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

[skybu...@hotmail.com]

Hello,

(This problem is probably too computationally intensive to solve with Python, though Python + Cuda could be interesting, and also Python has some interesting expressive powers, so it could be interesting to see how Python programmers might be able to express this problem with Python code, so I am going to give this Python group a try... maybe it will surprise me ! :) At least now you have a nice computational problem for those boring rainy days (when the net is down?and the offline games bore you ;) LOL :))

There are two groups of numbers which try to destroy each other:

Group X = 1,2,3,4
Group Y = 1,2,3,4

There is a 4 by 4 victory table which describes the chance of a number
destroying another number:

Victory table =
50, 3, 80, 70
90, 60, 20, 40
30, 90, 55, 65
75, 90, 98, 60

(Currently implemented as a chance by diving it by 100 and storing as
floating point, but since these are subtracted only from 1.0 I guess they
can be stored as integers instead, even bytes)

This leads to the following computational problem as far as I am concerned:

Each number has an attack order permutation as follows (factorial 4 =
1x2x3x4 = 24)

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

(These attack orders can be numbered from 1 to 24 or 0 to 23 and then it's
attack order/permutation can be looked up to safe memory.)

Each number has it's own attack order and thus this leads to the following
combinational computational problem:

All combinations of permutations in which order group X can attack Group Y
and vice versa:

Group X = 24 x 24 x 24 x 24
Group Y = 24 x 24 x 24 x 24

So this is 24 possibility to the power of 8.

Final computation complexity at the very minimum is (24 to the power of 8)
multiplied by roughly 4 attacks perhaps even 5 or 6 to finally destroy a
group of numbers.

24 to the power of 8 = 110.075.314.176

I have already written a computer program which can solve this, however the
computer program estimates it takes 19 hours on a 2.0 gigahertz AMD Athlon
X2 core.

Using dual core could solve the problem over night, though I do not feel
comfortable running my PC at night unattended.

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.

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

My system has 4 GB of ram, so other ideas could be to store a data structure
partially which could keep some computations so that it doesn't have to be
done again... Though memory lookups might be a bit slow so not sure if that
makes any sense.

I might also try GPU/Cuda since there seems to be lots of loops/reoccurences
of the same computations that will happen over and over again... So maybe
cuda can detect "same branch execution" and some "computations" and might
speed it up, not sure about that.

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 4th 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 :)

Then those bits would still need to be extract and makes. So perhaps on
older systems this is not efficient.

The 8 indexes need at least 3 instructions, 1 index increment, 1
comparision, 1 jump.

The inner loop contains some while loops to increment attack index per
number.

Each number has a "alive" variable which starts at 1.0 and is decreased
everytime it's attacked.

Once a number is dead below 0.0000001 it's considered dead and can no longer
attack.

(Since victory table was described as integers above this can also be read
as: Alive starts at 100 and once it goes zero or negative it's dead).

Anyway the main reason why I wrote to this/these groups is that the numbers
themselfes are not that larger and can fit in a byte, even a few bits.

Thus they will fit into SSE registers and such and I also know SSE has some
permutations instructions.

I am not expert at SSE but I am wondering if there are perhaps some
SSE1/2/3/4/5 instructions which can help at solving/computing this problem ?

Now the question you might be wondering about is ? What am I actually trying
to compute ?

Well the final output could simply be the number of victories that each
attack order has had per number. I am particullary interested in victories
of number 4. So that would be sufficient for now.

Number 4 has 24 permutations.

So I want to know how each permutation of number 4 performs under all other
circumstances/permutations of all other numbers/combinations and so forth.

This basically requires the entire set to be computed and then record number
of victories for for example Group X number 4.

Only the results of one group needs to be outputted since the two groups are
a mirror of each other.

Also during the development of the computer program I finally had a
successfull implementation by keeping it as simple as possible and working
with direct variables, instead of much more complex arrays.

Later on I made a more code efficient version which uses arrays/lookups and
such. It was much harder to try the array approach at first since it becomes
mindly complex and can obscure "vision to a solution".

So I suggest anybody trying to implement a solver for this to keep the code
as simple as possible at first, since this is already an 8 dimensional
problem with a 9th dimension.

