Best attack order for groups of numbers trying to destroy each other, given a victory chance for number to number attack.

[skybuck2000 at hotmail.com]

Hello,

I received a reply from somebody on my ISP newsserver. Apperently his reply is not visible on google groups. I wonder why, maybe it's a banned troll or something, but perhaps not.

Anyway... my ISP has problems accessing their newsserver. They won't offer the service to new customers or changing subscriptions and they lack software to access the server. The server currently has a technical problem. Uploading messages is not possible. Some kind of bug... this has been going on for months. Seems like the bug will be ever lasting.

Just called ISP helpdesk... I forgot to ask them if they could simply reset the server... but with the little information I was giving it seems to be a "remote control problem".

The server is probably remotely controlled and somehow that remote control has been lost... Either password lost, or software is not working anymore... kinda strange story... especially for such a large ISP which should have sufficient technical people to solve this... weird story isn't it... perhaps they just don't want to fix it to drop people of of it....

This kinda sucks for me because using usenet via google newsgroups completely sucks... and is like 1.000.000 times more difficult with this very lacking interface.

But for messages that I consider worth it... like this one, I might keep on going(/presserve? gotta look that up in dictionary) for now... :)

Anyway here is my reply, it might enlighting others as well to this exact problem:


>So now I have the idea to make this program run when my computer is idling
>during the day, it should also be able to store it's progress so that it 
>can
>continue after it was shutdown.
>

"
Periodic snap-shots of the running environment will likely take up a
majority of the run-time.
"

(Since you the only one who has replied so far I will take some time to try 
and answer some of your questions to help you along and perhaps it will be 
usefull to others as well).

Haven't implemented this yet, but I don't see why that would be the case.

It would probably need to store very little. Only 8 indexes, and perhaps 
4x24 entries so that's nothing.

This could be then everything index4 increments for example, or index 3.

Somewhere below in this posting I will give some pseudo code for the indexes 
since it seems you might be struggling with that a little bit or you are 
trying to solve it a different way which is interesting to see but in this 
case I don't think it's better so I will adjust you there, but first

I reply to the rest of your posting so the pseudo code will be somewhere 
below...

"
Especially if your idea is to first generate two lists of the permutations 
of the inputs
"

The permutations were already given by me in my original post. No further 
permutation lists are needed. The permutation table was simple generated 
with some 1234 string with some Delphi code found from the internet.

Generating permutations is not the real issue here, since there is code on 
the internet which already solves that.

"
then generate a list of the "combat" permutations, and you want to be able 
to store-off/reload all
those lists.
"

I don't see why it would be necessary to store any lists at all, except from 
the permutation table as to avoid having to implement a complex permutation 
algorithm. Generating permutations is a topic in itself so I tried to avoid 
that by simply hard coding the small permutation list into the code to side 
step that sub problem.

Generating/storing/loading any kind combination list would either not be 
possible because of lack of memory or would require way too much time.

What should however be stored is the number of victories for each 
permutation.

>(Idea for now is to make it multi threaded and assign a low thread priority

"It's CPU-bound, so using multiple threads for the computation won't be
that effective..."

I disagree, the problem is pretty straight forward and can be split just 
fine by duplicating some simple indexes/data structures.

And should be able to run on each core at nearly 100% efficiency.

The results could be merged together at the very end.

At least in Delphi/native code this will work nicely...

"You add the system overhead of context switches between
the threads, and for common Python, you run into the GIL (so even if you
get subsets of processing assigned to each of multiple processor cores, the
GIL will block all but one from doing any work at any moment -- say you
partitioned it so core0 handles only the set where X begins [1, ...], core
1 handles [2, ...], etc.).
"

Your last sentence made the most sense to me... I don't know what GIL is or 
if Python has any multi threading issues or overhead.

I would assume it would not be to bad concerning overhead and that python 
threads can run pretty efficient as well, if not that would surprise me a 
little bit.

