding Catsdown)

Carol has also been on Beat the Chasers opposite former contestant Mark Labbett, though he's admittedly not a host. Matt Le Tissier and Jeff Sterling did a whole load of Soccer Saturdays together

[Graeme Cole]

Carol Vorderman appeared as a guest on HIGNFY on Friday, with former contestant Little Alex Horne as host. Is this the first time a former contestant has hosted a TV show with a former/current Countdown team member as a participant? (excluding Catsdown)

No, it isn't; Carol Vorderman appeared in a special New Year episode of Taskmaster in 2023.

[Gavin Chipper]

Here's one for the database - does Carol Vorderman remember Alex Horne from when he was on Countdown?

[Andres Sanchez]

I wouldn't think so in all honesty, don't really know how much she'd even remember contestants that stood out to her. Could be podcast material if she was on one tho.

Don't even know if Alex is still enthused about Countdown as I assume he was back then.

[JackHurst]

Carol Vorderman appeared as a guest on HIGNFY on Friday, with former contestant Little Alex Horne as host. Is this the first time a former contestant has hosted a TV show with a former/current Countdown team member as a participant? (excluding Catsdown)

No, it isn't; Carol Vorderman appeared in a special New Year episode of Taskmaster in 2023.

A rare lapse in discipline see Graeme making a rod for his own back by answering questions unrelated to the Countdown Database.

Here's one for the database - does Carol Vorderman remember Alex Horne from when he was on Countdown?

Gevin makes a humorous (albeit slightly facetious) comment to get the thread back on track.

I wouldn't think so in all honesty, don't really know how much she'd even remember contestants that stood out to her. Could be podcast material if she was on one tho.

Don't even know if Alex is still enthused about Countdown as I assume he was back then.

An American takes sarcasm in earnest.


I enjoyed this sequence of posts. Does the database agree with me?

[Andres Sanchez]

That's America for ya

[Fiona T]

With the X currently awol and stories of the J having taken an extended holiday "back in 2002 or something", what are the longest gaps between individual letters appearing?

[Gavin Chipper]

The Ð hasn't appeared for over 700 years.

[sean d]

Possibly an unanswerable question, but.... has anyone ever 'pencilled' a new word on Countdown (i.e. made the first declaration of that word, as a max winner) before it was pencilled on Apterous. After apterous had bedded in, of course

[Adam Gillard]

Possibly an unanswerable question, but.... has anyone ever 'pencilled' a new word on Countdown (i.e. made the first declaration of that word, as a max winner) before it was pencilled on Apterous. After apterous had bedded in, of course

2000 so before Apterous but MYOGLOBIN is the one that sticks in my mind.

[JackHurst]

Possibly an unanswerable question, but.... has anyone ever 'pencilled' a new word on Countdown (i.e. made the first declaration of that word, as a max winner) before it was pencilled on Apterous. After apterous had bedded in, of course

I think there's a rule on the show that if it hasn't been declared on Apterous then it's not valid, so by that logic this would be impossible.

[Adam S Latchford]

https://www.apterous.org/viewgame.php?g ... #r53049629

Pencilled that after seeing Dan and Ahmed declare it in COC despite nearly being a clear and obvious words (muppets)

Pretty sure mabati was declared in coc, then pencilled after filming by a coc player, then it aired for a different one

[Martin Hurst]

Possibly an unanswerable question, but.... has anyone ever 'pencilled' a new word on Countdown (i.e. made the first declaration of that word, as a max winner) before it was pencilled on Apterous. After apterous had bedded in, of course

I think there's a rule on the show that if it hasn't been declared on Apterous then it's not valid, so by that logic this would be impossible.

This can't be true can it?

[Martin Hurst]

Surprised nobody has asked this yet, but on the show which contestant has submitted the most words that were both added as part of the great influx of 2015 and subsequently recently removed?

[JackHurst]

Possibly an unanswerable question, but.... has anyone ever 'pencilled' a new word on Countdown (i.e. made the first declaration of that word, as a max winner) before it was pencilled on Apterous. After apterous had bedded in, of course

I think there's a rule on the show that if it hasn't been declared on Apterous then it's not valid, so by that logic this would be impossible.