Also it was interesting to see the Delphi for loops not allowing array
fields as loop variables, so those loops will need to be fleshed out anyway,
or one big linear loop could be used and then 8 indexes calculated from
that.

That approach will probably be necessary for a cuda solution anyway... 32
bit might be sufficient if remainders are reincluded in the conversion from
thread/block dimensions to linear dimension back to 8 dimensional indexes.

Perhaps such computation might even be a bit quicker than the 3 instructions
per loop.

For example 8 divisions and 8 remainders will be necessary to compute 8
indexes from one big linear indexes. Since div/mod can be the same
instruction this might only require 8 instructions to compute these loop
indexes from a big linear index.
However computing the big linear index already requires between 6 or 10
instructions.

So just to compute those 100+ billion data entries requires something like
20 instructions just to be able to compute those loop indexes.

This is my finding with bigger data sets which consists out of small little
data units... The closer the number of entries/data items get to the
actually processing computing power the more time/processing/instructions
are wasted on just computing these loop indexes.

It makes sense from this perspective: A problem of 100 items only needs 100
loops. Thus lots of processing power remains for the data. But for 2 billion
data items, the number of items already matches the gigaherts of the core...
so the core is already swamped... with just loop index calculations.

I hope this reasoning/explanation convinces some CPU/GPU designers to
include more instructions to compute loop indexes in all kinds of ways that
could speed that up somewhat and safe some processing time.

Anyway... let me know if you think SSE could be of some help in solving this
permutation/combination problem ?!

Also for the python newsgroup:

Maybe python is more powerfull than I thought and it has some weird/kinda crazy/cool new permutation/combination algorithmic classes that can solve these kinds of problems faster than just the average run of the mill general code ! ;)
(Or perhaps build in solver support, that will be my next try/posting :P :))

Bye,
Skybuck.

[skybu...@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.

[Peter Otten]

skybu...@hotmail.com wrote:

> 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.

No, that's Dennis Lee Bieber who doesn't want his posts to be kept, and
seems to be the only one to post here with the X-No-Archive flag set.

[Random832]

On Thu, Dec 15, 2016, at 08:31, Dennis Lee Bieber wrote:
> As for my posts disappearing: I run with "X-NoArchive" set. I have from
> before Google absorbed DejaNews. Back then, most news-servers expired
> posts
> on some periodic basis (my ISP tended to hold text groups for 30 days or
> so, binaries groups cycled in less than 36 hours). When DejaNews arrived,
> many objected to the non-expiration facet:
> https://en.wikipedia.org/wiki/Google_Groups#Deja_News

As I recall, what most people *actually* said they objected to was the
fact that they profited from showing ads. X-No-Archive was just a
convenient blunt weapon to hit them with.

[Terry Reedy]

On 12/15/2016 6:23 AM, skybu...@hotmail.com wrote:

> Anyway... my ISP has problems accessing their newsserver. ...

If you want to read python-list as a news group, you might try
news.gmane.org. About once a year, it goes down for a few hours to a
day, but has otherwise been dependable. I found it when my ISP dropped
newsgroup access around a decade ago.

[skybu...@hotmail.com]

Hi thanks for your (Dennis) reply,

You seem to have two main questions:

1. Is the attack order sequential in time or is it positional ?

The answer to this question is kinda:

Both, (which is kinda funny, since you did not think of this possibility that it could be both, which you also did with the other issue, see below ;))

It indicates which object should be attacked first. And ofcourse objects have a position in the real world, so this also implies position to some degree.

2. Do the numbers mean types or instances ?

Again the answer to this question is kinda:

Both, (^<-which is the real funny one, because the original model where there were only 4 types and 7 instances was still too large to compute within reasonable time. So the number of instances has been brought back to the number of types to represent each type exactly once so to at least keep the model somewhat realistic and include all types which is kinda important. I am particularly interested in type 4 so it has to be in the model :) Type 4 can attack the other 3 types with easy this gives you some hint at what kind of type it might be ;)).

(So there are 4 types, and 4 instances, which happen to overlap each other, so you can consider them the same thing type=instance (to simplify the program)).

These were your two most important questions, however you seem to have some additional (sub) questions which I will also try and answer.


