Bagh Chal

Apparently, Bagh Chal originated in Nepal and I learned how to play with Dr Dave on igGameCenter in Feb 2023.  The board is the same as is used for Alquerque and has the familiar symmetric pattern of Fanorona, where not all points have the same flexibility.  For example, a piece on B2 has 8 possible moves, but on C2 only 4.  It reminds me of playing Fox & Hounds on a Draughts board, where 4 hounds try to box in the more agile fox.  Here, 20 goats win by immobilising 4 tigers, but they can can eat isolated goats!  Tigers win by eating 5 goats.  The game starts as in the diagram above.  The first 20 moves by the Goats must be to place a goat on a vacant point.  Thereafter, a goat can move to any adjacent, vacant point but only if they are connected by a line on the board - e.g. B2-C3 is allowed, but C2-D3 is not.  Tigers move in exactly the same way, but they can also capture and remove a goat from the board (i.e. eat it) by jumping over it to a vacant point (again only where the lines on the board allow).    See full rules on igGamesCenter.

The start of the game is uneventful for 20 moves.  Goats have to be careful with their placement, to avoid capture.  This is much easier playing around the edge of the board and goats need to be in pairs, or solid groups.  Not much to do for the Tigers but to prowl around looking for stragglers.  Then, the game is suddenly critical!  If Goats have succeeded in not losing one of the herd (there are several collective nouns used for goats!) there is only one vacant point on the board.  Since a player cannot pass on a turn, this might mean that a goat has to move into danger (cf zugzwang in chess) and be captured.  It might also mean that a tiger has to move to a point where it can be trapped.  Manoeuvring on the cramped board is tricky and probably depends on the setup from those first 20 goat placements.  I played against the computer at Play Tigers and Goats and lost playing both Goats and Tigers!  Must play more to improve . . . 

I then found this research paper by Lim Yew Jin & Jurg Nievergeld online - Tigers & Goat.pdf, which describes (with extensive use of computer power) that, under optimal play, Bagh Chal is a draw.  I am not too surprised at this, if either Goats or Tigers had a definite win, then this would surely have been empirically noticed with many years of play in Nepal and elsewhere!  This does not mean (as in Noughts and Crosses) that it is not worth playing by adults.  The theoretical draw is only found by exhaustive techniques and there is no human guide (as far as I know) for best play.  However, the following points from the paper are interesting . . .

• If the first goat is placed on any of the 9 points in the centre of the board, then Tigers can soon capture a goat.  The only safe first move is in the middle of an edge.
• In the sliding phase, if there are no more than 17 goats remaining on the board, then a goat sliding move is always possible.
  With 18 or more goats, the goats can be trapped and the authors says this is a win for Tigers, as there is no legal move for Goats.  However, I cannot find references to corroborate this interpretation of the rules. 
• There are approximately 33,000,000,000 different positions after the goat placement phase.  No wonder it is hard for humans to play well!
• Tigers can force the capture of a goat by the time 15 goats have entered.  This surprised me, as it felt possible to place all 20 goats without losing one, unless I made an error.
• Tigers can force the capture of 2 goats by the end of the placement phase.  Even more surprising to my limited experience.
• The winning condition that the Tigers have to eat 5 goats to win, not 4 or 6, is reflected in their statistical analysis which indicates 5 goats is the best target to balance the game between the two players.  4 goats too easy for Tigers, 6 goats too easy for Goats.
• Their statistics indicate that unless Tigers eat 2 goats by the end of the placement phase, they have little chance of winning!  However, I can have 20 goats and still lose, so I must be a very poor player!

Is Bagh Chal a good game for humans?  I think it depends on the style of game that you like to play.

More general info at Bagh-Chal - Wikipedia.