Several times, we mentioned the importance of blocks in Ataxx, notably in the used strategies. So, to delimit each game configuration, it is logical to define a code wich allows to precisely determine the place of each block on the board. We call it Blocks-Config.
This codification was invented in july 1997, in this Pressibus site.
Squares numerotation
Remind that, in accordance with the Ataxx standard rules, blocks are symmetrically placed around the centre of the 7x7 board, and that no one is in the 4 corners, reserved for the beginning positions. So, only 15 squares are to be codified, in the high-left quarter without its corner :
d
e
4
a
g
f
5
b
c
h
6
1
2
3
x
It is easy to remember by the location of the following sequences : 123-456-abc-def-gh-x.
Code structure
Now we may define a code by spelling the digits / letters were are the blocks, in the following order : 1 2 3 4 5 6 a b c d e f g h x.
For example, this board has the Blocks-Config 3ghx :
d
e
4
a
g
f
5
@
b
c
h
6
@
1
2
3
x
@
@
@
@
@
By convention, the board having no block has the Blocks-Config 0 (the digit).
To find others example of Blocks-Configs, see under and on the Ataxxlet game area.
More, by going to the Rondão Attax page, you may download (as well as the program) a configuration file having 40 blocks-Configs ready to play.
Twins, horizontal preference and weight
d
e
4
a
g
f
5
b
c
h
6
@
@
@
1
2
3
x
@
@
@
@
@
@
d
e
4
@
a
g
f
5
@
b
c
h
6
@
1
2
3
x
@
@
@
@
@
@
The two above configurations, bch and efh may be considered as similar. We call them as twins. Both are good, but, to restrict configurations numbers, it is a good thing to prefer one of the twice. Chiefly by reference to the Millennium Attaxx, preference is given to the first one, and, more generally to rather horizontal configurations. Of course, this preference never was used before the Blocks-Configs creation (even by Millennium), as it is shown in many illustrations of this site.
The rule, so, consist to mesure the weight of each Blocks-Configs and to choose the lower weight.
The weight of the number of the digits and letters that the Blocks-Config has in {1, 2, 3, a , b, c}. If there is tie, the Blocks-Config with the smaller digit / letter is chosen (in the order : 1, 2, 3, a, b, c).
Examples of preference
(above boards) bch has a weight of 2 (because a and b) and efh has a wight of 0 (nothing in {1, 2, 3, a , b, c}. So, bch is prefered.
5ch and 2fh have a weight of 1 and 1. 2fh is chosen because 2 is smaller than 5.
2df and 5ac have a weight of 1 and 2. 5ac is chosen.
15chx and 24fhx have a weight of 2 and 1. 15chx is chosen.
afg and cdg have the same weight of 1. afg is chosen, because a is smaller than c.
234d and 156a have the same weight of 2. 156a is chosen, because 1 < 2.
3h and 6h have a weight of 1 and 0. So, 3h is chosen, although 6h is more horizontal (but the "horizontal preference" is very approximative, it is only a pretext too choose a rule...).
Calculation of the twin Blocks-Config
Each Blocks-Config has one twin Blocks-config, which may be itself (notably when it is only coded with g, h and x). it is enough to replace 1, 2, 3, a, b, c respectively by 4, 5, 6, d, e, f, and conversely 4, 5, 6, d, e, f by 1, 2, 3, a, b, c, and then to order digits and letters (g, h and x being unchanged).
Examples :
2fg has for twin 5cg. 2fg is prefered to 5cg (same weight, but 2 < c).
35chx has for twin 62fhx, that is to say 26fhx. 35chx (weight 2) is prefered to 26fhx (weight 1).
Blocks number
Each blocks-Config allows to quickly count the number of blocks on the board. The number of digits between 1 and 6 is multiplied by 2, the number of letters between a and h is multiplied by 4, and 1 is added if the letter x is present.
So, for instance, 3bhx has 2+4+4+1 = 11 blocks, 2bg has 2+4+4=10 blocks.
There are good and bad Blocks-Configs to play...
Blocks and strategies
The influence of blocks on the strategy has already be evoked at the page strategies. Now, it may be illustrated by two configurations. The first, very straight, 6bch, is favourable to the human who has a good management of the geographic effects of the blocks. The second, with scattered blocks, 14cfgx, is favourable to the computer, for the reverse reason. It may be verified with the Rondão Attax, at level 3 (the 2 Blocks-Configs are available in the configuration file that may be downloadable on this page).
List of first Blocks-Configs
Corresponding to what is said above, this is the lists of all the Blocks-Config having the smaller number of blocks :
0 block : 0
1 block : x
2 blocks : 1, 2, 3
3 blocks : 1x, 2x, 3x
4 blocks : 12, 13, 14, 15, 16, 23, 25, 26, 36, a, b, c, g, h