This can't be true can it?

Yep I heard it straight from Mr Eadie. He also told me about the new 100pt word rule they are introducing. Any round where LLLGBUIE is in the selection you get 100pts for declaring an 8.

[Steve Hyde]

Surprised nobody has asked this yet, but on the show which contestant has submitted the most words that were both added as part of the great influx of 2015 and subsequently recently removed?

Can anyone beat four in https://wiki.apterous.org/Episode_8024 - RITUALITY, HENWARE, MIAGITE and OSETROVA?

[Steve Hyde]

Surprised nobody has asked this yet, but on the show which contestant has submitted the most words that were both added as part of the great influx of 2015 and subsequently recently removed?

Can anyone beat four in https://wiki.apterous.org/Episode_8024 - RITUALITY, HENWARE, MIAGITE and OSETROVA?

Episode 7932 equalis it with ALAZONS, LIFERENT, DOUGLAS and AMBREINE, with the first three being declared by both players

[Gavin Chipper]

I think Richard Brittain had 5 against Jon Corby but they weren't valid at the time.

[Marc Meakin]

Sorry if it's been asked before bit are there more 9 letter words that are plurals (ending in S) than those that don't.

On the same subject. If every conundrum 9 letter set from the first episode of the show was unique without repeats , how long before we would run out ?

[Peter Thomas]

What's the highest maximum score potential recorded in the standard 15 round game? (Episode 8400's was 165.)

[Steve Hyde]

What's the highest maximum score potential recorded in the standard 15 round game? (Episode 8400's was 165.)

175 - https://wiki.apterous.org/Episode_6745 , https://wiki.apterous.org/Episode_7341 and https://wiki.apterous.org/Episode_7945 . It'll be a while before we hit those heights again with the current dictionary

[Philip A]

What's the highest maximum score potential recorded in the standard 15 round game? (Episode 8400's was 165.)

175 - https://wiki.apterous.org/Episode_6745 , https://wiki.apterous.org/Episode_7341 and https://wiki.apterous.org/Episode_7945 . It'll be a while before we hit those heights again with the current dictionary

To be fair, the max in Episode 7341 would be only one point fewer without the OED words.

[Steve Hyde]

It has been a while since episode 7341

[Gavin Chipper]

Has it been asked what the most offered words are by contestants, and also contestants + DC combined? Which words are the real leotards?

[Peter Thomas]

Has there ever been more than two impossible numbers games in one show?

[Gavin Chipper]

I don't remember this being asked - what are the most commonly offered words ever on Countdown? Like top 50 or something.

Words sorted by the number of times they have been validly offered up to the end of series 69...

Code: Select all

     1. RATION       126
     2. TRAINED      125
     3. TRAILED      107
     4. RATIONS      102
     5. ROASTED       96
     6. POINTED       92
     7. PAINTED       90
     8. LOITERS       78
     9. PANTIES       77
    10. COATED        76
    11. COASTED       68
    12. DONATES       67
    13. GLOATED       66
    13. SOLDIER       66
    13. STAGED        66
    16. FLOATED       63
    16. ORANGES       63
    16. WAITER        63
    19. PAINTER       62
    19. RELATION      62
    21. BOASTED       61
    21. MOISTER       61
    21. REASON        61
    24. STONED        60
    25. FLOATER       58
    25. GORIEST       58
    25. STRAINED      58
    28. GOITRE        57
    28. LOITER        57
    28. PRAISED       57
    28. RADIOS        57
    32. POINTER       56
    33. DREAMS        55
    33. POSTAGE       55
    35. ELATION       54
    35. MOANERS       54
    35. PLAITED       54
    35. POLITE        54
    39. COASTER       53
    39. LOANERS       53
    39. MOIST         53
    39. RATIOS        53
    43. IMAGES        52
    44. FASTEN        51
    44. STAINED       51
    46. FAINTED       50
    46. TOILED        50
    46. WAITED        50
    49. POUTED        49
    50. FOISTED       48
    50. PARTIED       48
    50. WAITERS       48

Thanks for that, Graeme. No LEOTARD then!

This one's already been asked.