3. One of your questions was: why are the indexes called "index1,index2" and so forth. This is simply because there are 8 objects. Each object needs it's own index to create a brute force algorithm which can create all combinations of the object attack patterns. The code for this is pretty simple/straight forward so I will mention it below, I will also rename these indexes as you requested to give them more meaning, pascal style:

for FriendlyIndex1 := 1 to 24 do
for FriendlyIndex2 := 1 to 24 do
for FriendlyIndex3 := 1 to 24 do
for FriendlyIndex4 := 1 to 24 do
for EnemyIndex1 := 1 to 24 do
for EnemyIndex2 := 1 to 24 do
for EnemyIndex3 := 1 to 24 do
for EnemyIndex4 := 1 to 24 do
// ComputeCombat( FriendlyIndex1,FriendlyIndex2,FriendlyIndex3,FriendlyIndex4, EnemyIndex1,EnemyIndex2,EnemyIndex3,EnemyIndex4)

So these indexes are simply 8 integer variables used to generate all possible attack orders (permutation number).

Each index can then be used to look up the actual permutation and used in combat...

So this iteration code is a big help to make sure and produce all combinations, it's simple, it's effective, it's clear to what it's doing.

ComputeCombat could be a routine or simply replaced with actual code to prevent "variable sharing issues". My suggestion in case you ever do try to write code for it is to keep everything "global" or simply inside a single routine... so
that parameter hell or whatever doesn't occur... keep it as simple as possible for a first version... then later it can be enhance with nice python features. Ofcourse if you think the problem is simple enough to try using more advanced features at first you welcome to try that as well but I would find it very funny if that fails... so when it does fail... fall back to ultra-simple code :) Perhaps python doesn't even have ultra simple data structures which might actually complexify your capability of solving this problem, which would be somewhat of an interesting conclusion regarding the python language as a whole ! Consider yourself challenged by me to solve it and prove that Python is not a bad language ! LOL :) Yes little bit trollish but for good reason. Eventually I do suspect python might be of some help... at least you mentioned it can generate permutations... but that is a sub problem in this case...

4. There was one more somewhat interesting sub question, your question seems to be about the attack/victory table, you seem to wonder about symetrical/asymetrical, and why it would not be symetrical ?

I think I can explain this issue for you. The reason why it's not symetrical is that tanks for example have different armor thickness depending on their angle. So let's say Tank X sneaks up on Tank Y and Tank X manages to hit the Tank X in the back... then Tank X's victory chance is much higher then if Tank X was sneaked up on by Tank Y... in that case Tank X's victory chance would be much lower.

I think this is the main reason why you are seeing an asymterical victory chance table. I hope that clears it up for you ;)

I think I have solved all your confusion, you should now have enough information to write a computer program that could solve the problem. Solving the problem entirely would not be necessary for you to share any possible python enhancements or pseudo code or own techniques or (computing efficiency) ideas you would have come up with it. Just compiling it and running it a little bit should be sufficient to see if it actually works.

Bye,
Skybuck.

[skybu...@hotmail.com]

A nice chinese-like saying might have come out of this, perhaps it even already exists:

"When you confused, the answer might be fused !" :)

Sounds like TZen Su ! That dude from Art of War or something like that :)


I will take this chance to correct a little pretty obvious typo corrected:

(*) Tank X changed to Tank Y

So let's say Tank X sneaks up on Tank Y and Tank X manages to hit the (*) Tank Y in the back... then Tank X's victory chance is much higher then if Tank X was sneaked up on by Tank Y... in that case Tank X's victory chance would be much lower.

[Grant Edwards]

On 2016-12-16, Dennis Lee Bieber <wlf...@ix.netcom.com> wrote:
> On Thu, 15 Dec 2016 13:34:32 -0500, Terry Reedy <tjr...@udel.edu> declaimed the following:

>>
>>If you want to read python-list as a news group, you might try
>>news.gmane.org. About once a year, it goes down for a few hours to a
>>day, but has otherwise been dependable. I found it when my ISP dropped
>>newsgroup access around a decade ago.
>

> And I found it when the spam on comp.lang.python got overly
> annoying.

I didn't notice much spam on c.l.p (but then again, I filter out all
posts from google-groups). The problem on c.l.p that caused me to
switch to gmane's NNTP server was the number of broken references.
They both have references that break in various scenarios, but my
tests indicated that it was worse on c.l.p. [Yes, I actually wrote a
Python program that used an NNTP client library to check all the
reference values in a large sample of posts from both sources.]

