Twenty questions strategy

From: Gretchen Caldwell (boston.rott@verizon.net) | Date: 2006-06-16 13:06:02 UTC-04:00

Ok, I had to be a geek and google this. Here is from Wikpedia:

"The game suggests that the information (as measured by Shannon
's entropy
statistic) required to
identify an arbitrary object is about 20 bits
. The game is often used as an example
when teaching people about information theory
. Mathematically, if each
question is structured to eliminate half the objects, twenty questions will
allow the questioner to distinguish between 220 or 1,048,576 objects.
Accordingly, the most effective strategy for Twenty Questions is to ask
questions that will split the field of remaining possibilities roughly in
half each time. The process is analogous to a binary search algorithm
in computer
science."

:-)

BostonRott

[Non-text portions of this message have been removed]

Re: [LbNA] Twenty questions strategy

From: (LundyandVickster@aol.com) | Date: 2006-06-16 20:48:53 UTC-04:00

Folks,

I have a theory.

Right now we stand at 88 communities remaining. If we use the best approach
as posted by Boston Rott (see below), after our next question (#11) we will be
down to 44, then 22 (#12) and so on until question # 17 gets us to 1
community. This will leave us 3 questions to figure out which rock it is under. This
may be all we need but for some reason, I don't think so.

Now starting at question 17 and working our way back to where we are today
and doubling it each time, we only need to be at 64 after the next question to
still get down to 1 after 17 questions (see the following chart).

After Q 10 = 88
After Q 11 = 44 or 64
After Q 12 = 22 or 32
After Q 13 = 11 or 16
After Q 14 = 6 or 8
After Q 15 = 3 or 4
After Q 16 = 2 or 2
After Q 17 = 1 or 1

These numbers are worse case scenario. Now it is possible that we could get
down to 1 after 16 questions if the Q 16 answer gets us to 1 instead of 2.

If we ask a risky question at this point (one that will either eliminate 24
or 64) and we fail and leave 64 left, we have only lost the opportunity to
get down to 1 after Q 16 however, if we are correct, the rest of the process
looks like this (worse case scenario):

After Q 11 = 24
After Q 12 = 12

After Q 13 = 6
After Q 14 = 3
After Q 15 = 2
After Q 16 = 1

And if we are lucky on Q 15, we get to 1 community. We also get to apply
this logic again and try to get down to 8 or 16 after Q 12. I think this
increases our reward without a proportional increase in the risk.

Does anyone see any errors in my math or fault to this logic?

Larry
Lundy and Vickster
North Shore, Massachusetts

In a message dated 6/16/2006 2:12:24 P.M. Eastern Standard Time,
boston.rott@verizon.net writes:

Accordingly, the most effective strategy for Twenty Questions is to ask
questions that will split the field of remaining possibilities roughly in
half each time.

[Non-text portions of this message have been removed]

Re: [LbNA] Twenty questions strategy

From: Jim Plouffe (jimplouffe@comcast.net) | Date: 2006-06-16 22:31:47 UTC-04:00

I don't see any problem whatsoever about your logic. I think that your
point is extremely important. I think you may be onto something.

Now, looking really far into the question asking.... once we get the
town/city, how the heck are going to determine what trail, bench or fire
hydrant this box is located next to? Will we be asking whether the box
is next the twelfth tree after the third rock on a particular trail?
I'm sure there will have to be some sort of gimme when we get that close
or else it'll be one heck of a search party. I can imagine lines of
people with sticks and possibly a dog trained to sniff out Mastercarve.

Blax

P.S. All I have to offer are two cats, but I don't think they like
Mastercarve too much. Give 'em a moth and they're happy.

