💡📝H. G. Muller wrote on Tue, Oct 21, 2014 08:24 AM UTC:
I examined the 3-vs-2 end-games now, and the situation really isn't that much different from normal Chess. There are 6 different ways in which you can pick 2 out of the 4 'minors' you start with. In orthodox Chess one of these is BB, one NN, and the other 4 are BN. There are 4 possible ways to select the defending minor, (in Chess 2x B and 2x N), for 24 possible 3-vs-2 end-games with minors. In Chess only 2 of those 24 are won (BB vs N).
In Team-Mate all 24 possibilities are different. As the Mammoth is significantly weaker than the other minors, it is useful to distinguish strong teams (without M) and weak teams (with M). Turns out all teams (except N+M, which does not have mating potential even against a bare King, and thus is the N+N equivalent of orthoChess) beat K+M, and all strong teams beat K+E. The others are general draws. So 8 of the 24 possible 3-vs-2 end-games with minors are won, against only 2 for orthoChess!
Some of those are only 'half won', however. In particular, when both sides have a color-bound piece (and the defender always has E or M, or it couldn't be won to start with), then a win can in general be forced only if these are on the same color. This is understandable, as when they are of different color the opponent will build his fortress on his color, so that your color-bound piece only hits thin air, and it is basically 2-vs-2. Only F+E vs M can still be won when E and M are of different color, no doubt due to the general clumsiness of the M. For E+M to beat M, the latter must be on the color of the E (to attack it without allowing it to trade?).
It is worth noting that the initial setup dictates that two (opposing) E or M will be on different color, while M vs E will be on the same. This spoils many of the wins, and might actually be an argument to switch to a point-symmetric initial setup. (Tabulated numbers are longest distance to forced 'conversion', i.e. mate or winning capture. Italics means that they refer to a color binding different from in the initial position.)
NF
NE
FE
FM
EM
F
-
-
-
-
-
F
-
-
-
-
-
E
74
127/-
86/-
-
-
M
53
46/-
49/88
134/-
97/-
In orthodox Chess Rook vs minor is always draw, so the fact that a single Rook-class piece in Team-Mate has no mating potential does not hurt there. Rook + minor vs minor is a general win in Chess, however. Turns out it is the same in Team-Mate: (U or C) + (F, N, E or M) vs (F, N, E or M) is a general win in any of the 32 possible combinations.
UF
UN
UE
UM
F
39
43
43
50
N
30
43
48
49
E
25
34
32/29
45/30
M
22
22
21/22
25/27
CF
CN
CE
CM
F
46
40
43
56
N
42
43
37
69
E
29
31
38/28
38/32
M
23
22
22/22
27/25
The surprise came from the Adjutant (J), which I considered a Queen replacement due to its quite-high middle-game value of 7. But in the end-game it turns out pretty weak. Its color binding handicaps it against color-bound defenders, for the same reason as with color-bound minors: the opponent withdraws to the other color, and it becomes useless. And a useless strong piece is just as worthless as a useless weaker piece. Only J+E vs M and J+F vs M can be won on both colors (provided J and E are on different colors, of course), again due to the general weakness of M. J+M cannot beat F or N, however, and J+N cannot beat N. None of this is really a problem, though, as the Adjutant can only be obtained through promotion, and you can opt for C or U instead, which always do the job.
JF
JN
JE
JM
F
59
95
37
-
N
42
-
45
-
E
29/-
34/-
21/-
29/-
M
16/51
17/-
16/31
23/-
In Chess 2R vs R is won. In Team-Mate there are two different Rook-class pieces, Cobra and Unicorn, and the C+U team beats both U and C. The latter takes very long, though (164 moves), and might be draw in practice. Teams with an Adjutant again do not do well: only J+U can beat C, and the other 3 are draw. (Note that anything I state about Cobra here is really for the Gnu, which unlike Cobra cannot be blocked on the N squares for reaching the (3,1) destinations. But blocking isn't expected to play a significant role in this stage of the game, with hardly anything on the board.)
Because of the poor performance of J the C and U become more likely promotion choices, so the homogeneous pairs U+U and C+C become of interest. U+U vs U is draw. (Probably for the same reason as that KBBKB is draw: it is too difficult to attack the defender without giving him the opportunity to trade.)
CU
JC
JU
UU
CC
JJ
U
97
-
-
-
39
30
C
164
-
51
34
56
11
Note that JJ also does pretty well here, (when on different color!), probably because they have the property they can drive a bare King with checks to an edge mate without help of their King.
In Team-Mate all 24 possibilities are different. As the Mammoth is significantly weaker than the other minors, it is useful to distinguish strong teams (without M) and weak teams (with M). Turns out all teams (except N+M, which does not have mating potential even against a bare King, and thus is the N+N equivalent of orthoChess) beat K+M, and all strong teams beat K+E. The others are general draws. So 8 of the 24 possible 3-vs-2 end-games with minors are won, against only 2 for orthoChess!
Some of those are only 'half won', however. In particular, when both sides have a color-bound piece (and the defender always has E or M, or it couldn't be won to start with), then a win can in general be forced only if these are on the same color. This is understandable, as when they are of different color the opponent will build his fortress on his color, so that your color-bound piece only hits thin air, and it is basically 2-vs-2. Only F+E vs M can still be won when E and M are of different color, no doubt due to the general clumsiness of the M. For E+M to beat M, the latter must be on the color of the E (to attack it without allowing it to trade?).
It is worth noting that the initial setup dictates that two (opposing) E or M will be on different color, while M vs E will be on the same. This spoils many of the wins, and might actually be an argument to switch to a point-symmetric initial setup. (Tabulated numbers are longest distance to forced 'conversion', i.e. mate or winning capture. Italics means that they refer to a color binding different from in the initial position.)
In orthodox Chess Rook vs minor is always draw, so the fact that a single Rook-class piece in Team-Mate has no mating potential does not hurt there. Rook + minor vs minor is a general win in Chess, however. Turns out it is the same in Team-Mate: (U or C) + (F, N, E or M) vs (F, N, E or M) is a general win in any of the 32 possible combinations.
The surprise came from the Adjutant (J), which I considered a Queen replacement due to its quite-high middle-game value of 7. But in the end-game it turns out pretty weak. Its color binding handicaps it against color-bound defenders, for the same reason as with color-bound minors: the opponent withdraws to the other color, and it becomes useless. And a useless strong piece is just as worthless as a useless weaker piece. Only J+E vs M and J+F vs M can be won on both colors (provided J and E are on different colors, of course), again due to the general weakness of M. J+M cannot beat F or N, however, and J+N cannot beat N. None of this is really a problem, though, as the Adjutant can only be obtained through promotion, and you can opt for C or U instead, which always do the job.
In Chess 2R vs R is won. In Team-Mate there are two different Rook-class pieces, Cobra and Unicorn, and the C+U team beats both U and C. The latter takes very long, though (164 moves), and might be draw in practice. Teams with an Adjutant again do not do well: only J+U can beat C, and the other 3 are draw. (Note that anything I state about Cobra here is really for the Gnu, which unlike Cobra cannot be blocked on the N squares for reaching the (3,1) destinations. But blocking isn't expected to play a significant role in this stage of the game, with hardly anything on the board.)
Because of the poor performance of J the C and U become more likely promotion choices, so the homogeneous pairs U+U and C+C become of interest. U+U vs U is draw. (Probably for the same reason as that KBBKB is draw: it is too difficult to attack the defender without giving him the opportunity to trade.)
Note that JJ also does pretty well here, (when on different color!), probably because they have the property they can drive a bare King with checks to an edge mate without help of their King.