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Endgames

An error to be avoided

N : 1 1 1 1 1 1
S : 2 8 0 0 0 0
Whites : Kb2, a2
Blacks : Kg7, h2
The whites have the move. North have the move and plays a very bad move which gives the whole point :
1.f(3)?? 1. 0 h1:Q 2. 0 2.B(8) 0 3. a4 0 4. a5 0 5. a6 0 6. a7 e 3.Df 4.Ea 5.F(2) 0 7. a8:Q a 6.Db 7.Ec 8.Ad 9.Be 10.Cf 11.A(3) 0 8. Qxh1 win easily.

Surprising

The beginner at Chess finds hard to believe that the endgame without pawn with 2 knights of the same color against the lone king is a draw. Still more impressive : the same endgame does not win at Awarichess even with a maximum number of powers !

Concerning endgames : king and pawn again king, the strong camp is winning although king is in touch with his pawn and that the pawn is not on columns a or h. Even a bad suite of powers does not prevent a progress and the finish always comes.

Draw	The whites win

Little study at Awarichess

We are at the initial position on the mancala.
The blacks have the move in the position :
Whites : Ke4, Qa4
Blacks : Kh2, Ng4, d2
The following sequences of first seeds taking give the following results :
A) BBWWBB -> Draw.
B) BBWWWBBB -> Draw.
C) BBWWWBBWW -> White wins.

(A)

(B)

(C)

1. ...	d1:Q	1. ...	d1:Q	1. ...	d1:Q
2. 0	0	2. 0	0	2. 0	0
3. Qxd1	Nf2+	3. Qxd1	0	3. Qxd1	0
4. Kf3	Nxd1	4. 0	Nf2+	4. 0	Nf2+
		5. Kf3	Nxd1	5. Kf3	0
				6. Kxf2

Long study at standard Awarichess

With the last game of Awari, the situation seems desperate for the whites on the chessboard.

Whites : Kh1, Qc1
Blacks : Ke6, Qd6, Qa1, Qb1
The blacks have the move.

But South begins playing much better Awari than North : (as what, while there's life, there's hope)

1.Fc 2.Dd 3.Ff 4.Fb 5.Ef 6.C(5)d 7.Ac 8.Ee 9.Ed 10.Df(3) 11.Ba 12.Bb 13.Af 14.Ee 15.D(4)d 16.A North plays in a more than doubtful way since some moves. No compensation for the lost seeds. On the contrary.



In this position, North plays c?. It would have been necessary to play f which allows to make seeds circulate while the text move loses 5 seeds and leaves North in a very poor position. South has two very strong houses B and F. F with all its seeds is very promising. c? 17.C(5)



b? 18.B(3)b 19.F(5)a 20.E(4)f 21.F(2)d 22.Ae 23.Bf 24.Fa 25.C(2)a 26.Bb 27.Cc 28.Ad 29.Be 30.Cf 31.Fa 32.E(2)a 33.Ab 34.Bc 35.Cd 36.Dc? 37.F(4)



And in the position of the diagram, North plays d?? All the seeds are in the left of South and in this type of position all the remaining seeds will return to him. Now North would have won all the same two seeds by playing e or f. Now the whites are capable of winning at Chess ! d?? 38.Be 39.Bf 40.Ca 41.Bb 42.Cc 43.Ad 44.Fe 45.E(2)f 46.Da 47.F(2)a 48.Cb 49.Bc 50.Cd 51.Ae 52.Bf Famine 53.A(5)

It gives the following powers :

1:W 2:W 3:W 4:W 5:W 6:B 7:B
8:B 9:W 10:W 11:W 12:W 13:W 14:W
15:W 16:W 17:W 18:W 19:W 20:W 21:W
22:W 23:W 24:W 25:W 26:W 27:W 28:W
29:W 30:W 31:W 32:W 33:W 34:W 35:W
36:W 37:W 38:W 39:W 40:W 41:W 42:W
43:W 44:W 45:W 46:W 47:W 48:W

and at Chess :



1. ... (1)0 2. (2)Qxb1 (3)0 3. (4)Qxa1 (5)0 4. (6)0 (7)Kd7 The most resistant. The king has to protect the queen on a square in a straight line with her. With this precise move, the whites win only hardly. 5. (8)0 (9)0



6. (10)Qf6 (11)0 7. (12)Kg2 (13)0 8. (14)Kh3 (15)0 9. (16)Kh4 (17)0 10. (18)Kh5 (19)0 11. (20)Kg6 (21)0 12. (22)Kf7 (23)0 13. (24)Qe5 (25)0 14. (26)Qe8+ Kc7 The king does not protect the lady more than in diagonal.