[L'oisleatch McGraw]

It does not have to be Graeme...
...but I need a few smart people's takes on the following.

Myself and my family do a thing every year where we get a tiny piece of red paper (1/16th of an A4 page), and on that paper we write a secret New Year's resolution. This resolution must be something that is precise (not vague), has defined parameters, and that MUST include either an element of luck, or take a lot of hard work to pull off.
This year my Red Resolution reads as follows:-

"Live stream the Apterous daily duel, to YouTube EVERY day this year."

Now here's the thing... tonight I got home very very late, started setting up the duel just before 11:50pm. then to my dismay it turned out to be an annoyingly long duel 17 rounds of Hyper. I tried to blitz through it, not caring about the score, only caring about getting it finished... but I did NOT get it finished... BUT I did get live stream it to YouTube as per resolution. [https://www.youtube.com/watch?v=OeV7nGwFfmc]

In your opinion, have I failed my Red Resolution without even getting halfway through January... or is it still a runner?

[Gavin Chipper]

Does it not let you finish it? I thought you could continue after midnight but it wouldn't count.

But anyway you did to some extent live stream the duel...

[L'oisleatch McGraw]

Nope, irritatingly at the stroke of midnight it will freeze.
Not even a glass slipper to show for it...

[JackHurst]

At a Co-event, suppose somebody were to use the deck of small number cards as a target generator (without replacement) before/after drawing the 6 numbers, you end up with some selections which are not possible.

100, 1, 2, 3, 4, 5 -> 666 (There aren't three 6 cards to draw for the target)
100, 9, 9, 1, 2, 3 -> 9xx, x9x, xx9, 11x, 1x1, x11 etc.

There are also no 0 tiles, so there can never be a target like x0x or xx0

Of all of the possible combinations of numbers rounds, what proportionare impossible to generate with this selection method?

---

Note for readers: Adam's board doesn't do this, I believe he has extra cards for generating a target, what a champ.

[Thomas Carey]

When I've seen this done people tend to use the 10 as a 0 in the target. Some board games have the extras cards too, my version has 3 of each. Definitely better

[Stephen R]

At a Co-event, suppose somebody were to use the deck of small number cards as a target generator (without replacement) before/after drawing the 6 numbers, you end up with some selections which are not possible.

100, 1, 2, 3, 4, 5 -> 666 (There aren't three 6 cards to draw for the target)
100, 9, 9, 1, 2, 3 -> 9xx, x9x, xx9, 11x, 1x1, x11 etc.

There are also no 0 tiles, so there can never be a target like x0x or xx0

Of all of the possible combinations of numbers rounds, what proportionare impossible to generate with this selection method?

---

Note for readers: Adam's board doesn't do this, I believe he has extra cards for generating a target, what a champ.

TL;DR - 34.2%, worse if you pick 6S, better if you pick 4L.

This will be quite long, because my chosen methodology involved splitting the selections up into a bunch of subcases. I think I've done the maths right, but no promises.

Let's start by working out how many possible numbers selections there are in total. This has already been done, and we have 11905457 selections if there are no restrictions. To work out which ones are impossible, we'll split these up by how many large numbers there are (as these won't affect the small number deck) and how many repeated small numbers there are. We'll also need to check selections with 10s in them separately, as a target can't have a leading zero.

In each case, the small numbers (not 10) will be represented by the letters a, b, c, d, e, f. Different letters represent different small numbers. The target will be represented by xyz, where x, y, z are the digits of the target. 10s in the small numbers deck will be called zeros.

We'll also make the assumption that a 10 can be used as a 0 when generating a target.

Note: 9C3 means "9 choose 3", the number of ways of selecting 3 objects from a set of 9.

