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Two square rule question


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#1 TemplateRex

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Posted 25 June 2018 - 09:27 AM

It used to be that the two-squares rule had a maximum of 5 consecutive back-and-forths of the same piece between the same two squares. Now it is 3. As is spelled out in Vincent de Boer's thesis on Stratego programming from 2007, the possibility of placing 3 interposing moves at any point, will greatly inflate the required search depth to solve tactics.

 

I am in the process of programming a new Stratego AI and have found the same problem to be still a major obstacle on modern computers.So I wondered if a shortcut was possible that still gives the same game-theoretic results as for the official ISF rules, but which is a lot cheaper to compute. 

 

Modified two-squares rule: a piece cannot move more than 1 consecutive time between the same two squares, except to capture a piece that was placed on the just vacated square, or if the opponent revealed a new piece of information (moved an unknown piece, or revealed a piece's rank). 

 

Note that this is not a proposal to modify the ISF rules, just an experiment to greatly reduce a computer program's search depth to solve tactics. 

 

Question to the experts: is this rule modification consistent? In other words, are there any position where this rule (with at most 1 consecutive move, except for captures or to act on new information) gives a different outcome than the ISF rules (with at most 3 consecutive moves)?


Edited by TemplateRex, 25 June 2018 - 12:25 PM.

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#2 TemplateRex

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Posted 25 June 2018 - 12:20 PM

PEkbfOa.png

 

I guess this breaks my rule modification. Under the ISF 3-moves no exceptions rule, blue wins after 

 

E8-E7 F7xE7

F8-F7 E7xF7

E9-E7 F7xE7 (3rd time!)

F9-F7 E7-E8

F7-A7 B2-A2

A7xA2 E8-E9

A2xA1 blue wins

 

whereas under my suggested 1-move with capture exceptions, red could have captured for a 4th consecutive time to get the win. So the game result is not the same :(

 

Question: why doesn't the two-square rule make an exception for captures? Seems like a small edge for the attacker that is always good to have.


Edited by TemplateRex, 25 June 2018 - 12:21 PM.

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#3 The Prof

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Posted 29 June 2018 - 07:26 AM

Here's a situation where the modified rule makes a difference:  Blue colonel on C7, red general on E4, and blue sergeant on E5.  Red does not want to let the colonel come down his left side and attack his pieces over there.  It's his turn and he captures the blue sergeant.  Then Blue moves C7 to B7.  Red must be able to move back to E4 to be able to prevent the colonel access to his territory, however he is blocked from moving to E4 by the modified rule.

 

The Milton Bradley board game, which is all I knew growing up, gave this as the Two-squares Rule:  "A piece cannot move between the same two squares on three consecutive turns".  Thus, the limit was two moves.  I've always liked this, as it cut down on unnecessary moves, and it rmakes a player think if he really wants to move back to the square he just came from.  But this also has the issue of not allowing captures if it means too many moves between two squares.  

 

If I had to suggest a modified rule that would limit unnecessary moves but allow captures it would be:  "A piece may not move between the same two squares on three consecutive turns if his opponent has also just moved the same piece back and forth between two squares."   Thus the two-squares rule only comes into effect when both players are moving back and forth.  So it would work the same way for chasing and trapping, but wouldn't ever block capturing or moving back and forth while the opponent is advancing a piece or moving different pieces.


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#4 Napoleon 1er

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Posted 29 June 2018 - 11:58 AM

Not sure to understand. After
E8-E7 F7xE7
F8-F7 red moves E8 E9 E10 while blue cannot reach the red flag before red reaches blue flag?
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#5 TemplateRex

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Posted 29 June 2018 - 02:33 PM

@The Prof Yes, your example is also very clear. I guess I wasn't too careful in my formulation, but the intend was to reset the "N-move counter" for the Two-squares Rule for every capture. Without it, for any N-move rule, it's always possible to construct pathological examples where a lone sergeant cannot block N+1 scouts. I also prefer a 2-move version over the current 3-move one.


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#6 TemplateRex

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Posted 15 August 2018 - 11:18 AM

Not sure to understand. After
E8-E7 F7xE7
F8-F7 red moves E8 E9 E10 while blue cannot reach the red flag before red reaches blue flag?

 

E8-E7 F7xE7

F8-F7 E7-E8

F7-A7 E8-E9

A7-A1 blue is first (same when spy interposes)


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#7 GaryLShelton

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Posted 16 August 2018 - 03:50 AM

 
Question: why doesn't the two-square rule make an exception for captures? Seems like a small edge for the attacker that is always good to have.


