My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree3Thanks
Reply
 
LinkBack Thread Tools Display Modes
March 10th, 2018, 04:52 PM   #11
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,313
Thanks: 2447

Math Focus: Mainly analysis and algebra
There are certain positions that are drawn inasmuch as if both players play perfectly the game will be drawn. I would suggest that the opening position is drawn in this sense. You don't have to plan on a single strategy to force a draw.
v8archie is offline  
 
March 10th, 2018, 05:57 PM   #12
Math Team
 
Joined: Nov 2014
From: Australia

Posts: 686
Thanks: 243

Actually that is an unsolved problem. We know that chess is deterministic and we are pretty sure it is a draw with perfect play, but it is possible that there is a forced win for white or maybe even a forced win for black.

Either way, "perfect play" in chess is so complex that for practical human standards it may as well not exist. The positions where a draw is in fact force-able are few and very far between. And in any case they can be easily avoided by an opponent who knows what he is doing.

My argument is that we know for certain that there is a forced draw from the starting position in Right Tangle. Something we certainly don't know for chess. And from a competitive standpoint, this isn't ideal as the less experienced player can easily avoid a loss.
Thanks from Loren
Azzajazz is offline  
March 12th, 2018, 12:31 AM   #13
Senior Member
 
Joined: Apr 2014
From: UK

Posts: 871
Thanks: 316

If the 'defender' were determined to only move one piece, you could force it back to the start position by leaving it only one option each time (and thus only require 2/3 pieces to hold it) , but that's not really going to happen. I would advance my entire offence while the defender wanders his piece around. When I am sufficiently close, the defender will eventually have to make a move which lets me slip through. Granted, the defender could still move his single piece, unless I chase it down and trap it, but then the defender will just employ a second wanderer. However, I win on points since I got pieces home first
weirddave is offline  
March 13th, 2018, 03:53 PM   #14
Math Team
 
Joined: Nov 2014
From: Australia

Posts: 686
Thanks: 243

Quote:
Originally Posted by weirddave View Post
If the 'defender' were determined to only move one piece, you could force it back to the start position by leaving it only one option each time
How? To force a single move from your opponents marker in the middle of the board, you would need 7 of your 8 pieces. However on the next move, your opponent would have at least 4 options. You can only move one marker at a time, so he will have at least 3 options for his next move.

Quote:
Originally Posted by weirddave View Post
However, I win on points since I got pieces home first
If there were a point system, then yes. Loren hasn't stated one in the rules.
Azzajazz is offline  
March 13th, 2018, 05:00 PM   #15
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 363
Thanks: 26

Math Focus: Number theory
Quote:
Originally Posted by Azzajazz View Post
If there were a point system, then yes. Loren hasn't stated one in the rules.
Good point. I had envisioned the players to contest each game directly, as in (but not "too similar" to) checkers -- or even markers behaving somewhat (see rules) like chess pawns (without the ability to promote). I consider the pieces themselves to have no point value.
Loren is offline  
March 13th, 2018, 11:03 PM   #16
Math Team
 
Joined: Nov 2014
From: Australia

Posts: 686
Thanks: 243

That's what I gathered. It's a good idea, and with some slight adjustments to the rules it could make for a very interesting game.
See post #6 for my suggestion on how to avoid the forced draw.

Edit: Actually my suggestion doesn't work. You can still move one marker onto the first row and leave it there the entire game.
Azzajazz is offline  
March 14th, 2018, 12:26 AM   #17
Senior Member
 
Joined: Apr 2014
From: UK

Posts: 871
Thanks: 316

Yup, leaving just one marker blocking is where I ended up going to force a draw too
Perhaps not being able to move backwards, giving a piece a maximum of 5 possible moves instead of 8? I suspect you'd have to also start on the 2nd row, otherwise you still have the possibility of keeping a defender at home.

Quote:
Originally Posted by Azzajazz View Post
How? To force a single move from your opponents marker in the middle of the board, you would need 7 of your 8 pieces. However on the next move, your opponent would have at least 4 options. You can only move one marker at a time, so he will have at least 3 options for his next move.
Let's just say it wouldn't be a fast solution

Quote:
Originally Posted by Azzajazz View Post
If there were a point system, then yes. Loren hasn't stated one in the rules.
Yeah, it was for my convenience
weirddave is offline  
March 14th, 2018, 02:16 AM   #18
Math Team
 
Joined: Nov 2014
From: Australia

Posts: 686
Thanks: 243

Yeah, I thought about only moving forward too. It just seems a bit limiting as far as the complexity of the game play goes.
It actually begins to remind me of a variant of chess where both sides have only pawns. The game becomes more about tempo and less about strategy (tempo is a chess term for timing).
Azzajazz is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
tangle



Thread Tools
Display Modes






Copyright © 2018 My Math Forum. All rights reserved.