[Consim-l] Re: GO TO rules vs COME FROM prediction

[Mike NotSpecified]

Ok John and Mircea, I'll take a stab :)

John used an example, "For example, from the
>situation in Europe in April, 1945 I think we know for sure than an 
>amphibious invasion must have occurred."

I'm going to disagree, and make two suggestions of additional information that 
is required to go from end positions back to an amphibious invasion.  It may 
be nit-picking, and perhaps John and Mircea are inclined to simply assume 
certain information that I'm incorporating into my suggestions, but that is 
the nature of bull sessions?

My first suggestion is that to work backwards from April 1945 you have to know 
quite a bit about the capabilities of the units.  How do the armies move?  How 
far?  How fast?  Do you need bridges, or can tanks swim rivers?  Without this 
information I don't see why an amphibious invasion is any more necessary than 
postulating a big air drop.  It's only when you understand the limitations of 
airdrops that you can say with confidence that nobody air dropped all that 
amour right into Germany.

My second suggestion goes back a bit further, and is perhaps a little harder 
to swallow, but I'm going to suggest that you also have to know something 
about the beginning state of nature, the world before the war.  Although the 
relative facings of the end state Anglo, German and Soviet armies gives a 
pretty clear picture of who was fighting who, it would be pretty hard to guess 
even something as basic as how long had then been in those positions?  It 
seems obvious to us that the American army was raised and trained in America, 
thus had to be transported to Europe, but that is because we are so used to 
the history, not because the end state necessarily indicates that.  Humor me 
with an example?

In the late 30's France is swept with a new economic theory, out-sourcing. 
 The military is identified as a huge cost and the decision is made to hire 
mercenary armies from the US and British Commonwealth, which are stationed 
along the Maginot Line.  A token French force is retained for reasons of 
national pride, and to emphasize the economic miracle, they are named the 
"Free French".  Germany invades, the mercenaries are pushed back, portions of 
France are overrun, but then the mercenaries get their act together, and led 
by the brave lads of the Free French, obtain the end positions we see in April 
1945.

I don't think there is anything about the end positions to contradict this 
scenario.  Even if you accept my first suggestion that you have to know 
something about the middle game (i.e. how armies move and interact), you could 
still come up with the above starting positions.

Another example.  Suppose you walk into a stadium where an American style 
football game has just been concluded.  The scoreboard shows the Home team 
finished with 8 points.  Could you work backward from that to establish how 
the game went?

Well, I think you'd have to first accept my first suggestion.  You'd have to 
know how American Football is scored.  If you proposed there were two scoring 
plays of four points each, you'd be wrong.  You might suggest there were two 
field goals (3 points each) and a safety (2 points) and you could be right, 
but most knowledgeable fans would tell you it is far more likely there was one 
touchdown (6 points) followed by a two point conversion.  But if you didn't 
how the scoring worked, or didn't know how the armies moved, you couldn't 
really tell that from the final score/ending positions.

Would you have to have to accept my second suggestion, that you need to know 
something about the beginning state, in this example?  Well, it gets a bit 
more farfetched, but how safe is your assumption that the score started at 
zero?  What if the home team starts with two points for being the home team? 
 What if today's game is one in a series and the teams carry forward the 
points earned in previous contests?  Given that you know the scoring system 
from the previous paragraph you know there are no negative scores so it 
couldn’t have started at say 10 and lost two points (think gymnastics), but 
that would otherwise be a possibility.

Given the ending positions of the armies in April 1945, could you work 
backward through the war, even just as far back as June 1944?  I don't think 
so, not given ONLY that information.  I think you'd absolutely need to know 
something about how the armies move and interact to even begin to know where 
they COULD have been.  Even March 1945 would be a mystery, how far can an army 
travel in a month?  And while that information could let you theoretically 
list all the possible positions and events as far back as you want to go, I 
think your set of possibilities would be so infinite that absent some 
information on the beginning state you'd have no basis for preferring my Free 
French scenario to any other.

