another two player game

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another two player game

Postby evert » Fri Mar 17, 2006 10:00 pm

ab wrote:I'm wondering if the player playing first has too much of an advantage? It depends how easy it is to take the lead from him. A rule change that would get around this is as follows:

First lets create some terminology. If you place the first number in a group of symmetric cells (whatever the symmetry you're using) we'll say you're starting an orbit. An alternative rule could be that each player can start one orbit. Then on any turn you can play in either of the two orbits, but you can only start a new orbit when the orbit you started has been completed. That way you can still sometimes have control over where your opponent plays, but the power does not lie solely with one player.


Ok we should try this. The notation should include the played cell - because I suppose the forced cells that come after it are not involved in the symmetry rules. Do you agree?

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
1. R7C6 1      ....?
2. etc...


BTW For the records, the rules for this 2-player game have been pointed out in this topic:
http://forum.enjoysudoku.com/viewtopic.php?t=3287&postdays=0&postorder=asc&start=0
I started a 2nd topic in order to keep some overview.
Last edited by evert on Sat Mar 18, 2006 7:13 pm, edited 1 time in total.
evert
 
Posts: 186
Joined: 26 August 2005

Re: another two player game

Postby ab » Sat Mar 18, 2006 12:57 am

evert wrote:
ab wrote:I'm wondering if the player playing first has too much of an advantage? It depends how easy it is to take the lead from him. A rule change that would get around this is as follows:

First lets create some terminology. If you place the first number in a group of symmetric cells (whatever the symmetry you're using) we'll say you're starting an orbit. An alternative rule could be that each player can start one orbit. Then on any turn you can play in either of the two orbits, but you can only start a new orbit when the orbit you started has been completed. That way you can still sometimes have control over where your opponent plays, but the power does not lie solely with one player.


Ok we should try this. The notation should include the played cell - because I suppose the forced cells that come after it are not involved in the symmetry rules. Do you agree?

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
1. R7C6 1      R4C3 6
2. etc...


Shall we try using a different symmetry?
How about both diagonals?
ab
 
Posts: 451
Joined: 06 September 2005

Postby evert » Sat Mar 18, 2006 3:04 pm

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . |-2 . . |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
1. R7C6 1      R4C3 6
2. R6C7 2


Does that symmetry mean that my orbit consisted of R7C6, R6C7,R4C3 and R3C4?
evert
 
Posts: 186
Joined: 26 August 2005

Postby ab » Sat Mar 18, 2006 5:07 pm

evert wrote:
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . . |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
1. R7C6 1      R4C3 6
2. R6C7 2 R5C5 6


Does that symmetry mean that my orbit consisted of R7C6, R6C7,R4C3 and R3C4?


That's right
ab
 
Posts: 451
Joined: 06 September 2005

Postby evert » Sat Mar 18, 2006 11:22 pm

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . |-4 . . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . . |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4


I'm caught in my orbit because I'm not allowed to start a 2nd one.
You're about to profit from the 6s.

I'm looking for some kind of strategy here.
evert
 
Posts: 186
Joined: 26 August 2005

Postby ab » Sun Mar 19, 2006 3:44 am

evert wrote:
Code: Select all
+-------+-------+-------+
| . . . | . . . | . 6 . |
| . . . | . . . | . . . |
| . . . |-4 . . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6


I'm caught in my orbit because I'm not allowed to start a 2nd one.
You're about to profit from the 6s.

I'm looking for some kind of strategy here.


I don't gain a lot really, 'cos you're free to play anywhere now and can make another 6 if you want.
ab
 
Posts: 451
Joined: 06 September 2005

Postby evert » Wed Mar 22, 2006 12:18 am

Code: Select all
+-------+-------+-------+
| . . . | . . . | . 6 . |
| . . . |-6 . . | . . . |
| . . . |-4 . . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . . . | . .-6 | . . . |
+-------+-------+-------+
1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6

The sixes are indeed popular:)
Should there be a rule in order to maintain a higher variety of numbers in the early stage of the game?

Please mention if you actually wanted a higher frequency of moves.
Shortly I moved house and it's still chaotic.
evert
 
Posts: 186
Joined: 26 August 2005

Postby ab » Wed Mar 22, 2006 3:15 am

evert wrote:
Code: Select all
+-------+-------+-------+
| . . . | . . . | . 6 . |
| . . . |-6 . . | . . . |
| . . . |-4 . . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+
1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8

The sixes are indeed popular:)
Should there be a rule in order to maintain a higher variety of numbers in the early stage of the game?

