Listener 4158 - Two Little Words by Danda

[starwalker]

Another week, another puzzle, another debut.
Straightforward and fairly easy. Once the phrase is found everything falls neatly.
Thanks D and A (?)

[TheBear69]

Staurologist, your math is a bit off, I think.

If there are 500 entries, your chance of NOT being winning one of the three prizes is 499/500 * 498/499 * 497/498 = 497/500 = .994

The number of weeks you have to enter until your odds of NOT winning drop below 50% then is n where (.994)^n = .5.


n*log(.994) = log(.5)

n = log(.5)/log(.994) ~= 115

Note that this computation is greatly skewed by the assumption that each week has 500 entries. Suppose there are in two tweeks there are 900 entries and 100 entries respectively. Then the odds of NOT winning are 897/900 * 97/100 < .97 whereas two weeks in a row with 500 results in still > 99% and of course if there are 997 entries one week followed by 3 the next (and you are fortunate enough to be one of the geniuses among the 3), then the average number of entires is still 500 but you are 100% certain to be a winner.

[TheBear69]

"What's more irritating than a nice, satisfying solve - as this was - full of clever but accessible clues, followed by a last step out of all proportion difficulty-wise to what has preceded it - simply for the sake of being difficult."

And I have to disagree with that...if you really solved the clues, then you will have already identified the letters absent from the wordplay and thus the key phrase is apparent and the last step is quiite easy, except arguably that one ironic entry.

Now last week's final step, to me, was tough, after an easy grid fill; so we each have our own blind spots to overcome, I guess.

[contendo]

TheBear - The spread of the number of entries is actually surprisingly narrow. Last year the highest number was 718 and the lowest 291, though I know this doesn't alter the basis of your argument.

To change the subject, I like clues where the subtlety lies in the definition rather than the wordplay. 33D is a good example.

[ichkeria]

""What's more irritating than a nice, satisfying solve - as this was - full of clever but accessible clues, followed by a last step out of all proportion difficulty-wise to what has preceded it - simply for the sake of being difficult."

And I have to disagree with that...if you really solved the clues, then you will have already identified the letters absent from the wordplay and thus the key phrase is apparent and the last step is quiite easy, except arguably that one ironic entry. "

No, you've misunderstood my point. I wasn't criticising the puzzle - I was praising it for not trying to compensate for its (alleged) lack of difficuly hitherto, with a pointlessly obscure final step.

[Alan7777]

Having only recently started challenging myself with the Listener, either I'm improving or the last three weeks have been relatively easy - assuming that my solutions are correct.

On the subject of winning prizes, I submitted solutions to The Times Jumbo for several years and was lucky twice in about 18 months. I still do the crossword but don't bother to submit. Based on the probabilities calculated by TB69 I think I'm going to have to buy the latest BRB rather than hope I get lucky.

[Ruthrobin]

Alan7777, it is a fine thing to possess, though I am reeling from a spelling error I have just spotted on page 64 of the red-edged new section - exactly half way down the page.

[Alan7777]

Besides the BRB, what books and electronic sources do people tend to use? I've a birthday coming up.

[tenflags]

Arrrr the bear now I see why you are such a whizz at the numericals..
I find those probability things interesting - a bit like the monty hall problem.

Is there another numerical one on the horizon or are we done with numbers for this year..? I can't remember how many we have done.

In any event we must be due a tough puzzle soon I reckon.

[perseverer]

Tenflags - Numerical due 18/19 November. Penultimate Saturdays of Feb, May, Aug, Nov.

Alan7777 - Bradford's Crossword Dictionary is well worth getting f you don't have it. Online Chambers Word Wizard and Quinapalus Word Matcher are invaluable (though bear in mind neither use the content of the BRB,)

http://www.chambersha...ards/wwizards.py/main

http://www.quinapalus.com/matcher.html

[dead-eye]

Alan7777,having won a Chambers Crossword Dictionary as one of my prizes last year(sorry everyone)it has proved to be of immense benefit and I strongly recommend it. My Birthday is fast approaching as well. Hoping for a new BRB.

