Why minimax is fundamentally flawed

[hgm]

I think they address different problems. Tapering the score towards draw as the 50-move counter increases only has any effect when there are moves that can reset the 50-move counter. It would not help in a case like KBNK, where the mate must be achieved with reversible moves only, but is beyond the horizon, while the heuristic evaluation in non-monotonous, because you cannot drive the bare King towards the corner without allowing him to temporarily leave the edge.

Also the 50-move-based tapering is a long-term mechanism; usually you ounly start to discount the score when the counter gets above 50 ply. This to prevent the detrimental effects on hash consistency in cases where progress is no problem at all. The delayed-loss mechanism would make you prefer the shorter path to a gain also when the 50-move counter is very low.

I also expect the effect on behavior to be sort of opposite. If pushing a Pawn ends badly, (e.g. the Pawn is not safe in its new location, and will eventually get lost), but is the only way to avoid a 50-move draw in an imagined better position, the engine will try to postpone it to just before the horizon, pushing the loss of the Pawn out of sight, but still reaping the benefit of resetting the 50-move counter. So it will only start to see trouble when it gets so close to the 50-move limit that it is forced to push the Pawn so close to the root that still enough depth is left after it to spot the loss. A delayed-loss bonus would penalize postponing the gain due to the counter reset, and make the engine realize much earlier that this plan isn't any good: if you push the Pawn early, you see that you lose it. If you push it just before the horizon, you incurr a large delayed-loss bonus. If you don't push it at all, the 50-move counter is high, and your score gets reduced because of that, So if there are any prospects for resetting the counter in another way, they will become attractive much earlier, and the engine will have more time to prepare them. Or perhaps avoid the situation where it became dependent on the Pawn push altogether, because it could already see at the time where there were still alternatives that it was no good, rather than fooling itself with the idea it could always push the Pawn just before the horizon.

[Aleks Peshkov]

I think it is good to make score correction at different conditions:

1) any irreversible move triggers score deflation.
2) score is always decreasing towards draw value, not towards window bounds.

So winning side want to make early progress and losing side is constantly trying to create a fortress.