Horse endgames

One horse (漢馬楚)

A horse can at most influence two points in the palace at a time and is unable to mate on its own.

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Two horses (漢馬馬楚)

There exists some theoretical mating positions like

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but Cho cannot be forced into any of these so the endgame is in general a draw.

Two horses and an elephant (漢馬馬象楚)

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Use two of the pieces to restrict the king to one point. Then mate with the remaining piece.

1.57漢象74
2.4241
3.37漢馬45
4.45漢馬24
5.24漢馬43
6.47漢馬26
7.26漢馬14
8.14漢馬22

Two horses and a soldier (漢馬馬兵楚)

A horse and a soldier cannot win if the soldier is on the second rank. The addition of a horse will turn such positions into wins. A soldier on the back rank can still not force a win together with two horses.

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1.25漢馬13
2.13漢馬34
3.4233
4.36漢馬57
5.57漢馬45
6.3343
7.2232
8.34漢馬55

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Horse and elephant (漢馬象楚)

This endgame also have some theoretical mates that can be avoided. For example:

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Horse, elephant and soldier (漢馬象兵楚)

A horse and soldier or elephant and soldier can win except when the soldier has advanced to the second or first rank. The addition of a horse or an elephant will allow Han to win even in positions where the soldier is on the second rank.

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1.37漢象65
2.4231
3.45漢馬33
4.2221
5.3132
6.33漢馬12
7.12漢馬24

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Horse and two elephants (漢馬象象楚)

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1.57漢象74
2.4243
3.37漢象5
4.4940
5.47漢馬66
6.4039
7.66漢馬45
8.5漢象37
9.37漢象9
109漢象26

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Horse and soldier (漢馬兵楚)

A horse and a solder will together mate a lone king.

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1.6漢馬27
2.3242
3.27漢馬46

The horse ends the bigjang threat.

4.7464
5.6454
6.4960

To free the horse

7.46漢馬34
8.4243
9.5453
10.4333
11.34漢馬13
12.13漢馬21
13.3332
14.5342

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The horse both guards the soldier and stops the general from escaping behind the soldier. If the soldier has advanced to the back rank the position cannot be won and if the soldier is on the second rank the position cannot in general be won as the king can go behind the soldier. For example:

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1.2232
2.4233

The horse cannot move or else the soldier will be lost, nor can the soldier move into the centre of the caslte. A soldier on the third rank can win:

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1.15漢馬36
2.4232
3.3949
4.3242
5.36漢馬44
6.4939
7.44漢馬25
8.2333
9.4253
10.25漢馬13
11.13漢馬34
12.3342

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Horse and soldier versus chariot (漢馬兵楚車)

A chariot can easily draw versus one horse and a soldier. The chariot can be sacrificed for one piece or engage in perpetual checking.

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1.3433
2.4241
3.25漢馬44
4.44漢馬63
5.71楚車51

or

5.71楚車79

Horse and soldier versus cannon (漢馬兵楚包)

The cannon is unable to defend against horse and soldier.

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As the cannon is stopping the soldier from directly entering the castle some other way of entry has to be found.

1.5444
2.31楚包53

Delaying the maneuvering of the horse

3.65漢馬73
4.53楚包31
5.73漢馬85
6.4252
7.6049
8.5242
9.85漢馬64
10.4443
11.4251
12.64漢馬45
13.31楚包61
14.45漢馬26
15.61楚包41
16.4940
17.41楚包61
18.26漢馬34
19.61楚包31
20.4049
21.4342

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Horse and soldier versus horse (漢馬兵楚馬)

A horse can defend against a horse and a soldier.

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The horse stops the soldier from going to the centre of the palace.

Horse and soldier versus elephant (漢馬兵楚象)

An elephant can defend against a horse and a soldier.

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1.56漢馬35
2.14楚象37
3.35漢馬23
4.37楚象14

The elephant can stop the soldier from advancing to the centre of the palace

Horse and soldier versus soldier (漢馬兵楚卒)

A soldier in defence cannot stop Han from winning.

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1.58漢馬37
2.37漢馬56
3.4454
4.3534
5.56漢馬35
6.5464
7.3444
8.4443
9.4252
10.35漢馬23
11.23漢馬11
12.5251
13.4353
14.11漢馬23
15.5342

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Horse and soldier versus officer (漢馬兵楚士)

An officer in defence is solid against the horse and soldier. This endgame is a draw.

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The soldier cannot enter the palace without being captured by the officer.

Horse and two soldiers (漢馬兵兵楚)

A horse and a soldier cannot win if the soldier has advanced to the second rank. The addition of an extra second rank soldier doesn’t create a win for Han.

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