Ofcourse there would only be 2 threads since it's a dual core system. If you 
ment running more than 2 threads then yes there would be context overswitch 
overhead.

But why would anybody want to run more threads than the number of cores ?! 
;) Since it's not necessary to run more threads to divide up the problem.

>so it can run during the day when I use my computer and it's not doing much
>so it can use the reserve computational horse power).
>(I still have to try these "idle/reverse" ideas to see which one works best
>without interrupting my web browsing or music listening too much ;))
>

<snip>


"
Not seeing any code makes it hard to estimate where your slow-downs
would be, however all your mentions of keeping "index" values implies (as I
mention above) that you are trying to build huge tables of permutations
first, then beating each entry against those of the other.
"

I quickly realised that this approach (generating huge lists) won't work 
because out of memory.

So instead each possibility is simply calculated and only results are 
stored.

"In truth, I can't figure out what you consider a combat"

I did not use the term "combat". I do think of them as "attacks".

We could define "combat" as simple "one of the possibilities".

So let's look at a single possibility to explain it to you.

I will simply produce a random index example:

Index1: 7
Index2: 22
Index3: 12
Index4: 10
Index5: 4
Index6: 9
Index7: 11
Index8: 5

Now the task for program is to calculate the outcome of battle.

The program will eventually lookup the permutations from the permutation 
table so let's get those first:

First let's copy & paste the permutation table from original posting:

1,2,3,4    // 1
1,2,4,3    // 2
1,3,2,4    // 3
1,3,4,2    // 4
1,4,2,3    // 5
1,4,3,2    // 6
2,1,3,4    // 7
2,1,4,3    // 8
2,3,1,4    // 9
2,3,4,1    // 10
2,4,1,3    // 11
2,4,3,1    // 12
3,1,2,4    // 13
3,1,4,2    // 14
3,2,1,4    // 15
3,2,4,1    // 16
3,4,1,2    // 17
3,4,2,1    // 18
4,1,2,3    // 19
4,1,3,2    // 20
4,2,1,3    // 21
4,2,3,1    // 22
4,3,1,2    // 23
4,3,2,1   // 24

Now let's retrieve the permutations for the indexes:

(instead of calling it a permutation I will now call it an "attack order"):

Index1: 7  Attack order: 2,1,3,4
Index2: 22  Attack order: 4,2,3,1
Index3: 12  Attack order: 1,3,2,4
Index4: 10  Attack order: 2,3,4,1
Index5: 4  Attack order: 1,3,4,2
Index6: 9  Attack order: 2,3,1,4
Index7: 11  Attack order: 2,4,1,3
Index8: 5  Attack order: 2,1,4,3

Now the computer program can perform the combat.

However perform I explain further how a combat would be performed I will try 
to answer the rest of your questions:

", what you consider a number,"

A number is a tag uppon an object. The object could be a ship, a tank, an 
airplane, or whatever the real world scenerio is behind the problem.

I was considering mentioning this, but I thought it let it out just for the 
fun of it. Consider "number" the number of the object performing the attack.

Perhaps giving some context to these numbers might have helped to imagine 
the problem better. If this is indeed the case then perhaps a little "sorry" 
might be in place.

Numbers usually don't fight each other... so that concept/idea is kinda 
weird/vague... I was kinda hoping that people would find it a bit funny... 
but could see through that and understand by themselfes that these
numbers probably could represent a solder,tank,plane,ship and so forth. I 
also want to conceal what this program will be used for just to thart any 
possible/potential enemy that might read these postings ! :)
But if you must know it's written to help me understand which attack 
strategies work better and which work less well in a specific online game... 
but that's all I will say about it... perhaps you can now already interfere 
which game it might be ;)

"nor how your result table works"

Hmmm fair enough point I guess perhaps that wasn't so clearly described. If 
you want me to give you an exact definition then fair enough.

The results table is simply the number of numbers on each team dimensionally 
multiplied by the number of permutations (=attack orders).

