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Reinhard: Within the boundary condition that the game should be played wth a strategy belonging to a sub-class of all possible strategies, (in this case a strategy with an evaluation based on additive piece values that are constant throughout the game), there is a best strategy. And the strategy will not lead to deterministic play, as there is often choice between moves that are evaluated equal, and the choice between them is based on random factors outside the strategy. So the outcome of a position under such a strategy is not fixed, but probabilistic.

That the strategy is not globally optimal, and that there exist strategies (not based on piece value but, for example, material tables), is not a problem if the playing strength of the piece-value-based strategy is not very much below the global optimum. And, considering the success that current engines hae in being the best Chess entities on the planet, I would say the piece-value-based strategies are doing a pretty good job. In particular, Joker80 is doing a pretty good job for 10x8 Chess. The strategies of our best engines are such that the variability of the result obtained from the set of positions with a certain material composition is not dominated by errors that the engines make in playing out such positions, but by the W/D/L statistics within the set. At that point, there would be very little change on improving the quality of play any further.

To give ane example: without knowledge of other details, it is better to have two minors than a Rook in a position which otherwise contains only equal numbers of Pawns (plus Kings). This despite the fact that zillions of KRPPPBNPPP positions are won for the Rook side. It is just that there are far more that are won for the B+N side. That the engines you use to decide which positions are won and which are lost (for a sample of the positions) now and then bungle a won game that was close to the limit, on the average cancels out, provided it is only the games close to the win/loss boundaries that can be bungled by the average playing inaccuracy. Because the narrow strips on either side of the boundary have equal area. Only if the accuracy gets very low, so that games very far from the boundary can still be bungled, the exact shape of the boundary (e.g. its curvature) becomes important.