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dvonn (2) overload

By lieven

In the previous post we have seen that it is important to have lots of mobile pieces around in the endgame and that it is hard for a computer-program to evaluate a position correctly. In fact, we illustrated this with a position which ‘clearly’ looks much better for Black (the computer) whereas it is already lost! In fact, the computer lost this particular game already 7 plies earlier. Consider the position

\xymatrix@=.3cm @!C @R=.7cm{.& & & & & & & & & & & & & \\ & & & \SBlack \connS & & \bull{d}{5} \conn & & \bull{e}{5} \conn & & \bull{f}{5} \conn & & \bull{g}{5} \conn & & \bull{h}{5} \conn & & \SWhite \connS & & \SWhite \connS & & \SWhite \conneS & & & \\ & & \SBlack \connS & & \SBlack \connS & & \Black{6} \connS & & \bull{e}{4} \conn& & \bull{f}{4} \conn & & \bull{g}{4} \conn & & \bull{h}{4} \conn & & \SWhite \connS & & \SWhite \connS & & \SWhite \conneS & & \\ & \SBlack \connbeginS & & \SBlack \connS & & \BDvonn{2} \connS & & \bull{d}{3} \conn & & \SBlack \connS & & \BDvonn{3} \connS & & \White{4} \connS & & \SWhite \connS & & \Dvonn \connS & & \SWhite \connS & & \SWhite \connendS & . \\ & & \Black{5} \connbeginS & & \SBlack \connS & & \SBlack \connS & & \bull{d}{2} \conn & & \SBlack \connS & & \bull{f}{2} \conn & & \bull{g}{2} \conn & & \SWhite \connS & & \SWhite \connS & & \SWhite \connendS & & \\ & & & \bull{a}{1} \con & & \bull{b}{1} \con & & \Black{5} \conS & & \bull{d}{1} \con & & \bull{e}{1} \con & & \bull{f}{1} \con & & \bull{g}{1} \con & & \bull{h}{1} \con & & \White{2} & & & \\ .& & & & & & & & & & & & & }

Probably, Black lost the game with its last move d1-f3 thereby disconnecting its pieces into two clusters. White (the human player) must already have realized at this moment he had a good chance of winning (as indicated in the previous post) by letting Black run out of moves by building large stacks on the third row, White building a stack of the appropriate size which then jumps on the largest Black stack on the final move. Btw. this technique is called sharpshooting in Dvonn-parlance

The concept of manipulating the height of a stack so that it can land precisely on a critical space. It’s a matter of counting and one-digit addition. Notice that this doesn’t necessarily mean putting your own stacks atop one another - the best sharpshooting moves are moves which also neutralize. To counter a sharpshooting move is called “spoiling”.
But for this strategy to have a chance, White must keep the Black stacks containing the Dvonn pieces on the third row. At the moment the stack on c3 can move to c1 or to c5 and with his next move White counters this by overloading the stack, that is
To spoil a move or prevent a lifting move by moving atop the enemy stack. Even if the opponent has enough control to retake the stack, he cannot move it because it has become taller.
So, White sacrifies his height 4 stack on g3 with the move g3-c3. Black must take back immediately (if not, White moves c3-i3 and all Black’s material in the farmost right cluster is lost) but now the previously mobile Black height 2 stack at c3 has become an immobile (or old stack) height 7 stack which has no option but to stay on c3 (clearly Black will never move it to j3…). Next, White performs a similar startegy to neutralize the young height 3 Black stack on f3 by overloading it by 2 and hence after the forced recapture it becomes a height 6 Black stack which must remain on f3 forever. Here are the actual moves 1) g3-c3 b2-c3 2) h2-h3 b4-c5 3) h3-f3 e2-f3 and we end up with the situation we analyzed last time, that is

\xymatrix@=.3cm @!C @R=.7cm{.& & & & & & & & & & & & & \\ & & & \Black{2} \connS & & \bull{d}{5} \conn & & \bull{e}{5} \conn & & \bull{f}{5} \conn & & \bull{g}{5} \conn & & \bull{h}{5} \conn & & \SWhite \connS & & \SWhite \connS & & \SWhite \conneS & & & \\ & & \bull{b}{4} \conn & & \SBlack \connS & & \Black{6} \connS & & \bull{e}{4} \conn& & \bull{f}{4} \conn & & \bull{g}{4} \conn & & \bull{h}{4} \conn & & \SWhite \connS & & \SWhite \connS & & \SWhite \conneS & & \\ & \SBlack \connbeginS & & \SBlack \connS & & \BDvonn{7} \connS & & \bull{d}{3} \conn & & \SBlack \connS & & \BDvonn{6} \connS & & \bull{g}{3} \conn & & \bull{h}{3} \conn & & \Dvonn \connS & & \SWhite \connS & & \SWhite \connendS & . \\ & & \Black{5} \connbeginS & & \bull{b}{2} \conn & & \SBlack \connS & & \bull{d}{2} \conn & & \bull{e}{2} \conn & & \bull{f}{2} \conn & & \bull{g}{2} \conn & & \bull{h}{2} \conn & & \SWhite \connS & & \SWhite \connendS & & \\ & & & \bull{a}{1} \con & & \bull{b}{1} \con & & \Black{5} \conS & & \bull{d}{1} \con & & \bull{e}{1} \con & & \bull{f}{1} \con & & \bull{g}{1} \con & & \bull{h}{1} \con & & \White{2} & & & \\ . & & & & & & & & & & & & & }

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Posted in games
Written on Wed, 11 January 2006 at 11:30 am
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