So since momentarily the team consists out of 4 contenders/numbers and since 
attack orders are 24 the entire result table would be a 2D table: 4 by 24.

"you don't identify x vs y"

X is a group
Y is a group

I think this was pretty clearly defined ? However I can see how your 
question might be related to the victory table since you seem to be unsure 
what the rows and columns represent.

I was kinda hoping that you would automatically understand what it ment 
based on the description of "numbers fighting each others". But perhaps that 
description was too vague and too multi-interpretable. Or simply too 
confusing/unclear to what it relates.

To put it simply: The victory table describes the "number to number" attack 
chance. Which means the individual chance of an individual number attacking 
another individual number. In other words the victory table has nothing to 
do with the groups themselfes.

Since there are only two groups I don't see how a victory table could be 
related to the groups themselfes. However the groups were tag as X/Y also to 
prevent confusing with the speaking term "a table", "a bank", "a bike".

However now that I see me writing this table if you plot the table versus 
the x-axis and the y-axis... and put some numbers on it... it might have 
been more clear. I am afraid that apperently it's still not clear ?!

So I will have to explain harder... at least for you... maybe for others 
two... perhaps an example will help to clearify how the Victory Table is to 
be used.

Also perhaps I should have mentioned that each number is also a type. That 
might have made it more clear how the envision the victory table.

So to help you understand I will now describe that number 1 could represent 
a horse, number 2 could represent a tank, number 3 could represent a plane, 
number 4 could represent a ship.

What the numbers/types truely represent will remain concealed for now to 
thart any enemies reading this text :)

However I hope by "applieing" types/classes to the numbers that maybe now it 
is starting to make some sense to you.

The victory table basically describes what the chance is that for example a 
horse will win from a tank.

Or what the chance will be of a tank winning against a ship.

Or what the chance will be of a plane winning against a ship.

So basically the Y-Axis describes the source=attacker

So basically the X-Axis describes the destination=target

Finally the chance in the table itself thus describes the chance of the 
attacker killing the target.

(The chance could also be interpreted as "damage done" which is actually 
what my code uses for now).

", and since it is not diagonally symmetric that makes a difference... "

I don't quite understand this sentence of yours... a bit weird... but I 
guess this was because of your confusion and because you trying to sum the 
entries in the victory table for some reason, which is because of 
misunderstand... it's not necessary, I hope to have cleared that up above 
and will continue with an example below.

"nor do the rows/columns sum to 100%)"

Not required.

Finally an example.

Let's say a horse attacks a tank.

What would it's chance of winning be ?

Let's first define the numbering as describes above:
Horse=1
Tank=2
Plane=3
Ship=4

Let's re-examine our victory table:

Let's apply some row/column numbering perhaps that will clearify it a bit 
for you.

    1   2   3   4
1: 50,  3, 80, 70
2: 90, 60, 20, 40
3: 30, 90, 55, 65
4: 75, 90, 98, 60

Now the program wants to know what is the chance of a horse defeating a tank 
?

So horse = 1

So proceed to row.

So tank = 3

So proceed to column 3.

This gives the horse a winning chance of 80%.

Ofcourse this makes completely nosense with these horse, tank, plane,ship 
descriptions.

But I hope you get the idea.


So finally what could a possible solution program do to calculate outcome of 
battle ?!? Let's proceed with the example:

Index1: 7  Attack order: 2,1,3,4
Index2: 22  Attack order: 4,2,3,1
Index3: 12  Attack order: 1,3,2,4
Index4: 10  Attack order: 2,3,4,1
Index5: 4  Attack order: 1,3,4,2
Index6: 9  Attack order: 2,3,1,4
Index7: 11  Attack order: 2,4,1,3
Index8: 5  Attack order: 2,1,4,3


Index 1,2,3,4 belongs to group X
index 5,6,7,8 belongs to group Y (5,6,7,8 renumbered as 1,2,3,4)


>From the information above it's now clear how group X will attack group Y 
and how group Y will attack group X.