Case 1: 4 large / 2 small

10, 10: 9 pairs in the deck
xyz target: 9C3 x 6 = 504
xxy target: 9 x 8C1 x 3 = 216
Total of 720 valid targets, 720 possible rounds

10, a: 8 pairs, 1 singleton, 1 zero in the deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 8 x 9C1 x 3 = 216
less 0xx (8) = 208
Total of 856 valid targets, x9 = 7704 possible rounds

a, a: 8 nonzero pairs, 1 zero pair in the deck
xyz target: 9C3 x 6 = 504
less 0bc (8C2 x 2) = 448
xxy target: 9 x 8C1 x 3 = 216
less 0xx (8) = 208
less 00x (8 x 2 + 1) = 191
Total of 639 valid targets, x9 (9 valid choices for a) = 5751 possible rounds

a, b: 7 nonzero pairs, 1 zero pair, 2 singletons in the deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 8 x 9C1 x 3 = 216
less 0xx (7) = 209
less 00x (9 x 2 + 1) = 190
Total of 838 valid targets, x9C2 (a, b) = 30168 possible rounds

Total of 44343 possible 4L rounds, out of a potential 49445 without restrictions (89.7%)

Case 2: 3 large / 3 small

10, 10, a: 8 pairs, 1 singleton in the deck
xyz target: 9C3 x 6 = 504
xxy target: 8 x 8C1 x 3 = 192
Total of 696 valid targets, x9 (a) x4 (larges) = 25056 possible rounds

10, a, a: 8 pairs, 1 zero in the deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 8 x 8C1 x 3 = 192
less 0xx (8) = 184
Total of 632 valid targets, x9 (a) x4 (larges) = 22752 possible rounds

10, a, b: 7 pairs, 2 singletons, 1 zero in the deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 7 x 9C1 x 3 = 189
less 0xx (7) = 182
Total of 830 valid targets, x9C2 (a, b) x4 (larges) = 119520 possible rounds

a, a, b: 7 nonzero pairs, 1 zero pair, 1 singleton in deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 8 x 8C1 x 3 = 192
less 0xx (7) = 185
less 00x (8 x 2 + 1) = 168
Total of 616 valid targets, x9x8 (a, b) x4 (larges) = 177408 possible rounds

a, b, c: 6 nonzero pairs, 1 zero pair, 3 singletons in deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 7 x 9C1 x 3 = 189
less 0xx (6) = 183
less 00x (9 x 2 + 1) = 164
Total of 812 valid targets, x9C3 (a, b, c) x4 (larges) = 272832 possible rounds

Total of 617568 possible 3L rounds, out of a potential 755160 without restrictions (81.8%)

Case 3: 2 large / 4 small

10, 10, a, a: 8 pairs in deck
xyz target: 8C3 x 6 = 336
xxy target: 8 x 7C1 x 3 = 168
Total of 504 valid targets, x9 (a) x6 (larges) = 27216 possible rounds

10, 10, a, b: 7 pairs, 2 singletons in deck
xyz target: 9C3 x 6 = 504
xxy target: 7 x 8C1 x 3 = 168
Total of 672 valid targets, x9C2 (a, b) x6 (larges) = 145152 possible rounds

10, a, a, b: 7 pairs, 1 singleton, 1 zero in deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 7 x 8C1 x 3 = 168
less 0xx (7) = 161
Total of 609 valid targets, x9x8 (a, b) x6 (larges) = 263088 possible rounds

10, a, b, c: 6 pairs, 3 singletons, 1 zero in deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 6 x 9C1 x 3 = 162
less 0xx (6) = 156
Total of 804 valid targets, x9C3 (a, b, c) x6 (larges) = 405216 possible rounds

a, a, b, b: 7 nonzero pairs, 1 zero pair in deck
xyz target: 8C3 x 6 = 336
less 0ab (7C2 x 2) = 288
xxy target: 8 x 7C1 x 3 = 168
less 0xx (7) = 161
less 00x (7 x 2 + 1) = 146
Total of 434 valid targets, x9C2 (a, b) x6 (larges) = 93744 possible rounds

a, a, b, c: 6 nonzero pairs, 1 zero pair, 2 singletons in deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 7 x 8C1 x 3 = 168
less 0xx (6) = 162
less 00x (8 x 2 + 1) = 145
Total of 593 valid targets, x9x8C2 (a, b, c) x6 (larges) = 896616 possible rounds

a, b, c, d: 5 nonzero pairs, 1 zero pair, 4 singletons in deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 6 x 9C1 x 3 = 162
less 0xx (5) = 157
less 00x (9 x 2 + 1) = 138
Total of 786 valid targets, x9C4 (a, b, c, d) x6 (larges) = 594216 possible rounds

