Winning with as small a word knowledge as possible

[Craig Beevers]

No idea if anything like this has been discussed before but I was reading another thread which gave me an idea for something that could be quite interesting in a Steve Davis kind of way.

The hypothetical scenario is that a bloke goes on Countdown and writes down say 100 words on his pad from memory. During a letters game he goes through the 100 words and sees if any of them are in the selection and picks the best one. He spots those words (with 100% accuracy) and only those words. If none of them come up he scores zilch. Ignoring the other rounds (numbers & conundrum) what would be the best 100 words for hypothetical bloke to memorise? Is it possible to beat a decent proportion of opponents just using that many words? And so on.

It's something I'm curious about, my hunch is you could probably win pretty often with more like 500 words as so many come up time and again.

I'm counting stuff like LEOTARD and LEOTARDS as two different words by the way.

[Charlie Reams]

It's an interesting question. I think Sid had some ideas about this, I'll prod him in the direction of this topic.

[Ryan Taylor]

I have no statistical input that I can offer. But based on a hunch I reckon 100 words would be far too few to ensure winning a game against normal opposition. 500 words is definitely more like it but yeah I pretty much have no idea.

[Gavin Chipper]

How many words did Sponge know when it started beating people?

[Kai Laddiman]

How many words did Sponge know when it started beating people?

I'm sure one could estimate based on the number of games it'd played before its first game, but for some reason it doesn't have Superstats while the other bots do.

[Charlie Reams]

I came up with a rough strategy for learning words based on learning maxes which don't co-occur with other maxes and so on. This may be the exact same idea that Sid had, I can't remember, but some credit goes to him either way.

So based on my sample of 100,000 rounds (which is not many, I know, but I will update these numbers when the hardware allows), you can max more than 1% of rounds with just 20 words:- ANEROIDS, APNOEA, ASTEROID, DARIOLE, DIATOM, DONATES, NOTATES, OPALINE, OPIATES, PAROTID, PROTEAN, RADIATE, RATIONED, RETINOL, ROADIES, ROMANISE, TALONED, TARDIER, TOADIES and UNIPEDS. I imagine most people reading this were familiar with all of those.

With a 100 words, you can get up to 3.7% maxes, which is still not really enough to be dangerous -- the 100th word is RADIOS. Learning up to the 500th word, FATTIER, gets you to a more respectable 11.6%, or (throwing in numbers and conundrum) 5.3 maxes a game.

To turn it around, let's assume for the sake of argument that you wanted to max half the rounds (decent octochamp form) and you nail all the numbers and conundrums, so you need about 31.8% maxes on the letters. You'd also be scoring fairly solidly on the rounds you didn't max, since you've picked up a lot of high probability stuff. How many words would you need to learn? By my very rough reckoning, no more than 2,800. That's about a quarter of the average person's working vocabulary.

A few facts about those 2,800: only 35 of them are nines, even though a nine is certainly the max whenever it occurs; 801 are eights, 1265 are sevens, 550 are sixes, and the remainder are fives except for PAUA, the only 4. I'd be interested to know how far down the list the top players have to go before they start learning anything new. At a glance I can see a handful of words in the top 500 which are new to me (RAMOSE, ADNATE, TAMARI, NEUMES), generally shorter words since those are presumably less well-studied. But better players probably know those too.

You could probably do even better with a different word learning strategy, or taking into account non-max words more directly, but I'll leave that to someone else. At some point I'll re-run the numbers with a larger sample and post the top few thousand words for everyone to review.

[Craig Beevers]

I reckon you could probably beat a few opponents on the letters rounds with no or very few maxes, consistently scoring would be enough. Is it possible to figure out raw score or things like how often in rounds you'd score?

[Rhys Benjamin]

Two words: Apterous Prune

[Charlie Reams]

I reckon you could probably beat a few opponents on the letters rounds with no or very few maxes, consistently scoring would be enough. Is it possible to figure out raw score or things like how often in rounds you'd score?

The difficulty with that is that your score becomes very dependent on what your opponent knows and can spot, which we don't have any good model for. However for your amusement I could simulate what such a player would've scored in, say, all the Classic games and see how s/he would've done.

[Craig Beevers]

Yea sure running it through any actual games would be good.

[Charlie Reams]

So it looks like I significantly overestimated how good the Nugget would need to be. Of the 3286 Classic games in the database, he could be armed with only 2721 words and still win about 90% of them (ignoring strategic considerations). At the other end of the scale, if we assume the other player got every conundrum (even if they didn't in the real game), the Nugget still wins 71%. And even then the average winning margin is around 15 points, so you could weaken the numbers quite considerably too and still have a better-than-even chance of winning.

Most of the lost games are fairly predictable, like an 83-point defeat in the famous Fell 146, but a few of them are quite curious. For example the Nugget would be 24 points behind before the conundrum against Beth Sutton here.

(Oh and the database is somewhat biased towards high-level games, so the real figures are probably even higher.)

[Craig Beevers]

So it looks like I significantly overestimated how good the Nugget would need to be. Of the 3286 Classic games in the database, he could be armed with only 2721 words and still win about 90% of them (ignoring strategic considerations). At the other end of the scale, if we assume the other player got every conundrum (even if they didn't in the real game), the Nugget still wins 71%. And even then the average winning margin is around 15 points, so you could weaken the numbers quite considerably too and still have a better-than-even chance of winning.