--
Grant Edwards grant.b.edwards Yow! I wonder if I could
at ever get started in the
gmail.com credit world?

[D'Arcy Cain]

On 2016-12-16 10:11 AM, Grant Edwards wrote:
> I didn't notice much spam on c.l.p (but then again, I filter out all
> posts from google-groups). The problem on c.l.p that caused me to

Yes, blocking GG was the biggest improvement to my reading this list
(mailing list in my case). That and a few judicious PLONKs and it is
now useful.

Al I need to do now is figure out how to filter out the almost daily
Windows installer questions.

--
D'Arcy J.M. Cain
System Administrator, Vex.Net
http://www.Vex.Net/ IM:da...@Vex.Net
VoIP: sip:da...@Vex.Net

[Tim Golden]

On 16/12/2016 16:12, D'Arcy Cain wrote:
> On 2016-12-16 10:11 AM, Grant Edwards wrote:
>> I didn't notice much spam on c.l.p (but then again, I filter out all
>> posts from google-groups). The problem on c.l.p that caused me to
>
> Yes, blocking GG was the biggest improvement to my reading this list
> (mailing list in my case). That and a few judicious PLONKs and it is
> now useful.
>
> Al I need to do now is figure out how to filter out the almost daily
> Windows installer questions.
>

The ever-so-slight irony is that Mailman decided it didn't like this
post and held it for moderation! (Something to do with the headers; I
didn't bother to check since I recognised the sender).

TJG

[D'Arcy Cain]

On 2016-12-16 08:16 PM, Dennis Lee Bieber wrote:
> Unfortunately, my client can only "pre filter" on subject and author; I
> could kill all @gmail.*, but could not focus on just Google Groups
> submissions...

I don't know what client you use but perhaps you can adapt this procmail
recipe.

:0 Hir
* ^List-Id:.*python-list.python.org
* ^From:.*@gmail.com
* ^Newsgroups:.*
/dev/null

[Grant Edwards]

On 2016-12-17, Dennis Lee Bieber <wlf...@ix.netcom.com> wrote:
> On Fri, 16 Dec 2016 15:11:54 +0000 (UTC), Grant Edwards
><grant.b...@gmail.com> declaimed the following:

>
>>I didn't notice much spam on c.l.p (but then again, I filter out all
>>posts from google-groups). The problem on c.l.p that caused me to

>>switch to gmane's NNTP server was the number of broken references.
>>They both have references that break in various scenarios, but my
>>tests indicated that it was worse on c.l.p. [Yes, I actually wrote a
>>Python program that used an NNTP client library to check all the
>>reference values in a large sample of posts from both sources.]
>

> Unfortunately, my client can only "pre filter" on subject and author; I
> could kill all @gmail.*, but could not focus on just Google Groups
> submissions...
>

> Probably time for me to spend the $19 to upgrade from Agent 6.0

Or use the One True Newsreader: SLRN.

;)

--
Grant

[Grant Edwards]

On 2016-12-17, D'Arcy Cain <da...@vex.net> wrote:
> On 2016-12-16 08:16 PM, Dennis Lee Bieber wrote:

>> Unfortunately, my client can only "pre filter" on subject and author; I
>> could kill all @gmail.*, but could not focus on just Google Groups
>> submissions...
>

> I don't know what client you use but perhaps you can adapt this procmail
> recipe.
>
>:0 Hir
> * ^List-Id:.*python-list.python.org
> * ^From:.*@gmail.com
> * ^Newsgroups:.*
> /dev/null

That's not what he wants to do. He wants to filter out posts made via
Google Groups, not posts sent from people who use gmail addresses.

Here's the rule for slrn:

Score:: =-9999
Message-ID: .*googlegroups.com

[skybu...@hotmail.com]

Unless you are capable of expressing problems in numerical terms you'll have very hard luck having it computed by a computer ! ;)

I did find some interesting docs about "decision trees".

Exhaustive search
Branch and Bound
Hill Climbing
Random/Best Effort Solutions

and so forth.

A computer programmer should be able to handle abstract descriptions as well like I gave in my initial posting.