X1 will first attack Y2
X2 will first attack Y4
X3 will first attack Y1
X4 will first attack Y2

Y1 will first attack X1
Y2 will first attack X2
Y3 will first attack X2
Y4 will first attack X2

>From looking at this first round of attacks from above it's already pretty 
clear that Group Y has "chosen" to attack X2 with 3 objects. Thus it's very 
likely that X2 will be destroyed.

Funny enough groupX is also attacking Y2 but only with 2 objects. So Y2 is 
also likely to be destroyed but a bit less likely.

How the program now proceeds with calculations is open to debate.

There are two possibilities:

Either the program considers X2 destroyed if the chances are subtracted from 
100 and it goes below 0. (The chances are lookup in the victory table as 
describes in the example above for horse vs tank).

This I would call the "dynamic" approach... it complexifies the problem 
somewhat... a number which is destroyed cannot further attack so it will not 
take part in the next round of attacks.

However another approach could be taken which stays more true to the concept 
of a "decision tree". Instead of subtracting the chances, the chances could 
also be multiplied... this will reduce the chance of X2 being alive, but it 
is still allowed to participate in the fight assuming
it had a very low chance of surviving but might have miracously survived. To 
compensate for this perhaps further attacks from X2 should have it's chance 
of success reduced... to make the computation a bit more realistic but still 
computationally easy to do: just a multiplication, no branches.

So for now I will explain how my program proceeds. Without actually looking 
up the chances... which would be a bit much work to do... I will simply 
assume that X2 died and perhaps Y2 too.

So the next round commences as follows:

(attack targets/indexes acquired from attack order from above):

X1 will first attack Y1
X2 (destroyed)
X3 will first attack Y3
X4 will first attack Y3

Y1 will first attack X1
Y2 (destroyed)
Y3 will first attack X4
Y4 will first attack X1

Perhaps after this second round Y3 is destroyed, perhaps X1 is destroyed

So round 3 commences:

X1 (destroyed)
X2 (destroyed)
X3 will first attack Y2
X4 will first attack Y4

Y1 will first attack X4
Y2 (destroyed)
Y3 (destroyed)
Y4 will first attack X4

Apperently group Y had the more lucky permutation of attack orders, here 
they jointly attack 4 so it's likely 4 was described which gives them a 
better chance of winning since now they are +1 vs the enemy, while Y2/Y4 are 
only damaged but not yet destroyed.

Let's see what happens in potentially the final round:

X1 (destroyed)
X2 (destroyed)
X3 will first attack Y4
X4 (destroyed)

Y1 will first attack X2, cycles to X1, cycles to X3
Y2 (destroyed)
Y3 (destroyed)
Y4 will first attack X3

Here my program if I remember correctly will detect that enemy X2 is already 
destroyed so it's starts cycling/wrapping it's attack order index to find 
which one it should attack next until it finds X3 still alive and attacks 
it.
(First Y1 tried X1 according to it's attack order "table" but X1 is also 
already destroyed so it proceeds to X3).

>From this "permutation" example it seems likely that X3 was destroyed and 
group Y might be the winner.

However if group Y is truely the winner will depend on the actually victory 
chances... perhaps something weird occured and one of the objects was easily 
destroyed by a high victory chance... even though it was 1 vs 1... thus this 
might have completely altered the outcome of battle.

So that's what the computer program will have to do/compute.

Also finally let's look at the results table.

For this outcome the results table would be adjusted as follows:

Group Y won, so no adjustment. Only Group X is examined, since it's a mirror 
of each other.

However let's assume that the exact same battle happens but vice versa. 
Group X/Y swapped.

