I like giving names to these positions.xr_a_y wrote: ↑Wed Aug 21, 2019 6:10 pmWhat if White to play. First move of the supposed deep mate sequence for White is a quiet move (for instance a pawn push to reduce King mobility). Best answer for black is in fact a shorter mate or a dramatic material gain that White is not viewing because it starts by a queen sac.
* Starting position: P. Lets assume a "pruned" search only searches the first 6 moves (#1 through #6) per position. The reality is that 36 moves are available per ply however.
* AIs always consider the first move-chain first. Lets say at 10-ply, position P.184.108.40.206.220.127.116.11.1.1 (that is: White plays move#1, followed by Black plays move#1... for 10 ply) results in a "deep mate" where White wins. I'll call this position P(1^10) for short.
* Black apparently finds a shorter-mate at P.18.104.22.168.22.214.171.124 (Black wins). (At 5th ply, Black leaves the principal variation and starts to search move#7 instead, which eventually results in Black-wins position). P(1^5).7.1.2 for short.
Remember: White is pruning only to the first 6 moves in the assumption. So white will never consider move#7 at any ply. Black "doesn't prune", so move#7 at P(1^5) is certainly a consideration: resulting in the position P(1^5).7.
Does the above notation describe what you are worried about adequately? I'm just trying to assign names to your hypothetical positions, so that we can speed up the discussion.
If you wanted to be "sure" of anything, you wouldn't be pruning in the first place! The idea of pruning is that you're willing to draw conclusions from only a subset of the analysis.It feels to me that if White want to be sure of its supposed mate, pruning shall be switch off.
White, across the 10-ply, only has to consider a search tree of size ~60 Million. Black, searching the whole 36-moves per ply, will instead have a search tree of size 3.6 Quadrillion. White can perform its 10-ply analysis in a incredibly small fraction of the time it takes for Black to consider all the moves.
But consider how the "deep mate" found in P(1^10) looks like to white's PVS search. P(1^10) is black to move (can't move, so checkmate). White, at P(1^9) sees that position as +infinity. Black, at P(1^8), sees the position as -infinity, which fails-low.
Since -infinity fails low, White's AI is going to search P(1^8).2, P(1^8).3, P(1^8).4... etc. etc. The only way "checkmate" gets passed up through the P(1^8) position is if all moves under consideration (move#1 through move#6, assuming heavy pruning) all result in checkmate.
Then again, when the "checkmate" is returned to P(1^6) (two ply up higher), the checkmate has to survive through another fail-low check across the positions P(1^6).2, P(1^6).3, P(1^6).4.
Even with deep pruning, I am unsure of how White's "deep mate" gets passed all the way up to the eval(P) level.