Jump to content


Photo

Scout endgame hypothesis (more to come later)


  • Please log in to reply
10 replies to this topic

#1 Unladen Swallow

Unladen Swallow

    Miner

  • Members
  • PipPipPipPipPip
  • 155 posts
  • Coat of arms
  • Platinum Marshal

Posted 23 May 2017 - 05:38 PM

Sir_richard and I have been analysing scout endgames on gravon. The scout is able to be captured with 4 pieces, in nearly all "normal" gameplay positions. This is the most complex position we found where it was possible to capture the scout with 4 pieces:

 

PqOSSdv.png
This is a difficult position and certainly not easy to force the win here. On each side of the board there is a 6x4 box, which we wager is the minimum squares necessary to capture the scout with perfect play from the scout. Any more room, and the scout will be able to escape.

 

The scout's goal is to fly between the top and bottom, and the pieces first have to force the scout into one of the two 6x4 boxes before progressing any further. 

 

 

---

 

As an illustration, a position with no bombs first 3 rows requires a minimum of 5 pieces to capture the scout, as the scout can otherwise alternate between 3 available squares. It is impossible to capture the scout in the below position.

 

FY1lAXg.png

 


  • Major Nelson and groundbob like this

#2 Napoleon 1er

Napoleon 1er

    Colonel

  • Moderators
  • 1,871 posts
  • Coat of arms
  • Platinum Marshal

Posted 23 May 2017 - 07:32 PM

In the first pic above you can get him with 3 pieces thanks to bomb placement. In the situation with no bomb or flag i don't know but these are impossible situation in reality. As minimum you will have 2 open flags extremely vulnerable. In real situation with a single scout at least your flag needs to be sealed.
The effective most difficult situation is when your flag is sealed in bottom corner left and your opponent flag sealed in top corner right. In rhis situation you need 4 pieces.

If you don't know where you go ... you have a lot of chance to arrive elsewhere ...


#3 Unladen Swallow

Unladen Swallow

    Miner

  • Members
  • PipPipPipPipPip
  • 155 posts
  • Coat of arms
  • Platinum Marshal

Posted 23 May 2017 - 07:59 PM

I invite you to try it with me on gravon one day. I don't think the first example is possible with 3 scouts in a 6x4 box. 

 

The #2nd example is merely an illustration. In this example the scout can move between open files. You can not force the scout on one side of the board with 4 pieces (takes 5 minimum)


Edited by Unladen Swallow, 23 May 2017 - 08:02 PM.


#4 Dobby125

Dobby125

    Miner

  • Members
  • PipPipPipPipPip
  • 150 posts
  • Coat of arms
  • Silver Major

Posted 24 May 2017 - 01:59 AM

Watch Stratego with Bob(and friends) capture a scout with 3 pieces.  That was a very nice ending.

 

https://youtu.be/WBxuJrVzlFY?t=3567


  • groundbob likes this

#5 Napoleon 1er

Napoleon 1er

    Colonel

  • Moderators
  • 1,871 posts
  • Coat of arms
  • Platinum Marshal

Posted 24 May 2017 - 07:21 AM

Yes we can try on gravon. Next 4 days i have holidays and could arrange any time if i know it 24 hours in advance (except after 20:00 gmt.
In the mean time you can check my quizz no 6 which is precisely on scout capture with 3 pieces.

If you don't know where you go ... you have a lot of chance to arrive elsewhere ...


#6 groundbob

groundbob

    Bomb

  • Members
  • PipPipPip
  • 36 posts
  • Coat of arms
  • Gold Spy

Posted 24 May 2017 - 02:17 PM

Thanks Dobby,

 

I was just about to post the same thing,as it was a great learning experience for me. I learnt about the 2 square rule better and also how to trap a scout.

 

I hope my commentary of the help people were giving in the chat,will also help others to understand it,like it did me (even though I took an age to actually work things out haha).

 

 

Watch Stratego with Bob(and friends) capture a scout with 3 pieces.  That was a very nice ending.

 

https://youtu.be/WBxuJrVzlFY?t=3567


Edited by groundbob, 24 May 2017 - 02:20 PM.