In that case the results table would be adjusted as follows:

Index1: 7   Victories +1
Index2: 22  Victories +1
Index3: 12  Victories +1
Index4: 10  Victories +1

This basically means that the permutation 7 for object 1 has +1 victories 
independently record of what the rest did.
This basically means that the permutation 22 for object 2 has +1 victories 
independently record of what the rest did.
This basically means that the permutation 12 for object 3 has +1 victories 
independently record of what the rest did.
This basically means that the permutation 10 for object 4 has +1 victories 
independently record of what the rest did.

So basically in C/Delphi like terminology:
ObjectPermutationVictories[1,7]++
ObjectPermutationVictories[2,22]++
ObjectPermutationVictories[3,12]++
ObjectPermutationVictories[4,10]++


*** Continueing with the rest, unrelated to above ***

(By the way I made a little typo in this weird text below 3th should have 
been 5th, I thought 3 bits would be enough but it actually needed 5 bits):

"
Just the 8 index loops already cost a lot of instructions. Since there are
only 24 permutation it would be enough to store it in 5 bits. Perhaps a
rounded floating point which increases by 1/24 might be enough to trigger
the 5th bit from incrementing when it actually needs to.
2x2x2x2x2 = 32  (it should increment bit 6 when the 5 bits reach 24).
So the idea here was to create 8 indexes from just 1 index being incremented
to create the 8 combinations of indexes "instruction cheaply".
Not sure if this will work, just an idea I might try :)
"

If you don't understand this crazy idea above in quotations then you can 
safely ignore it. It is not used it was an experimental thought how things 
might be done differently in regards to advancing the indexes.

***


Now continueing with the rest of your questions


"
>>> import itertools
>>> for x in itertools.permutations("1234"):
... xout = "".join(x)
... for y in itertools.permutations("1234"):
... print xout, "".join(y)
...
1234 1234
1234 1243
1234 1324
1234 1342
1234 1423
1234 1432
1234 2134
1234 2143
1234 2314
1234 2341
"

I don't quite understand that python code, but I can imagine what it might 
be doing... but it's probably not correct, it's too simplistic. Or perhaps 
this was just to generate the permutations.

As I wrote above... generating the permutations is not really the problem, 
they can be looked up from the permutation table.

"
Replace the print with something to compute just the win/loss stuff for the
single x vs y, and save the result off -- since I couldn't work out your
scoring I can't say if a dictionary keyed by the permutation makes sense...
"

For now I will not reply to this...  there seems to be some understanding in 
what you wrote... but for now I will wait to see if this new reply of mine 
will have clearified a lot for you and thus perhaps I do not need to respond 
to the text above.


"
And are you generating random numbers to determine the winner/loser?
"

No, brute force is applied to calculate which group wins, in case you ment 
which group wins/losses. If you ment which number wins, then that is giving 
by a chance lookup and perhaps a health variable per object which is 
decremented. However you are free to decide what
to do... kill of numbers ? keep them alive ? Use a different way of 
reasoning what should happen to them. The victory chance should be applied 
somehow though. It definetly should influence the outcome of battle somehow.

" How many cycles -- loop on random values until one or the other is "dead". 
"

A "while loop" which examines the "alive status" of each number/object is 
used to examine if the battle came to an end. As long as each team has an 
alive member the fight/combat continues.
Once the numbers of one group are completely destroyed, the other group 
wins. In case both groups destroy each other at the same time, it's a draw.

"What is the statistics? How many combats the digits took (ie, number of 
cycles of random)... How many it took for all four digits to die?"

Nice question.

This depends on the approach taken. I decided to take a "natural" feeling 
approach, which I call the "dynamic approach". The combat for each 
possibility is continued until one group dies. Therefore it's hard to say 
what the exact number of "rounds" or "cycles" as you call them it will take.

However it will probably be something like 4 or 5 cycles. This is kind of an 
interesting question. Some additional statistical analysis variables could 
be added to the code to track what the average number of rounds is, what the 
minimum was and what the maximum was !

Thanks for this feedback it's kinda interesting ! ;)

Bye,
  Skybuck.