Thanks for asking!  If nothing else, you've provided me with some amusement 
thinking this over.



On Sun, 28 Dec 2008 11:54:31 -0600
  "John Best" <jlbest at advancenet.net> wrote:
> It was back in September, 2008 that Mircea Pauca posted the following:
> 
> 
>>    I thought... most game rules are like imperative programming
>> languages: do this and that, loops, IF/THEN, GO TO and
>> player decisions at specified places. It's reasonably easy to track,
>> even if some purist programmers said "GOTO considered harmful".
>> To get a distribution of results, one way is Monte Carlo simulation, 
>> effectively playing (with automated decisions or rules) many times.
>>
>>    But - I found trying to deduce a theoretical distribution of results
>> even for the simplest games, like Axis&Allies or Knizia's Decathlon
>> is more like the mythical COME FROM instruction, devilishly difficult to 
>> conceive and debug. For each game state one must try to consider ALL 
>> situations and decisions that can lead to it.
>>
>>    This links again with my old thread on "simulating backwards in time".
>> Deterministic differential equations or even some simple random noise
>> are easily reversible in time, but add *decisions* and it becomes hairy...
>>
>> ... From the ruins of Hiroshima a wondrous un-bang reconstitutes centuries 
>> of layered architecture, then a parachute flies up with atomic bomb into 
>> the belly of a B-29 flying back from base...
>> but how to know what was before if one doesn't even know the ruins,
>> as they are 'nothing' in game terms ? There are many kinds of nothing...
>>
> Ok, I've had this in my inbox for over 3 months, puzzling over it, thinking 
>I've understood the point of it, and then, having it slip away.  At one 
>level, I thought this was something like the following:  Let's look at a 
>military situation, let's say Europe in April, 1945.  Then we say, ok, let's 
>take this situation as the "end of the game" and then say ok, "What *had* to 
>happen in order for this situation that we see on the board to have 
>occurred?"  But, under that viewpoint, isn't the answer to that question 
>"There is very little that necessarily *had* to happen?"  I'm making an 
>analogy with chess.  If we show a grandmaster a game board showing a won 
>game, and ask him or her the following question, "What had to happen on the 
>last move in order for this situation to have been achieved?".  The 
>grandmaster may be able to show us two or three possible last moves that 
>could have been made (or more, it depends in part on how many pieces are left 
>on the board) .  And from there,  the grandmaster might be able to show us 
>three or four next-to-last moves, and so on.  If we run the game backwards 
>like this to the beginning conventional chess position, we might a be able to 
>come up with a set of 10^20 games that could have been played to arrive at 
>the situation at the end of the game (which was the situation we started 
>with--very confusing!).  I'll grant that this is a big reduction from the 
>10^40 or so games of chess that can be played forward from the conventional 
>chess position.  And that means that the final chess position, and the 
>situation in Europe in April 1945, are both informative--they have traces of 
>the decision making process that got them there.  For example, from the 
>situation in Europe in April, 1945 I think we know for sure than an 
>amphibious invasion must have occurred.  But where and when?  Could or would 
>the Allies have achieved the end-of-game position that we see in April 1945 
>if they had never invaded anywhere in France, or the Netherlands, but instead 
>pushed up strictly from Italy?  It seems highly unlikely that the board would 
>look like it did in 1945 if there had been no invasion of France.  But that's 
>not the question.  The question is *could* the board have looked that way if 
>the Allies had not invaded in France?  And I think that answer is yes, 
>however remote/crazy/absurd that possibility seems. Ok, well let's see if I'm 
>even remotely on the right track with this, and if so, what analytic tools 
>could we bring to bear to try to extract the structure from an existing 
>situation in a way that Mircea envisions.  He mentioned deterministic 
>differential equations (which I think would lead to a Fourier analysis if I'm 
>on the same page with him).  In the meantime, I'll keep thinking about the 
>intriguing statement, "There are many kinds of nothing."  Thanks for offering 
>this Mircea, and thanks for reading.
> John Best
> jlbest at advancenet.net 
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