15. (27)Qe6 (28)0 16. (29)Kf6 (30)0 17. (31)Kf5 (32)0 18. (33)Qd5 (34)0 19. (35)Ke4 (36)0 20. (37)Kd4 (38)0 21. (39)Kc4 (40)0 22. (41)Kb5 (42)0 23. (43)Qd4 (44)0 24. (45)Qa7+ Kd8 The king does not protect the lady anymore. 25. (46)Qd4 (47)0 26. (48)Qxd6+ wins easily.

3 little synchronous studies

N : 0 0 1 0 0 0
S : 0 1 1 0 0 0
Whites : Ke2, Rd1
Blacks : Ke7, Qd8
The whites and South play and win : 1.Cd 2.De 3.Bf 4.A(3) 1. (1)Rxd8 (2)0 2. (3)Rd3

N : 4 1 0 0 0 1
S : 0 4 0 0 0 1
Whites : Kc1, Rg5, Rg6
Blacks : Kh1, Qh2
The blacks have the move. South plays and draw.
At Awari, the best is : B! who gives three seeds more for South while F? gives one seed more for North.
Nevertheless in Awarichess, F! lead to the draw while B? is loosing :
F(2)!e Bf(6) and South starves North (3) and at Chess : 1. ... 0 2. Rg1+ Qxg1+ 3. Rxg1+ Kxg1 Draw.
But on B?, f!(4) is very strong at Awarichess because although 7 remaining seeds return to South, it is too late.
1) ... Qf4+ 2) Kc2 Qxg5 3) 0 Qxg6 who wins easily.
This study shows that generally the primary materialism on the mancala pays already more in Awarichess than in Awari.
There are nevertheless exceptions as the following case shows it.

Blancs : Ka1
Noirs : Ka8, Rh2
The whites have the move :
W*4 B*2 W*13 is just a draw.
1. Kb1 0 2. Kc1 0 3. 0 Rh8 4. Kc2 0 5. Kc3 0 6. Kd4 0 7. Ke5 0 8. Kf6 0 9. Kg7 0 10. Kxh8 Draw
W*5 B*2 W*12 and the result depend of the following game of Awari.
1. Kb1 0 2. Kc1 0 3. Kd1 Rh8 4. 0 0 5. Kd2 0 6. Kd3 0 7. Kd4 0 8. Ke5 0 9. Kf6 0 10. Kg7 -/+

Required precision

Application of the previous case :
N : 0 0 0 0 1 1
S : 5 1 2 3 1 0
Whites : Ka1
Blacks : Ka8, Rh2
Big advantage of the blacks on the whites but also of South on North.
The blacks have the move. South draw but by playing very precise only :
(The moves from South marked by one "!" are uniques although more or less difficult to find. North defends his advantage the best that he can)
1.D!(2) 1. ... 0 2. Kb1 ... b 2.F!a 3.C!b 4.B!c 5.C!e 6.A!d 7.C!f 8.B!e 9.A!f 10.F!a 11.B!b 12.E(2)! 0 3. Kc1 a 13.D(3)! 0 4. Kd1 0 a 14.F(2)! 5. Ke1 0 a 15.Eb 16.Ac 17.Cd 18.Be 19.Df 20.Ea 21.F(2)! 6. Kf1 0 a 22.Cb 23.Dc 24.Ad 25.Be 26.Cf 27.A(3) 7. Kg1 0 8. Kxh2 Draw

Also :
N : 1 1 0 1 2 1
S : 8 1 2 0 0 1
Whites : Ka1
Blacks : Kc3, Ra8
Whites have the move naturally. South draw by being very precise :
(With the same convention for the "!")
1. Kb1 1.A(7)! 0 2. Kc1 0 3. Kd1 0 4. Ke2 0 f 2.B!e 3.A!f 4.F!a 5.D!b 6.F!a 7.C!a To try to exhaust South. Other moves are equivalent. 8.E(3)! 5. Ke3 0 6. Ke4 d 9.B!e 10.A!c 11.D!d 12.C!a 13.F(2)! 0 7. Kd5 a Regrettably for North, seeds are too much in their right 14.Bb 15.E!c 16.D!d 17.Cf 18.A!e 19.A!f 20.F!a 21.Eb 22.Dc 23.Bd 24.Ae 25.Df 26.Ea 27.F(2) 0 8. Kc6 a 28.Cb 29.Bc 30.Ad 31.Ce 32.Bf 33.C(4) 0 9. Kb7 0 10. Kxa8 Draw.