[Alan7777]

Perseverer - many thanks.

[AndrewG-S]

TB69, thank you for the more detailed analysis. I should then have my first win on the 7 July next year.

[Staurologist]

Thanks to TB69 for an excellent analysis. To put it into context, you will need to submit about 500 correct entries, with a weekly entry of 500, to have a 95% chance of winning. More generally, you will need to submit about x correct entries with a weekly entry of x to have a 95% chance of winning. This is approximately true down to very low numbers of entries, three being the reductio ad absurdum (although it has happened). Keep trying AndrewG-S >:)

[Staurologist]

Following the discussion about grid sizes, here, for cross-reference, are the widths (in cm) of the 15 x 15 cryptic blocked grids in a selection of UK papers, as measured this week:

FT 7.2
Guardian 8.3
Telegraph 8.3
Observer (Everyman) 8.3
Sunday Times 9.0
Times 10.3
Independent 10.4
TLS 10.8

Is there an ideal size?

For comparison, the 15 x 15 barred grid in the Spectator is 8 cm wide and the 12 x 12 Azed and Mephisto are 8.2 and 9.0 cm respectively.

[Staurologist]

Apologies to the Spectator. It is a 14 x 14 grid.

[Ruthrobin]

Thanks, Staurologist and the Bear69 (for dashing any hope I had of winning!) but that information is very useful. I know that the IQ Editor has more constraints on space than the EV Editor (and that is evident if you look at clue length and grid size). My feeling is that the more space crosswords fill, the better off we are. We'll watch for your name next July, AndrewG-S (but I don't think statistics work that way) - I don't ever expect to win; that way I shall never be disappointed.

[trux]

fascinating stuff, everyone - do you think there is any restriction on one particular person winning too often ? (And who, indeed, is the current holder of the Jammy Cup ?) Perhaps, like setters, the powers that be should not allow two appearances in winners' row in the same calendar year ? And then what would be the odds of an all-correct person winning ? Over to you TB69 - (assume only 500 weekly but only 50 all-correct - or does that not make a difference ?) ... No wonder I don't like numericals ....

[TheBear69]

My apologies to ichkeria!

OK, if there are 500 correct entries each week and no repeated winners are allowed then the odds of not winning are and it's the same 500 entrants:

Week 1: 499/500 * 498/499 * 497/498 = 497/500
Week 2: (Only 497 entries are eligible now): 496/497*495/496*494/495 = 494/497 => odds of not winning for both weeks = 494/500
Week 3: (Only 494 entries are eligible now): 491/494 => odds of not winning for all 3 weeks = 491/500
...
Week 52: Only 347 entries left: 344/347 ... odds of NOT winning all year = 344/500, which is still not very good!

Of course there are a lot of assumptions built in such as the assumption that it's the same set of entrants each week.

Note that this is equivalent to having the competition for a single week and giving out 156 prizes: 499/500 * 498/499 * ... * 344/345 = 344/500.

[TheBear69]

"assume only 500 weekly but only 50 all-correct - or does that not make a difference ?"

That's a lot harde (at least to get a precise answer). You need to know something about the likelihood of a person being among the 450 people who are correct in a week but not among the 50 all-correct. If person A is correct 51 times then you need to perturb the above computation with factors for the chance that person A is among the already-winners and the 51/52 probability that he is among that week's 500. If person B win's week 1 and is never correct again then the pool of eligible winners does not decrease in size due to B. Too complicated for me!

[contendo]

Talking of prizes, in the 1980s the prize used to be a book token for £15 (£15 in 1980 = £56 today) with an "Ex Libris --- Listener Crossword Prize" label to stick in your chosen book. I still have my Times Atlas from that era. It's a much better idea than a BRB which most solvers will already have, but no doubt The Times get a special deal from Chambers.