Please mention if you actually wanted a higher frequency of moves.
Shortly I moved house and it's still chaotic.


post when you wish. moving house is stressful, I'm sure you have other things on your mind! Also I've been glued to the superior puzzle thread started by Tarek. It's pretty cool.
ab
 
Posts: 451
Joined: 06 September 2005

Postby evert » Wed Mar 22, 2006 10:44 am

Code: Select all
+-------+-------+-------+
| . . . | . . . | . 6 . |
| . . . |-6 . . | . . . |
| . . . |-4 . . | . . . |
+-------+-------+-------+
|-7 . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | . . . |
| . . . | . . . | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+
1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8
5. R4C1 7
evert
 
Posts: 186
Joined: 26 August 2005

Postby ab » Wed Mar 22, 2006 6:33 pm

Code: Select all
+-------+-------+-------+
| . . . | . . . | . 6 . |
| . . . |-6 . . | . . . |
| . 6 . |-4 . . | . . . |
+-------+-------+-------+
|-7 . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | 6 . . |
| 6 . . | . . . | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+
1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8
5. R4C1 7 R8C1 6
ab
 
Posts: 451
Joined: 06 September 2005

Postby evert » Mon Mar 27, 2006 10:25 pm

Code: Select all
+-------+-------+-------+
| . . . |-3 . . | . 6 . |
| . . . |-6 . . | . . . |
| . 6 . |-4 . . | . . . |
+-------+-------+-------+
|-7 . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | 6 . . |
| 6 . . | . . . | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+

1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8
5. R4C1 7 R8C1 6
6. R1C4 3
evert
 
Posts: 186
Joined: 26 August 2005

Postby ab » Tue Mar 28, 2006 12:30 am

Code: Select all
+-------+-------+-------+
| . . . |-3 . . | . 6 . |
| . . . |-6 . . | . . 9 |
| . 6 . |-4 . . | . . . |
+-------+-------+-------+
|-7 . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | 6 . . |
| 6 . . | . . . | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+

1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8
5. R4C1 7 R8C1 6
6. R1C4 3 R2C9 9

ab
 
Posts: 451
Joined: 06 September 2005

Postby evert » Tue Mar 28, 2006 2:38 pm

Code: Select all
+-------+-------+-------+
|-5 . . |-3 . . | . 6 . |
| . . . |-6 . . | . . 9 |
| . 6 . |-4 . . | . . . |
+-------+-------+-------+
|-7 . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . . . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | 6 . . |
| 6 . . | . . . | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+

1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8
5. R4C1 7 R8C1 6
6. R1C4 3 R2C9 9
7. R1C1 5
evert
 
Posts: 186
Joined: 26 August 2005

Postby ab » Tue Mar 28, 2006 2:58 pm

Code: Select all
+-------+-------+-------+
|-5 . . |-3 . . | . 6 . |
| . . . |-6 . . | . . 9 |
| . 6 . |-4 . . | . . . |
+-------+-------+-------+
|-7 . 6 | . . . | . . . |
| . . . | . 6 . | . . . |
| . . . | . 3 . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | 6 . . |
| 6 . . | . . 3 | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+

1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8
5. R4C1 7 R8C1 6
6. R1C4 3 R2C9 9
7. R1C1 5 R6C5 3
ab
 
Posts: 451
Joined: 06 September 2005

Postby evert » Tue Mar 28, 2006 4:11 pm

Code: Select all
+-------+-------+-------+
|-5 . . |-3 . . | . 6 . |
| . . . |-6 . . | . . 9 |
| . 6 . |-4 . . | . . . |
+-------+-------+-------+
|-7-2 6 | . . . | . . . |
| . . . | . 6-2 | . . . |
| . . . | . 3 . |-2 . 6 |
+-------+-------+-------+
| . . . | . .-1 | 6 . . |
| 6 . . | . . 3 | . . . |
| . 8 . | . .-6 | . . . |
+-------+-------+-------+

1. R7C6 1 R4C3 6
2. R6C7 2 R5C5 6
3. R3C4 4 R1C8 6
4. R9C6 6 R9C2 8
5. R4C1 7 R8C1 6
6. R1C4 3 R2C9 9
7. R1C1 5 R6C5 3
8. R5C6 2
evert
 
Posts: 186
Joined: 26 August 2005

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