f



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

Hello,

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 ?!

Bye,
  Skybuck. 
0
skybuck2000
12/9/2016 12:14:08 PM
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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 o=
r 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 softwa=
re to access the server. The server currently has a technical problem. Uplo=
ading 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... perhap=
s 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 complete=
ly sucks... and is like 1.000.000 times more difficult with this very lacki=
ng 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 p=
roblem:


>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 indexe=
s
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 fro=
m
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 priorit=
y

"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 yo=
u
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 muc=
h
>so it can use the reserve computational horse power).
>(I still have to try these "idle/reverse" ideas to see which one works bes=
t
>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 tr=
y
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 dimensionall=
y
multiplied by the number of permutations (=3Dattack orders).

So since momentarily the team consists out of 4 contenders/numbers and sinc=
e
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 tha=
t
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 t=
o
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 i=
t
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=3Dattacker

So basically the X-Axis describes the destination=3Dtarget

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=3D1
Tank=3D2
Plane=3D3
Ship=3D4

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 tan=
k
?

So horse =3D 1

So proceed to row.

So tank =3D 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 o=
f
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 fro=
m
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 no=
t
take part in the next round of attacks.

However another approach could be taken which stays more true to the concep=
t
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. T=
o
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 stil=
l
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 ar=
e
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 alread=
y
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 easil=
y
destroyed by a high victory chance... even though it was 1 vs 1... thus thi=
s
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 mirro=
r
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 =3D 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 incremente=
d
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 =3D "".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 i=
n
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 respon=
d
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 a=
n
interesting question. Some additional statistical analysis variables could
be added to the code to track what the average number of rounds is, what th=
e
minimum was and what the maximum was !

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

Bye,
  Skybuck.
0
skybuck2000
12/15/2016 11:30:01 AM
<skybuck2000@hotmail.com> wrote:

> 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.

You could try nntp.aioe.org. No password or registration required.

-- 
Mvh./Regards,    Niels J�rgen Kruse,    Vanl�se, Denmark
0
nj_kruse
12/17/2016 11:28:34 AM
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