What kind of "dressing" you want to give it is up to you, the dressing won't solve it though ! :)

Meanwhile I have also consider some kind of lookup table... or an intermediate table like you described...

Not yet sure if that will be of any help... (I am in doubt about the dynamic nature of the battles... perhaps an intermediate table would be wrong... or maybe it might be right, dynamic deaths vs staying alive inside intermediate table and such).

I also tried the static approach by multiplieing chances instead of subtracting the chances like damage done.

I also experimented with "Pascal/Delphi sets" in combination with arrays... this produced a very easy/simple permutation algorithm which consisted out of multiple for loops, which is kinda the obvious way of easily creating permutations... but it was still kinda interesting.

There is a problem with such loops though, also like the one you mention "for each" and "for in" and such... "under water" the compiler will loop the entire range of the type, and will use compare statements to see if it should enter the inner loop. So there is hidden overhead associated with it.

Thus such "generating" of permutations on the fly might have a hidden overhead cost associated with it, even if this was not the case, such for loop constructs will definetly have overheads in certain situations and this can quickly get out of hand and could even consume more processing time then the entire program.

I did also briefly considered this permutation loop, though it would require a lot of programming, 8x4=24 for loops, plus possible an additional attack loop.

You do have a little point that without a clear story it might be hard to understand the exact problem. I may consider describing the problem one more time, but it might still be with number or blue berries ! LOL :)

[skybu...@hotmail.com]

Specially for Dennis, a nice story:

There are four little animals. The first animal is a tiger, the second animal is a deer, the third animal a parrot, the fourth animal is a fish.

The animals are very angry at each other and want to EAT each other ! =D

However each animal has a certain specialization. For example, the tiger has very sharp teeth, but can't hold it's breath for long under water.

The parrot has the ability to drive others insane with his chilping. The fish can lure other animals into the water in hopes of drowning them.

And the deer can lure them into the swamp or make them fatigued from chasing them.

Fortunately for the four animals they don't need to EAT each other because another group of animals have arrived which are exactly like them.

So the four animals have decided to gang UP like negros in the GETTO ! LOL.

It's now GANG vs GANG.

But the poor little animals have run into a problem ?! Which of the other four animals should they EAT first ?! Or should they even attack multiple at the same time ?!

Should the tiger fight the tiger ?

Should the fish fight the fish ?

Should the parrot fight the parrot ?

Should the deer fight the deer ?

Or perhaps ?

Should the tiger eat the fish first ?

Should the fish try to drown the tiger first ?

Should the tiger and the fish gang up on the tiger ? But what about the enemy fish ? What will it do ?

Should all four animals attack the enemy tiger ? or another animal ?

Also for the gang to achieve victory all four enemy animals must be EATEN !

Now these animals wonder to themselfes ?

How should we attack the enemy ? Who should we attack first ?

Every individual attack has a chance of success as given by the victory table. (A survival table could be calculated as well. Which would be the inverse of this).

Many possibilities for attack exists ?!

Which one do you recommend for them ?!

Keep in mind that each animal is free to decide it's own attack plan. They do not need to agree with you.

Imagine yourself to be one of the animals.

Which attack strategy for yourself would be best to use to maximize your GANG of winning, no matter what other attack plans the animals have.

An example of a possible attack:


Red Tiger has his own attack plan eat in this order: Blue Tiger, Blue Fish, Blue Deer, Blue Parrot
Red Deer has his own attack plan eat in this order: Blue Fish, Blue Deer, Blue Parrot, Blue Tiger
Red Fish has his own attack plan eat in this order: Blue Fish, Blue Parrot, Blue Deer, Blue Tiger
Red Parrot has his own attack plan eat in this order: Blue Parrot, Blue Fish, Blue Deer, Blue Tiger

and vice versa for blue team ! ;) :)

[skybu...@hotmail.com]

Dennis wrote:

<snip>

"
Instead you /now/ have ONE set of R marching down FOUR sets of B

RT RD RF RP <- attackers
BT BF BF BP round 1
BF BD BP BF round 2
BD BP BD BD round 3
BP BT BT BT round 4
"

Yes this is how the problem works.

Also keep in mind that an attack is only valid if the target is still alive, otherwise the attacker would move to the next one.

So pre-computing an attack plan/outcome or storing it might not be so usefull for on color, since the other color might already be dead and thus attack plan was calculated incorrectly potentially.

