Kalah (#58)


#1

Both sides of the Kalah board are the same, with only the numbers of the
slots
changing. You can write a little code to make it so that your players
need not
be concerned with this minor difference. Here’s an example from Adam
Shelly:

#Adapter class - rotates the board so that player's Kalah is always 6
class KalahPlayer < Player
	def choose_move
	  n = (@side==KalahGame::TOP) ? 7 : 0
		@board = @game.board
		@board = @board.rotate n
		return get_move + n
	end

	#simulate a move
	def simulate board,i
		b = board.dup
		stones,b[i]=b[i],0
		while stones > 0
			i = 0 if (i+=1) >12
			b[i]+=1
			stones-=1
		end
		if (0..5)===i and b[i]==1
			b[6]+= (b[i]+b[opposite(i)])
			b[i]=b[opposite(i)]=0
		end
		b
	end
	def opposite n
		12-n
	end

end

As the comment suggests, this is the Adapter Design Pattern at work.
Player’s
original interface is that choose_move() should return a correct move
regardless
of which side of the board it is playing from. KalahPlayer changes that
interface to having get_move() see the board as if it was playing from
the
bottom and return only moves in that range.

This change is accomplished by defining a choose_move() the rotates a
board and
adds an offset to the players selected move, if needed. When the player
is on
the bottom, the board is rotated 0 and the selected move is added to an
offset
of 0, resulting in no change either way. When the player is on the top
though,
the board the player sees is flipped 180 degrees (rotate(7)), and the
player’s
move is raised by 7 to place it on the proper side of the board.

This class also defines the helper method simulate(), which given a
board and a
move, will return the resulting board. This makes searching a lot
easier for
the subclasses.

The above code makes use of a rotate() method we haven’t seen. It comes
from a
few helpers added to Array:

#Some helpers in Array
class Array
	def rotate n
		a =dup
		n.times do a << a.shift end
		a
	end
	def sum
		inject(0){|s,e|s+=e}
	end
	#choose randomly between all items with given value
	def random_index value
		n=rand(find_all{|e|e==value}.size)
		each_with_index{|e,i| return i if e==value and (n-=1)<0 }
	end
end

The first method is the rotate() call used earlier. It’s pretty simple,
just
returning a copy of the Array with the elements cycled in a circular
fashion the
requested number of times.

I really hope sum() needs no introduction by this point, as it’s
probably the
most popular helper method in Ruby Q. solutions. It just returns a
summation
of all elements in the Array.

Finally, random_index() selects a random element equal to the passed in
value.
In other words, if an Array contained [1, 2, 3, 2] and you call
random_index(2),
you have a 50/50 chance of getting 1 or 3 (the indices of the 2s)
returned.

Now we’re ready to actually build a player:

#Tries to find the biggest increase in score for a turn
class DeepScoreKalahPlayer < KalahPlayer
	def get_move
		best_move(@board)
	end
	def best_move board
		possible_scores = (0..5).map{|i| score_for(board,i)}
		possible_scores.index(possible_scores.max)
	end

	#find the increase in score if we make move m
	def score_for board,m
		return -100 if board[m]<1         #flag invalid move
	  b, taketurn  = board,true
		while taketurn
			taketurn =  ((b[m]+m)%14 == 6)  #will we land in kalah?
			b = simulate b,m
			m = best_move(b) if taketurn
		end
		b[6]-board[6]                     #how many points did we gain?
	end

end

This is a fairly uncomplicated player with the idea of find the most
points I
can get with my move. Remember, get_move() is the adapted interface, so
that’s
where we start. All it does is call best_move() passing in the current
board.

Now best_move() walks all possible moves calculating how many points we
would
earn by making the move. When it has that information, it selects the
highest
point move and returns to index for that slot.

The last piece of this puzzle is score_for(). Given a board and a move,
it
returns how many points you would gain by making the move. This is
slightly
complicated, because a move ending in the Kalah allows us to move again.
That
is handled with recursion by simply calling best_move() again on the new
board.
When that’s all done, subtracting the Kalah we started with from the
Kalah we
ended with gives us the points gained by the move or moves.

Adam doesn’t quit there though, there’s another player that inherits
from this
one. Let’s take a look:

#Tries to find the biggest increase in score for a turn
#subtracts opponent's possible score
class APessimisticKalahPlayer < DeepScoreKalahPlayer
	MaxDepth = 3
	def get_move
	  @level=0
		best_move(@board)
	end
	def best_move board
		return super(board) if (@level > MaxDepth)
		@level+=1
		possible_scores = (0..5).map{|i|
			score_for(board,i) - worst_case(simulate(board,i))
		}
		@level-=1
		possible_scores.random_index(possible_scores.max)
	end
	#biggest score the opponent can get on this board
	def worst_case board
		worst = 0
		opp_board = board.rotate 7
		6.times {|i|
				s = score_for(opp_board, i)
				worst = s if worst < s
			}
			worst
	end
end

This is a famous gaming algorithm known as a Minimax Search. The idea
is that
everyone is always going to make their best move, both you and your
opponent.
Given that, we want to find your best (or maximum) choice, but we also
need to
consider the opponent’s best response. We want to chose the path that
minimizes
the opponent’s potential to get back at us. The father ahead we can
look in
this fashion, the more intelligent of a decision we can make.

The code above is very similar to the last player we examined. The main
new
element here is worst_case(), which is just a tool to find the
opponent’s best
move (worst for us). Beyond that, you can see that get_move() and
best_move()
have been reworked to search down to a constant depth. In this case, a
depth of
3 was chosen. Of course we want to look as deep as possible, but memory
and
execution time can make deeper searches unrealistic.

Note that best_move() now subtracts worst_case() from score_for(), so
the
opponent’s response move is weighted against our own. This may even
yield
negative values for moves, because the opponent has a response better
than the
move we made.

If you want to take Minimax deeper, you have to cut down the work it has
to do.
A common technique is Alpha-Beta Pruning, which allows you to skip large
portions of the move tree in your search. I’m not going to show the
code here,
but be sure to look at David B.'s code which walks father along
this path.

My thanks to all the players who always share such interesting solutions
with
us.

Tomorrow I have a real treat for all you Ruby Q. fans, our first prize
awarding competition…


#2

There’s nothing like a code review to make you see ways to improve your
code…
Based on James description of what #worst_case is doing I realized I
could rewrite it in 2 lines:

The code above is very similar to the last player we examined. The main new
element here is worst_case(), which is just a tool to find the opponent’s best
move (worst for us).

So this function should simply be:
def worst_case board
opp_board = board.rotate 7
score_for(opp_board,best_move(opp_board))
end

Thanks for runing these always entertaining and educational quizes,
James.
-Adam


#3

On Dec 15, 2005, at 11:53 AM, Adam S. wrote:

                                    worst = s if worst < s

move (worst for us).

So this function should simply be:
def worst_case board
opp_board = board.rotate 7
score_for(opp_board,best_move(opp_board))
end

Hey, I like that.

Thanks for runing these always entertaining and educational quizes,
James.

Thanks for giving me something to talk about, Adam. :wink:

James Edward G. II