Total of 2425248 possible 2L rounds, out of a potential 3317310 without restrictions (73.1%)

Case 4: 1 large / 5 small

10, 10, a, a, b: 7 pairs, 1 singleton in deck
xyz target: 8C3 x 6 = 336
xxy target: 7 x 7C1 x 3 = 147
Total of 483 valid targets, x9x8 (a, b) x4 (larges) = 139104 possible rounds

10, 10, a, b, c: 6 pairs, 3 singletons in deck
xyz target: 9C3 x 6 = 504
xxy target: 6 x 8C1 x 3 = 144
Total of 648 valid targets, x9C3 (a, b, c) x4 (larges) = 217728 possible rounds

10, a, a, b, b: 7 pairs, 1 zero in deck
xyz target: 8C3 x 6 = 336
less 0ab (7C2 x 2) = 294
xxy target: 7 x 7C1 x 3 = 147
less 0xx (7) = 140
Total of 434 valid targets, x9C2 (a, b) x4 (larges) = 62496 possible rounds

10, a, a, b, c: 6 pairs, 2 singletons, 1 zero in deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 6 x 8C1 x 3 = 144
less 0xx (6) = 138
Total of 586 valid targets, x9x8C2 (a, b, c) x4 (larges) = 590688 possible rounds

10, a, b, c, d: 5 pairs, 4 singletons, 1 zero in deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 5 x 9C1 x 3 = 135
less 0xx (5) = 130
Total of 778 valid targets, x9C4 (a, b, c, d) x4 (larges) = 392112 possible rounds

a, a, b, b, c: 6 nonzero pairs, 1 zero pair, 1 singleton in deck
xyz target: 8C3 x 6 = 336
less 0ab (7C2 x 2) = 294
xxy target: 7 x 7C1 x 3 = 147
less 0xx (6) = 141
less 00x (7 x 2 + 1) = 126
Total of 420 valid targets, x9C2x7 (a, b, c) x4 (larges) = 423360 possible rounds

a, a, b, c, d: 5 nonzero pairs, 1 zero pair, 3 singletons in deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 6 x 8C1 x 3 = 144
less 0xx (5) = 139
less 00x (8 x 2 + 1) = 122
Total of 570 valid targets, x9x8C3 (a, b, c, d) x4 (larges) = 1149120 possible rounds

a, b, c, d, e: 4 nonzero pairs, 1 zero pair, 5 singletons in deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 5 x 9C1 x 3 = 135
less 0xx (4) = 131
less 00x (9 x 2 + 1) = 112
Total of 760 valid targets, x9C5 (a, b, c, d, e) x4 (larges) = 383040 possible rounds

Total of 3357648 possible 1L rounds, out of a potential 5221392 without restrictions (64.3%)

Case 5: 0 large / 6 small

10, 10, a, a, b, b: 7 pairs in deck
xyz target: 7C3 x 6 = 210
xxy target: 7 x 6C1 x 3 = 126
Total of 336 valid targets, x9C2 (a, b) = 12096 possible rounds

10, 10, a, a, b, c: 6 pairs, 2 singletons in deck
xyz target: 8C3 x 6 = 336
xxy target: 6 x 7C1 x 3 = 126
Total of 462 valid targets, x9x8C2 (a, b, c) = 116424 possible rounds

10, 10, a, b, c, d: 5 pairs, 4 singletons in deck
xyz target: 9C3 x 6 = 504
xxy target: 5 x 8C1 x 3 = 120
Total of 624 valid targets, x8C4 (a, b, c, d) = 43680 possible rounds

10, a, a, b, b, c: 6 pairs, 1 singleton, 1 zero in deck
xyz target: 8C3 x 6 = 336
less 0ab (7C2 x 2) = 294
xxy target: 6 x 7C1 x 3 = 126
less 0xx (6) = 120
Total of 414 valid targets, x9C2x7 (a, b, c) = 104328 possible rounds

10, a, a, b, c, d: 5 pairs, 3 singletons, 1 zero in deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 5 x 8C1 x 3 = 120
less 0xx (5) = 115
Total of 563 valid targets, x9x8C3 (a, b, c, d) = 283752 possible rounds