TemplateRex, I may be missing something here in the point of this, but if you are blocked from returning to a square you've just been to by the standard Two Squares Rule after three moves (or indeed even your modified single move limit) what piece that then moves into your rule-blocked square could you not have attacked already? It would only be a scout previously at a distance. Otherwise, any normal piece you would have been able to attack in the moving of the three times between the squares, right? And if that's so, why the concern over being able to attack it in a Two Squares exception?

i77rs4m.jpg

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#8 TemplateRex

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Posted 16 August 2018 - 08:10 AM



TemplateRex, I may be missing something here in the point of this, but if you are blocked from returning to a square you've just been to by the standard Two Squares Rule after three moves (or indeed even your modified single move limit) what piece that then moves into your rule-blocked square could you not have attacked already? It would only be a scout previously at a distance. Otherwise, any normal piece you would have been able to attack in the moving of the three times between the squares, right? And if that's so, why the concern over being able to attack it in a Two Squares exception?

 

My point was this: a Stratego analysis engine (doing look-ahead search, much like a chess engine) is severely hampered by interposing attacks of diagonal pieces. This will push the resolution of a tactic over the "search horizon", since each 5-move sequence delays the inevitable. Under the old 5-times ISF-rule, it was worse than under the current 3-times ISF-rule. The Prof mentions the 2-times Milton-Bradley version, which would be even better for engine.

 

The problem is that the diagram I posted in this thread, is a blue win under the current 3-times ISF-rule and was a red win under the old 5-times ISF-rule. So changing the number of 2-square shuffles from 5 to 3, changes the result of this (admittedly contrived) position. Lowering it further to 2 would change the result for more positions where a single piece chokes off 3 or more pieces in a narrow corridor.

 

BTW, it's not just positions with scouts, below it's a blue win under the current 3-times ISF-rule since the 4-th sergeant can escape the corridor :)

 

K4nrnLU.png


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#9 GaryLShelton

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Posted 16 August 2018 - 12:37 PM

Thanks for the clarification. Your first example several posts above is indeed changed by the 5 rule over the current 3. The piece positions were admittedly, by you, contrived but they nonetheless produced those results. The 5 move rule allows red the win, whereas the 3 move one allows blue to win. It must be further noted that under the old 1961 Milton Bradley rule of only 2 moves the result for the above example is still a win for blue.

By the way, here's the 1961 Milton Bradley rules right from my copy I snapped a pic of just now.

Stratego Board Game Rules, 1961 MB version https://imgur.com/gallery/oyyNQ3y

You can see at Rules for Movement #10 what The Prof is referring to.

Do the 5,3, and 2 move rules yield these same respective results under other scenarios? I'll let you forward thinkers ponder that. :) My suspicion is that more common scenarios might play out with the same result in all three versions.

i77rs4m.jpg

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#10 TemplateRex

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Posted 16 August 2018 - 07:24 PM

Do the 5,3, and 2 move rules yield these same respective results under other scenarios? I'll let you forward thinkers ponder that. :) My suspicion is that more common scenarios might play out with the same result in all three versions.

 

I think only positions with a cluster of pieces in a choke point area are affected by the differences between 5, 3, and 2 move rules. For analysis engines, it's better to use the 2-move rule version, since that cuts down on analyzing delaying moves.

 

BTW, my initial idea of having a 1-move rule is of course impossible, since it would not allow the 3-square defense, where you really need to be able to repeat 2 times. 


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#11 Don_Homer

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Posted 17 August 2018 - 04:31 PM

My point was this: a Stratego analysis engine (doing look-ahead search, much like a chess engine) is severely hampered by interposing attacks of diagonal pieces. This will push the resolution of a tactic over the "search horizon", since each 5-move sequence delays the inevitable. Under the old 5-times ISF-rule, it was worse than under the current 3-times ISF-rule. The Prof mentions the 2-times Milton-Bradley version, which would be even better for engine.

 

The problem is that the diagram I posted in this thread, is a blue win under the current 3-times ISF-rule and was a red win under the old 5-times ISF-rule. So changing the number of 2-square shuffles from 5 to 3, changes the result of this (admittedly contrived) position. Lowering it further to 2 would change the result for more positions where a single piece chokes off 3 or more pieces in a narrow corridor.

 

BTW, it's not just positions with scouts, below it's a blue win under the current 3-times ISF-rule since the 4-th sergeant can escape the corridor :)

 

K4nrnLU.png

 

I dont see how this is not a draw if both colours play it perfect (regardless of square rule). Maybe I miss something. If you like we can try it out. At gravon you can set up this setup and choose 3 square rule and 5 square rule. Im happy to defend the 4 sercheants :)


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#12 TemplateRex

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Posted 17 August 2018 - 06:57 PM

I dont see how this is not a draw if both colours play it perfect (regardless of square rule). Maybe I miss something. If you like we can try it out. At gravon you can set up this setup and choose 3 square rule and 5 square rule. Im happy to defend the 4 sercheants :)

 

It's blue to move. 