LundyandVickster@aol.com wrote:

>
>
>
> Folks,
>
> I have a theory.
>
> Right now we stand at 88 communities remaining. If we use the best
> approach
> as posted by Boston Rott (see below), after our next question (#11) we
> will be
> down to 44, then 22 (#12) and so on until question # 17 gets us to 1
> community. This will leave us 3 questions to figure out which rock it
> is under. This
> may be all we need but for some reason, I don't think so.
>
> Now starting at question 17 and working our way back to where we are
> today
> and doubling it each time, we only need to be at 64 after the next
> question to
> still get down to 1 after 17 questions (see the following chart).
>
> After Q 10 = 88
> After Q 11 = 44 or 64
> After Q 12 = 22 or 32
> After Q 13 = 11 or 16
> After Q 14 = 6 or 8
> After Q 15 = 3 or 4
> After Q 16 = 2 or 2
> After Q 17 = 1 or 1
>
> These numbers are worse case scenario. Now it is possible that we
> could get
> down to 1 after 16 questions if the Q 16 answer gets us to 1 instead
> of 2.
>
> If we ask a risky question at this point (one that will either
> eliminate 24
> or 64) and we fail and leave 64 left, we have only lost the
> opportunity to
> get down to 1 after Q 16 however, if we are correct, the rest of the
> process
> looks like this (worse case scenario):
>
> After Q 11 = 24
> After Q 12 = 12
>
> After Q 13 = 6
> After Q 14 = 3
> After Q 15 = 2
> After Q 16 = 1
>
> And if we are lucky on Q 15, we get to 1 community. We also get to apply
> this logic again and try to get down to 8 or 16 after Q 12. I think this
> increases our reward without a proportional increase in the risk.
>
> Does anyone see any errors in my math or fault to this logic?
>
> Larry
> Lundy and Vickster
> North Shore, Massachusetts
>

[Non-text portions of this message have been removed]

Re: [LbNA] Twenty questions strategy

From: david baril (gingerbreadjunk@yahoo.com) | Date: 2006-06-16 20:13:58 UTC-07:00

sounds like i need to go back to school and learn some math!

david (team new hampshire)
http://teamnewhampshire.blogspot.com

LundyandVickster@aol.com wrote:

Folks,

I have a theory.

Right now we stand at 88 communities remaining. If we use the best approach
as posted by Boston Rott (see below), after our next question (#11) we will be
down to 44, then 22 (#12) and so on until question # 17 gets us to 1
community. This will leave us 3 questions to figure out which rock it is under. This
may be all we need but for some reason, I don't think so.

Now starting at question 17 and working our way back to where we are today
and doubling it each time, we only need to be at 64 after the next question to
still get down to 1 after 17 questions (see the following chart).

After Q 10 = 88
After Q 11 = 44 or 64
After Q 12 = 22 or 32
After Q 13 = 11 or 16
After Q 14 = 6 or 8
After Q 15 = 3 or 4
After Q 16 = 2 or 2
After Q 17 = 1 or 1

These numbers are worse case scenario. Now it is possible that we could get
down to 1 after 16 questions if the Q 16 answer gets us to 1 instead of 2.

If we ask a risky question at this point (one that will either eliminate 24
or 64) and we fail and leave 64 left, we have only lost the opportunity to
get down to 1 after Q 16 however, if we are correct, the rest of the process
looks like this (worse case scenario):

After Q 11 = 24
After Q 12 = 12

After Q 13 = 6
After Q 14 = 3
After Q 15 = 2
After Q 16 = 1

And if we are lucky on Q 15, we get to 1 community. We also get to apply
this logic again and try to get down to 8 or 16 after Q 12. I think this
increases our reward without a proportional increase in the risk.

Does anyone see any errors in my math or fault to this logic?

Larry
Lundy and Vickster
North Shore, Massachusetts

In a message dated 6/16/2006 2:12:24 P.M. Eastern Standard Time,
boston.rott@verizon.net writes:

Accordingly, the most effective strategy for Twenty Questions is to ask
questions that will split the field of remaining possibilities roughly in
half each time.

[Non-text portions of this message have been removed]

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