10, a, b, c, d, e: 4 pairs, 5 singletons, 1 zero in deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 4 x 9C1 x 3 = 108
less 0xx (4) = 104
Total of 752 valid targets, x9C5 (a, b, c, d, e) = 94752 possible rounds

a, a, b, b, c, c: 6 nonzero pairs, 1 zero pair in deck
xyz target: 7C3 x 6 = 210
less 0ab (6C2 x 2) = 180
xxy target: 7 x 6C1 x 3 = 126
less 0xx (6) = 120
less 00x (6 x 2 + 1) = 107
Total of 287 valid targets, x9C3 (a, b, c) = 24108 possible rounds

a, a, b, b, c, d: 5 nonzero pairs, 1 zero pair, 2 singletons in deck
xyz target: 8C3 x 6 = 336
less 0ab (7C2 x 2) = 294
xxy target: 6 x 7C1 x 3 = 126
less 0xx (5) = 121
less 00x (7 x 2 + 1) = 106
Total of 400 valid targets, x9C2x7C2 (a, b, c, d) = 302400 possible rounds

a, a, b, c, d, e: 4 nonzero pairs, 1 zero pair, 4 singletons in deck
xyz target: 9C3 x 6 = 504
less 0ab (8C2 x 2) = 448
xxy target: 5 x 8C1 x 3 = 120
less 0xx (4) = 116
less 00x (8 x 2 + 1) = 99
Total of 547 valid targets, x9x8C4 (a, b, c, d, e) = 344610 possible rounds

a, b, c, d, e, f: 3 nonzero pairs, 1 zero pair, 6 singletons in deck
xyz target: 10C3 x 6 = 720
less 0ab (9C2 x 2) = 648
xxy target: 4 x 9C1 x 3 = 108
less 0xx (3) = 105
less 00x (9 x 2 + 1) = 86
Total of 734 valid targets, x9C6 (a, b, c, d, e, f) = 61656 possible rounds

Total of 1387806 possible 6S rounds, out of a potential 2562150 without restrictions (54.2%)

In total, of the 11905457 potential numbers rounds, 7832613 are possible with a standard deck of numbers cards using this method (65.8%). Just over a third of all numbers rounds are impossible to achieve.

The selection with the most available target numbers is 4L 10 a, with 856/899. The selection with the fewest available target numbers is 6S with three pairs of numbers, with 287/899.

[George Armstrong]

Or tl;dr use an rng - https://co-host.netlify.app/ <3

[Adam Dexter]

Has there ever been more than two impossible numbers games in one show?

Unsure if you mean totally impossible to score, or impossible to get 10 points.

If the latter, this fits the bill for 3. It's probably more common in series finals, due to the propensity to pick more awkward selections.

[Andy McGurn]

This week Pam Hill made a reappearance, she is the fourth of my opponents in my octorun to return (in regular heat games). Am I the only octochamp to have four opponents from my run reappear?

Also which other octochamps have had the most opponents later return?

[Fiona T]

During my telly run, I declared two words twice - adjoiner (no longer valid ) and watering.

3 part question -

a) what's the most times someone has declared the same one word in their telly run

b) what's the most number of different words that a player has declared more than once

c) has anyone declared 3 different words 3 times each (or 4, 4 or more?)

Thank you

[Ian Volante]

During my telly run, I declared two words twice - adjoiner (no longer valid ) and watering.

3 part question -

a) what's the most times someone has declared the same one word in their telly run

b) what's the most number of different words that a player has declared more than once

c) has anyone declared 3 different words 3 times each (or 4, 4 or more?)

Thank you

If I remember right, I think I managed two pairs (RELATIONS, SOUTANE).

[Peter Thomas]

Very nearly a nine letter Q-word in the selections today. Has this ever happened? What are the lowest probability words to come up?

[Johnny Canuck]

Very nearly a nine letter Q-word in the selections today. Has this ever happened? What are the lowest probability words to come up?

The Dinos Sfyris-Kai Laddiman special had QUODLIBET available

[Mark Deeks]

CUNJEVOIS has to be up there too.