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Fig. 6. Advantage in Win Rate of flux distance
The values indicate the difference in win rate, e.g., a value of +10 indicates that
flux distance won 55% of the games against flux basic winning 45% . Obviously the
proposed heuristics produces results comparable to the flux basic heuristics, with both
having advantages in some games. This has several reasons: Most importantly, our pro-
posed heuristic, in the way it is implemented now, is more expensive than the distance
estimation used in flux basic. Therefore the evaluation of a state takes longer and the
search tree can not be explored as deeply as with cheaper heuristics. This accounts
for three of the four underperforming games. For example in nim4, the flux basic dis-
tance estimation provides essentially the same results as our new approach, just much
cheaper. In chinesecheckers2 and knightthrough, the new distance function slows down
the search more than its better accuracy can compensate.
On the other hand, flux distance performs better in complicated games. There the
higher accuracy of the heuristics typically outweighs the disadvantage of the heuristics
being slower.
Interestingly the higher accuracy of the new distance heuristics is the reason for
flux distance losing in breakthrough suicide. The game is exactly the same as break-
through, however, the player to reach the other side of the board first does not win but
loses.
The heuristics of both flux basic and flux distance are not good for this game since
both are based the minimum number of moves necessary to reach the goal while the
optimal heuristic would depend on the maximum number of moves available to avoid
losing. However, since flux distance is more accurate, flux distance selects even worse
moves that flux basic. Specifically, flux distance tries to maximize (a much more ac-
curate) minimal distance to the other side of the board, thereby allowing the opponent
 
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