Even more spectacular :
N : 11 2 1 2 1 2
S : 10 0 0 0 0 2
Whites : Ka1
Blacks : Ke4, Ra8, Rh7
The whites have the move naturally. South draw :
The whites begin to react to the check while attacking both rooks ! : 1. Kb2 1.A(13)f 2.F(8) and with the white potential remainder, 10 seeds still on Mancala are for South. At chess, they will have 31 powers on 31! :



(1)0 2. (2)Kc3 [ But he must avoid the wrong road : 2. (2)Kc2? (3)0 3. (4)Kd2 (5)0 4. (6)Ke2 (7)0 5. (8)Kf2 (9)0 6. (10)Kg3 (11)0 7. (12)Kg4 (13)0 8. (14)Kg5 (15)0 9. (16)Kg6 (17)0 10. (18)Kxh7 (19)0 11. (20)Kg7 (21)0 12. (22)Kf7 (23)0 13. (24)Ke7 (25)0 14. (26)Kd7 (27)0 15. (28)Kc7 (29)0 16. (30)Kb7 (31)0 and the result of the game depends on whom will win the first one seeds at the next game of Awari. -/+ ] (3)0 3. (4)Kc4 (5)0 4. (6)Kc5 (7)0 5. (8)Kd6 (9)0 6. (10)Ke6 (11)0 7. (12)Kf6 (13)0 8. (14)Kg6 (15)0 9. (16)Kxh7 (17)0 10. (18)Kg7 (19)0 11. (20)Kf7 (21)0 12. (22)Ke7 (23)0 13. (24)Kd7 (25)0 14. (26)Kc7 (27)0 15. (28)Kb7 (29)0 16. (30)Kxa7 Draw.

Underpromotion

N : 1 1 0 0 0 0
S : 1 1 1 1 1 0
Whites : Kd2, Bc2, h7
Blacks : Kd8, a2
Thr black have the move and North play, but they can not avoid the defeat.
1.f(2) 1. ... a1:Q 2. 0 2.Ce 3.Bf 4.A(5) Famine. 0 3. h8:B! otherwise the blacks adorn the check with the biggest pleasure 0 4. Bxa1 0 This endgame is winning at Awarichess.

( ANIMATION 2 )

A complicated situation

N : 0 0 0 0 4 0
S : 0 0 0 0 4 0
Whites : Kf1, Qh4
Blacks : Kc8, Rb7
North is better because he has the seeds at his left.
The whites and South have the move.
There are two pairs of twin variants :
[1a] 1.Eb 2.F(2) 1. Qf2 0 e 3.Af(2) 2. 0 Rf7 4.Ad 5.Be 6.Cc (*) 7.Dd 8.Ee 9.Fa 10.Af(2) 3. 0 Rxf2 4. Kxf2 Draw
[1b] 1.Eb 2.F(2) 1. Qe1 0 e 3.Af(2) 2. 0 Rb1 4.Ad 5.Be 6.Cc (*) 7.Dd 8.Ee 9.Fa 10.Af(2) 3. 0 Rxe1 4. Kxe1 Draw
(*) The place being free, seeds are not coupled.
[2] 1.Ea 2.Fb 3.A and North will win the next two seeds -> [2a] 1. 0 Rb4!? [ or [2b] 1. 0 Rh7!? ]. South can arrange so that there is not seeds taking until the next game of Awari. (Why?). And to my knowledge we do not know who must win.
North has a "psychological" advantage because he can cross in the variant [1] and impose the draw or pass in the variant [2] which puts traps and which leads otherwise to an uncertain position.
For example, in the second variant an unrefined fault of South would be B instead of A at the third move of Awari and the 8 remaining seeds are collected by North : 1. 0 Rb4 2. 0 Rxh4 3. 0 Rh7 4. 0 Rd7 and the black rook being protected, the black win is absolutely assured.
As the endgame queen against rook is a draw in Awarichess, the blacks have even at their disposal the [2C] variant: 1. 0 0 which provides the draw with very few practical risks.