 

F8-F7 E7xF7 

E8-E7 F7xE7 

F6-F7 E7xF7 

E6-E7

 

and now the red lieut on F7 cannot move for a 4th time to capture the last blue sergeant. So blue runs to red's open flag. After each blue move, red has to capture, otherwise blue will get to the open flag with 2 sergeants, and only one lieut cannot stop that.


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#13 Don_Homer

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Posted 17 August 2018 - 07:49 PM

It's blue to move. 

 

F8-F7 E7xF7 

E8-E7 F7xE7 

F6-F7 E7xF7 

E6-E7

 

and now the red lieut on F7 cannot move for a 4th time to capture the last blue sergeant. So blue runs to red's open flag. After each blue move, red has to capture, otherwise blue will get to the open flag with 2 sergeants, and only one lieut cannot stop that.

 

I would move e6-e5 with sercheant if I was blue.


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#14 TemplateRex

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Posted 17 August 2018 - 08:40 PM

I would move e6-e5 with sercheant if I was blue.

 

Well you claimed it was a draw, and I showed how blue could win. What is your point?


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#15 GaryLShelton

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Posted 18 August 2018 - 05:34 AM

I would move e6-e5 with sercheant if I was blue.


Don, red can obtain a draw if blue does what you say. But if blue is smart, and starts coming right out with the sergeants, then red will exhaust his 3 moves under Two Square and be stuck. If, however, blue allows red to reach F7 before agressively moving out its sergeants, red can use the 2nd movable piece in the spy to maintain no block by the Two Squares on the lieutenant, and thereby achieve a draw.

But, again, if blue is smart and plays it like TemplateRex describes it, blue will win every time under the current Two Squares Rule.

EDIT NEXT DAY: Don is right with his 2nd suggestion below. Red can achieve draw. But not by doing the above. Rather, it achieves the draw by not killing the 3rd blue sergeant offered on the 7th rank but by killing the other sergeant remaining first.
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i77rs4m.jpg

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#16 Don_Homer

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Posted 18 August 2018 - 10:07 AM

Well you claimed it was a draw, and I showed how blue could win. What is your point?

My point is that your example is not accurate :). Blue cannot win. Also this situation never happens. I challenge you to make a realistic situation which shows significant difference between 3 and 5 square rule. 


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#17 Don_Homer

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Posted 18 August 2018 - 10:15 AM

.After each blue move, red has to capture, otherwise blue will get to the open flag with 2 sergeants, and only one lieut cannot stop that.

I think this is not right. 

 

 

 

But, again, if blue is smart and plays it like TemplateRex describes it, blue will win every time under the current Two Squares Rule. 

 Here is how it turns out I think:
 

F8-F7 E7xF7 

E8-E7 F7xE7 

F6-F7 E7xE6 

F6-F7 draw. 


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#18 GaryLShelton

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Posted 18 August 2018 - 01:57 PM

I think this is not right.


Here is how it turns out I think:

F8-F7 E7xF7
E8-E7 F7xE7
F6-F7 E7xE6
F6-F7 draw.


Well, Don, I gotta hand it to you. You're not just another pretty face. :)

Although your first answer about dropping down the sergeant was wrong, this one appears to be correct. Draw for red. Nice job. :)

The way for red to not lose the two squares game is not to play it in this case.

(The F6-F7 repeated move is wrong, though.)

i77rs4m.jpg

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#19 TemplateRex

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Posted 18 August 2018 - 03:26 PM

My point is that your example is not accurate :). Blue cannot win. Also this situation never happens. I challenge you to make a realistic situation which shows significant difference between 3 and 5 square rule. 

 

OK, I admit your E7xE6 moves kills the blue win for this position, since it takes too long for the blue sergeant to reach the flag. Nice find! I posted  a new position in the Training forum where I think blue can win no matter red's defense. 

I also admit (and have so from the beginning) that these positions are contrived. I just want to find out where the differences occur between 5-times, 3-times or even 2-times two-squares rules. 


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#20 Don_Homer

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Posted 19 August 2018 - 02:05 PM

Well, Don, I gotta hand it to you. You're not just another pretty face. :)

Although your first answer about dropping down the sergeant was wrong, this one appears to be correct. Draw for red. Nice job. :)

The way for red to not lose the two squares game is not to play it in this case.

(The F6-F7 repeated move is wrong, though.)

Thanks, Gary. I stick to my first answer though. Why would you offer your (3) valuable sercheants in this situation? They are cosy there ;).


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