So it's quite a difficult/complex/dynamic problem !

[skybu...@hotmail.com]

Skybuck wrote:

"
Also keep in mind that an attack is only valid if the target is still alive, otherwise the attacker would move to the next one.

So pre-computing an attack plan/outcome or storing it might not be so usefull for on color, since the other color might already be dead and thus attack plan was calculated incorrectly potentially.
"

^- Apperently this text/posting was essential/the key for Skybuck's Magical Brain to come up with a solution !

I love how Skybuck's Magical Brain comes up with solutions after some sleep ! =D

Just need to input the problem before sleeping, then in the morning ! TA-TA: Solution ! =D

I just woke up, thought a little bit and then came up with the following solution !

The problem with the lookup/intermediate table is ALIVE/DEATH of own object (also teammate objects), furthermore another problem is ALIVE/DEATH of enemy object(s).

So now the solution is obvious ! A special lookup table as follows:

(Furthermore I just had another idea to compute an enemy health reduction or perhaps enemy health outcome, both are possible ! ;) Yeah... enemy health calculation probably possible and accurate, since alive/death of enemy also known on input and thus result can be calculated/stored in table ! ;)

EnemyHealth (could also be EnemyHealthReduction if that were necessary for some reason ! ;) total damages would be summed, but probably not necessary to do it that way).


Enemy1Health,Enemy2Health,Enemy3Health,Enemy4Health =
Friendly1AliveStatus, Friendly2AliveStatus, Friendly3AliveStatus, Friendly4AliveStatus, Object1AttackPermutations, Object2AttackPermutations, Object3AttackPermutations,Object4AttackPermutations,Enemy1AliveStatus,Enemy2AliveStatus,Enemy3AliveStatus,Enemy4AliveStatus

^ So what I just tried to describe above is an 16 dimensional array as follows:

2x2x2x2x24x24x24x24x2x2x2x2

So computational complexity added by alive/death status is only x8 which is totally great... total complexity is therefore:

24x24x24x24x8

(For each attack the lookup table can be reused so that perfect too)

So the initial complexity of 24x24x24x24x24x24x24x24x4(?) has now been reduced too:

1x24x24x24x24x8 (computations)

It will probably still be necessary to "compute/lookup" all possibilities just to be sure, however doing an 16 way array lookup should be way faster than computing while loops and if statements and what not... though the table is quite large so some random access may occur.

16 random access is roughly 16x100 nanoseconds. Plus some 5 minute looping overhead or so so let's calculate rough indication of new processing time.

24x24x24x24x24x24x24x24x4(?) (look ups)


But first I try and calculate some kind of indicator of current per loop processing time.

24^8 = 110075314176 battles / 80.000 seconds = 1375941.4272 battles per second.

The 5 minute overhead is about 300 seconds so seems minimal not going to adjust for that for now.

Now let's compute new expected running time.

Perhaps crazyly inaccurate calculation since it does not account for data cache hits... but just worst case scenerio or something:

It will be at least 16x100 nanoseconds, then 8 branches or so to determine winner is about 8 x branch time which is roughly 15 cycle clocks of 2 gigahertz or so. Then also 8 data field fetches another 8x1 cycle, and perhaps 8 assignments or so to store healths so roughly 15+8+8 = 13 plus probably some while loop to repeat attacks until there is a winner though this was already accounted for in the branches above... so for now I'll stick with 31 cycles or so

So 31 cycles of 2.000.000.000 hz machine I would guess is roughly:

0.0000000155 seconds, roughly 15.5 nanoseconds so worst case scenerio:

16x100 = 1600 + 15 = 1615.5 nanoseconds to compute/lookup a battle.

Number of battles: 110075314176 x 1615.5 = 177826670051328 nanoseconds

= 177826.670051328 seconds.

According to my initial calculations it will be far worse off lol !

However the 8x dimensions could be put close together so that at least those are cached, then perhaps a lookup will only take 10 nanoseconds or something or maybe even less.

So then it becomes 8x10 nanoseconds + 8*100 nanoseconds = 880 nanoseconds

Seems like roughly a reduction... then I am back to square one roughly running time of 90.000 seconds. Plus ofcourse some pre-compute overhead...

