One quiz at a time

Doggett · Post by **Doggett** » 23:52 Mon 20 Mar 2017

Right ankle?

Post by **PhilW** » 07:00 Tue 21 Mar 2017

Doggett wrote: ↑23:52 Mon 20 Mar 2017Right ankle?

Best Western?

Post by **flash_uk** » 11:35 Tue 21 Mar 2017

PhilW wrote: ↑07:00 Tue 21 Mar 2017
Doggett wrote: ↑23:52 Mon 20 Mar 2017Right ankle?

Best Western?

Nope.

Doggett · Post by **Doggett** » 12:32 Tue 21 Mar 2017

Marriott?

Post by **PhilW** » 12:34 Tue 21 Mar 2017

jdaw1 wrote: ↑23:32 Mon 20 Mar 2017I can’t yet see what is the optimal guessing strategy.

Instinct suggests to me to halve the space, once a range is determined, by guessing half-way outside the known range.

To define the search space initially requires a minimum of three guesses, where the middle guess is the best (i.e. we require the best guess plus at least one either side of it). For example, A,B,C where A < B < C and B is closest; for sake of argument in this case, A is second, C is third.

Therefore:
B-X < X-A => X > (B+A)/2
X-A < C-X => X < (C+A)/2

This provides the initial bounds for a known range (essentially using the half-way position between each pair of the top two guesses). This can be halved with each subsequent guess, by guessing a half-range distance outside the known range in the opposite direction from second best. In this case therefore, the next guess would be:

D = Upper bound (since 2nd best is lower) + half range
D = (C+A)/2 + ( (C+A)/2 - (B+A)/2 )
D = (2C+A-B)/2

The order of guesses from best to worst will now either be BDA or BAD, in either case determining the upper or lower half of the previous range as the new valid range.

Notes:
- Additional points previously guessed outside this range provide no additional data (unless they already provided it previously and there has been redundancy in the later (and best) guesses.
- Guessing within the range can provide better or worse information than the 50% reduction strategy above. The reduction by guessing in the range *might* be a normal distribution depending on X, B and D, but seems to me more likely that the mean reduction in range would be less than 50%, based on perception of likelihood of being being proportionately more likely to be near the centre of the range, and then the reduction in range to be from half-way between B and new guess to the other limit end most of the time. If true, then the above halving strategy would be superior to guessing in the range, at least until the range is small enough that the chance of correct guess skews the probability for range reduction.

Post by **PhilW** » 12:37 Tue 21 Mar 2017

Novotel/Sofitel ?

Old Bridge · Post by **Old Bridge** » 13:01 Tue 21 Mar 2017

flash_uk wrote: ↑21:12 Mon 20 Mar 20172830

A lucky guess or a brilliant deductive power?
Well done.

Old Bridge · Post by **Old Bridge** » 13:07 Tue 21 Mar 2017

Hilton Hotels

Post by **PhilW** » 13:48 Tue 21 Mar 2017

Premier Inn?

Old Bridge · Post by **Old Bridge** » 14:04 Tue 21 Mar 2017

Radisson

Post by **PhilW** » 14:08 Tue 21 Mar 2017

Four pillars?

Old Bridge · Post by **Old Bridge** » 16:15 Tue 21 Mar 2017

Doubletree

Post by **flash_uk** » 17:00 Tue 21 Mar 2017

Old Bridge wrote: ↑13:01 Tue 21 Mar 2017
flash_uk wrote: ↑21:12 Mon 20 Mar 20172830
A lucky guess or a brilliant deductive power?
Well done.

Was employing the halfway point (roughly) in the range strategy!

Post by **flash_uk** » 17:01 Tue 21 Mar 2017

Old Bridge wrote: ↑14:04 Tue 21 Mar 2017 Radisson

Yes indeed, it was the Radisson Blu in Belfast. Your question.

Old Bridge · Post by **Old Bridge** » 17:09 Tue 21 Mar 2017

Rock and roll.
Port.
Find the one word I'm thinking connects the two very well.

Doggett · Post by **Doggett** » 17:22 Tue 21 Mar 2017

Berry

Old Bridge · Post by **Old Bridge** » 17:27 Tue 21 Mar 2017

Doggett wrote: ↑17:22 Tue 21 Mar 2017Berry

Brilliant! (Or too easy)
Your question Doggett.

Doggett · Post by **Doggett** » 20:21 Tue 21 Mar 2017

Old Bridge wrote: ↑17:27 Tue 21 Mar 2017 Brilliant! (Or too easy)

Let's go with brilliant

The question is:

How many many founding members were there of the Oporto British Club in May 1903, having paid £22 (100 milreis) each?

Post by **flash_uk** » 20:34 Tue 21 Mar 2017

Post by **jdaw1** » 20:46 Tue 21 Mar 2017

Doggett · Post by **Doggett** » 21:11 Tue 21 Mar 2017

Mike is closest so far...

Post by **jdaw1** » 21:21 Tue 21 Mar 2017

But the best guess can be irrelevant. Consider 24 is the best; 12 is second; 30 is third; and 8 is fourth.

Doggett · Post by **Doggett** » 21:32 Tue 21 Mar 2017

jdaw1 wrote: ↑21:21 Tue 21 Mar 2017 But the best guess can be irrelevant. Consider 24 is the best; 12 is second; 30 is third; and 8 is fourth.

Mike is still the closest. If there is another guess then Phil's logic may then be applied and tested.