  • Dobby125 likes this

#7 Napoleon 1er

Napoleon 1er

    Colonel

  • Moderators
  • 1,871 posts
  • Coat of arms
  • Platinum Marshal

Posted 4 weeks ago

I invite you to try it with me on gravon one day. I don't think the first example is possible with 3 scouts in a 6x4 box. 

 

The #2nd example is merely an illustration. In this example the scout can move between open files. You can not force the scout on one side of the board with 4 pieces (takes 5 minimum)

finally i think you are right with 2x 6x4 open squares you need 4 pieces to capture the scout but with anything less than that you can get it with 3 pieces.


  • Unladen Swallow likes this

If you don't know where you go ... you have a lot of chance to arrive elsewhere ...


#8 Sir_Richard

Sir_Richard

    Spy

  • Members
  • PipPip
  • 18 posts
  • Coat of arms
  • Silver Captain

Posted 4 weeks ago

I am unable to demonstrate capturing a scout with 4 pieces in the first position, where there are 2 6x4 open spaces.

The reason is that at some point, as the pieces close in, the scout has the option of escaping or remaining.  If he

remains within the box, he's captured; if he leaves the box, he can thereafter be excluded from it.  After exclusion,

he flees across the board, because the pieces are out of position to prevent him.  Then the same thing is repeated

in the other 6x4 box, and etc = draw.  But if only one such 6x4 box exists, the scout is excluded, confined to the other side of the board, forced into an area smaller than 6x4, and captured.

 

Furthermore, I believe that the capture/exclusion of the scout in the 6x4 area must pass through one of two mirror-image paradigmatic configurations of the 4 pursuit pieces, which assume knight's-leap (chess)

relationships to each other.  Optimal play of the scout can force the configuration to be assumed.  As a

consequence, the most expeditious procedure for the pursuit, is to ignore the scout, maneuver the pieces into

the paradigmatic configuration, and only then close in.  If the scout is outside the box at the time the configuration

is complete, they will exclude the scout, and confine it to the other side of the board, etc.

 

These are heady claims, and I'm willing to demonstrate them on Gravon, though optimal play with the scout is as demanding as playing the pieces.  An analytical approach is better, and I have one, almost complete.

 

Sir Richard



#9 Sir_Richard

Sir_Richard

    Spy

  • Members
  • PipPip
  • 18 posts
  • Coat of arms
  • Silver Captain

Posted 4 weeks ago

Thanks Dobby,

 

I was just about to post the same thing,as it was a great learning experience for me. I learnt about the 2 square rule better and also how to trap a scout.

 

I hope my commentary of the help people were giving in the chat,will also help others to understand it,like it did me (even though I took an age to actually work things out haha).

In the You Tube example, the largest open area on the board was 6x3, not including the 4th pursuit piece sitting within it.  So three pieces were enough.  But the pursuer had 4 pieces, not sure why the 4th piece wasn't used, as it would have made the process easier.  Sir Richard



#10 Sir_Richard

Sir_Richard

    Spy

  • Members
  • PipPip
  • 18 posts
  • Coat of arms
  • Silver Captain

Posted 4 weeks ago

finally i think you are right with 2x 6x4 open squares you need 4 pieces to capture the scout but with anything less than that you can get it with 3 pieces.

Hmmm.  How about 3 pieces in a 4x5 box?  They can keep the scout in the box, but I can't figure out how to close in.

I don't have an analytical proof of this one - proving a negative is much harder than proving a positive. 

Sir Richard



#11 GaryLShelton

GaryLShelton

    Marshal

  • Moderators
  • 4,023 posts
  • Coat of arms
  • Gold Sergeant

Posted 3 weeks ago

I'm no expert like Napoleon or US above, and I'd like to hear their comments on my theory. But the thing that I think helps when you try to chase down the scout in the first situation above is to gain the two squares advantage in the lanes he can use to cross the board, or the sideways lanes. If the scout has to cross your piece's path to get into the open rank or file in any lane, then you have the two squares advantage in that situation in that lane. So one has to try to position himself in the rank or file the scout will necessarily first have to cross to try to use any lane to escape.

The Two Squares rule for scouts is that a scout may not cross the same line between any two squares on more than three consecutive turns.
The complete GS&F Rules can be found here: http://forum.strateg...rum-rules-2016/

Draw Refusal Rules, specifically, can be read here: http://forum.strateg...604#entry339604




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users