Though I am kinda bad at estimating running time like this...

I am hopefully that the look ups will proceed much faster...

Sometimes of those 8x100 nanosecond seeks there will be some L1/L2 data cache hits hopefully so that should accelerate it somewhat.

What actually needs to be stored is enemy health... this can be done with one byte... 100 is near 128 bits... so at least 7 bits needed for 100, so only 1 bit could be saved so doesn't really seem worth it to save 4 bits in total ! ;)

The pre-compute time for the table lookups should be quite fast...

The main processing for generating the lookup is:

24^4 = 331776 x 8 = 2.654.208

That's nothing compared to the 110.000.000.000 that it used to be ! ;) :)

So I am very hopefull that I have found a nice data acceleration structure ! ;) :)

Having this conversation with you was usefull, thanks !

Bye,
Skybuck =D

[skybu...@hotmail.com]

Hmmm I see that I have made an old mistake of mine ;)

2x2x2x2 is not 8, it's deceptive... it looks like 4x2 = 8 but nope ! :)

This is 2x2=4x2=8x2=16.

and then the next 4 = 16x2 = 32x2 = 64x2 = 128 x 2=256

so it's roughly 24^4 x 256 = 84934656

[skybu...@hotmail.com]

Hmmm now I think the lookup table cannot work... at least not for the dynamic one... where health is subtracted...

The ships have a certain health... and not just an alive/dead status...

The way they and the enemy attack each other will probably influence the outcome of battle... and for the next round ships will have different health status... so just dead/alive is not enough...

Also pre-computing the table for all 4 or more rounds seems not possible because this again depends on what the enemy was doing...

So I don't think there is a way around the full 24^8 calculations...

Hmmm to bad...

[skybu...@hotmail.com]

I first explored the possibility of a lookup table to speed up calculations, this possibility would probably give wrong results.

I am interested in calculating all possibilities to see which one is truely best, I am also interested in trying to speed up calculations to be able to handle larger models.

Many other possibilities exist for further exploration:

1. One recursive function to try and split up the work as to recycle some of it.
2. Perhaps multiple recursive functions to include different functionality at different "depths".
3. Other tree like structures to try and safe some computations by recycling results from previous visits across nodes.
4. Manually incrementing indexes (though this would probably requiring storing results in some form or another, perhaps a stack based approach might work... pushing/popping as index returns to a certain one, perhaps a stack per index might work or something.
5. Detecting when index changes and then reloading previous computations.

I still believe that it should be possible somehow to save some computations.

Perhaps I am fooling myself ! Not sure yet ! ;) :)

6. Healths will need to be reset I think, however another possibility is copy&pasting healths to new nodes to compute them further.

Sort of like a propagation algorithm... spreading already calculated results to other nodes.

One problem with all that node thinking is that the system will run out of memory, which should be fine, memory can be pre-allocated to speed stuff up, one it runs out, it will have to do full calculations.

I wrote about this before but cancelled posting cause it was kinda messy... but now it makes a bit more sense, now this text a bit more clear.

7. Maybe cuda or some other SIMD solution. Still not sure if CUDA can detect that some instructions/data are being calculated... hmmm would guess not, not sure though.

It's kinda fun trying out all these possibilities to see which ones work... though I am also becoming a bit curious to what the actual outcome would be.

For now my heuristic for a "good enough" solution would be "object attack object with best victory chance".

This seems a bit too easy/cheesy heuristic and I want to know what is really the best way... is there perhaps a team strategy/combined attack effort that might work better ? ;)

I would also like to be able to change chances perhaps in feature or expand model a little bit so also speeding it up would be nice.

For now multi threading is doable... and the calculate while idle seems nice...

Though I am also kinda curious about cuda... these last ideas are probably easiest to implement and will give most statisfactory.

One problem with that is though, once I have the problem solved/calculated I might not be interested in trying out the harder possibilities.

So maybe it's best to try the hardest first... maybe I will learn something amuzing and even something usefull from it.

More failures perhaps, but in the end, success will come ! LOL.

[skybu...@hotmail.com]

I find this weird behaviour by google newsgroup.

At least google newsgroups could show his postings for something more reasonable like 30 days or something, instead of not showing it at all...

Totally weird. What's the point in posting then if software would not display it at all ? ;)