Post by **PhilW** » 21:43 Tue 21 Mar 2017

Post by **PhilW** » 21:55 Tue 21 Mar 2017

jdaw1 wrote: ↑21:21 Tue 21 Mar 2017 But the best guess can be irrelevant. Consider 24 is the best; 12 is second; 30 is third; and 8 is fourth.

Correct, but only at the time range is first established, or in the case of non-optimal guesses following range establishment. In some cases it would be possible when range is first established, to tighten that range based on previous guesses, and then proceed optimally. In others it may be that a non optimal guess may have been made after the range was established. You example could either of those cases depending on order of the guesses.

Post by **jdaw1** » 22:23 Tue 21 Mar 2017

Doggett · Post by **Doggett** » 22:50 Tue 21 Mar 2017

jdaw1 wrote: ↑22:23 Tue 21 Mar 201740?

Closest with 22 second, 6 in third and 108 trailing in the rear.
Edited after I saw Phil's guess

Post by **jdaw1** » 22:59 Tue 21 Mar 2017

Nice. So 40 is the best, and irrelevant.
• 6 worse than 108 says >57.
• 22 better than 108 says <65.
These bounds don’t use 40.

But what’s the best guess?

Edit: cancel that. Questioner changed answer.

• 6 better than 108 says <57.
• 40 better than 22 says >31.

But what’s the best guess?

Post by **flash_uk** » 23:06 Tue 21 Mar 2017

Doggett · Post by **Doggett** » 00:01 Wed 22 Mar 2017

40 is still the closest

Old Bridge · Post by **Old Bridge** » 06:11 Wed 22 Mar 2017

Doggett · Post by **Doggett** » 07:20 Wed 22 Mar 2017

Old Bridge wrote: ↑06:11 Wed 22 Mar 201741

We have a new closest.

Old Bridge · Post by **Old Bridge** » 08:19 Wed 22 Mar 2017

Doggett · Post by **Doggett** » 08:58 Wed 22 Mar 2017

Old Bridge wrote: ↑08:19 Wed 22 Mar 201748

Equal second...which should do it.

Old Bridge · Post by **Old Bridge** » 09:02 Wed 22 Mar 2017

Doggett · Post by **Doggett** » 09:10 Wed 22 Mar 2017

Old Bridge wrote: ↑09:02 Wed 22 Mar 201744

We have a winner... I believe we would have got there even quicker if Jdaw had had time to split his >31 and <57.

Anyway... The position of question master returns to Norway.

Post by **PhilW** » 09:15 Wed 22 Mar 2017

jdaw1 wrote: ↑22:59 Tue 21 Mar 2017But what’s the best guess?

An interesting point to note is that the "best" guess depends on whether the priority is to complete the game as quickly as possible, or to be the one who provides the winning guess.

At any time, with a range of N values remaining as possible:
- the strategy of guessing outside the range will reduce the range quickest, leading to smallest number of guesses required BUT the person guessing will be guessing values they know to be wrong, so no chance of winning until that final guess.
- with a 1/N chance of guessing the correct value, guessing the edge value keeps the range as wide as possible for your competitors, so could be argued as best competitive strategy.
- guessing within the range is a compromise between the two. You reduce the range for the subsequent competitor, but you do at least have a chance of winning as well; a fair collaborative strategy with chance of winning for all.

Old Bridge · Post by **Old Bridge** » 09:29 Wed 22 Mar 2017

Just wondering.
Does a reply from the questionmaster count as leave to make a new attempt, or do I have to wait my turn until someone comes up with a new guess?
If the latter, I think I might have broken the rule of the game and stand in shame.
If not, I shall try to come up with a new meaningless question soon.
Please advice.

Post by **flash_uk** » 09:55 Wed 22 Mar 2017

Haha. Yes supppsed to wait until someone else guesses. Might as well go ahead with a question though

Old Bridge · Post by **Old Bridge** » 10:02 Wed 22 Mar 2017

Thank you!

Old Bridge · Post by **Old Bridge** » 10:10 Wed 22 Mar 2017

Another guessing game.
My cellar contains: Wine, Fortified wine and whisk(e)y.
How old is the oldest?

Post by **flash_uk** » 10:32 Wed 22 Mar 2017

Old Bridge · Post by **Old Bridge** » 10:49 Wed 22 Mar 2017

Nearest so far.

Post by **PhilW** » 11:00 Wed 22 Mar 2017

flash_uk wrote: ↑10:32 Wed 22 Mar 20171832

... days, weeks, months or years old? Just trying to stop Mike claiming later that he meant months, when 153 years old turns out to be the right answer.

Old Bridge - do you want age (how old) or vintage guesses?

1927 / 90 years old (and just realised I should have guessed 1862 - the same whether vintage or months old)

Old Bridge · Post by **Old Bridge** » 11:05 Wed 22 Mar 2017

How old, as in 3 years old.

Post by **PhilW** » 11:06 Wed 22 Mar 2017

PhilW wrote: ↑11:00 Wed 22 Mar 201790 (years old)

Old Bridge · Post by **Old Bridge** » 11:15 Wed 22 Mar 2017

closest so far

Post by **flash_uk** » 11:47 Wed 22 Mar 2017

1888 (129 years old)

Old Bridge · Post by **Old Bridge** » 12:02 Wed 22 Mar 2017

2nd best guess.

CPR 1 · Post by **CPR 1** » 14:26 Wed 22 Mar 2017