Most of the lost games are fairly predictable, like an 83-point defeat in the famous Fell 146, but a few of them are quite curious. For example the Nugget would be 24 points behind before the conundrum against Beth Sutton here.

(Oh and the database is somewhat biased towards high-level games, so the real figures are probably even higher.)

Interesting. Thanks.

I presume multiple anagram sets have only one of the anagrams included?

Also was the average uniqueness of a max factored into the original list of maximum occurrence? As in if a word is a maximum, how many other maximums are there - does a particular maximum tend to crop up in very flat rounds. This element would obviously increase the rank of 9s (particularly if the score - 18 points - was part of the equation), and lower the rank of high probability 6s-8s. An optimum Nugget word knowledge would probably combine some high average equity loss words (ones that are often Darrenic etc.), with a good spread of high probability words and the odd shorter word.

Anyway time for my statistical brain to have a rest for the day.

Anyway

[Jon Corby]

I thought this thread was going to be about Kirk.

[Charlie Reams]

Interesting. Thanks.

I presume multiple anagram sets have only one of the anagrams included?

Also was the average uniqueness of a max factored into the original list of maximum occurrence? As in if a word is a maximum, how many other maximums are there - does a particular maximum tend to crop up in very flat rounds. This element would obviously increase the rank of 9s (particularly if the score - 18 points - was part of the equation), and lower the rank of high probability 6s-8s. An optimum Nugget word knowledge would probably combine some high average equity loss words (ones that are often Darrenic etc.), with a good spread of high probability words and the odd shorter word.

Anyway time for my statistical brain to have a rest for the day.

Anyway

Basically what I did was:

Take the word which occurs most as a max.
Ignore all rounds in which that word was a max.
Take the word which occurs most as a max in the remaining rounds.
Ignore all... etc

until the total % of maxed rounds was greater that 31.8. (So anagrams get removed automatically.) Ties are broken arbitrarily, which is a weakness. Overall it's pretty rough but quite easy to implement as a database query so that's the balance I struck. Smarter strategies would probably do even better, so you can consider the figures above to be lower bounds on how well you could do with that amount of learning. For example we don't currently give any credit to words which are often one away from the max but rarely the max. I'll see if I can integrate some of your ideas and rerun the numbers. This is quite a nice way to build a study list.

I thought this thread was going to be about Kirk.

[David Williams]

A long while back I think I raised a similar question. Suppose someone with total recall and impeccable word-spotting skills, but no knowledge of English (like a computer), started watching Countdown, and forming a vocabulary solely of words offered by contestants and Dictionary Corner. How long would it take before they became competitive?

Any way of checking that out these days?

[Charlie Reams]

A long while back I think I raised a similar question. Suppose someone with total recall and impeccable word-spotting skills, but no knowledge of English (like a computer), started watching Countdown, and forming a vocabulary solely of words offered by contestants and Dictionary Corner. How long would it take before they became competitive?

Any way of checking that out these days?

We ran that exact experiment on apterous. Sponge scored his first win after just 19 games. After 1626 games he's almost unbeatable (in English). At some point I should probably do a graph of the transition.

[Charlie Reams]

As promised. Note this only includes Standard-variant English games.

[Jon Corby]

Spongespots Rareplants.

[David Williams]

I didn't know about that. I can't read the numbers on your chart, but it got 'competitive' fairly quickly by the looks of it. I guess it would have been slower in real life as DC don't give as many words, but then again in real life I imagine the average standard of contestants is lower.

[Charlie Reams]

I can't read the numbers on your chart

Click for big version.

[Ben Wilson]

A long while back I think I raised a similar question. Suppose someone with total recall and impeccable word-spotting skills, but no knowledge of English (like a computer), started watching Countdown, and forming a vocabulary solely of words offered by contestants and Dictionary Corner. How long would it take before they became competitive?

Any way of checking that out these days?

We ran that exact experiment on apterous. Sponge scored his first win after just 19 games. After 1626 games he's almost unbeatable (in English). At some point I should probably do a graph of the transition.

I still think an 'Apterous Soap' style experiment (or anti-sponge, whatever) would be interesting to see just how quickly it descends through the ranks. I reckon it'd still be competitive at the hyper variants for a good long while.

[Craig Beevers]

Apterous Sieve presumably.

Suppose you could go more complex and mimic a human memory, have words stay for a certain period of time or use like a cardbox system if words come up frequently enough during a period that they 'stick' for longer. I presume the 'difficulty' of conundrums is used for the bots to determine a rough response time? That would go well with the human aspect. Anyways enough procrastination.

[Gavin Chipper]

Apterous Sieve presumably.

Suppose you could go more complex and mimic a human memory, have words stay for a certain period of time or use like a cardbox system if words come up frequently enough during a period that they 'stick' for longer. I presume the 'difficulty' of conundrums is used for the bots to determine a rough response time? That would go well with the human aspect. Anyways enough procrastination.

Just allow human players on Apterous.

[Lesley Hines]

Just allow human players on Apterous.

And you said that on Prune's birthday too. Man, that's cruel.