A Checkmate Evaluation Decision Tree • page 1/1 • General Chess Discussion • lichess.org

Approximation

I'm wondering if an Engine could be programmed in such a way, where it would choose the Best move based on 'A Checkmate Evaluation Decision Tree' criteria.

Is there a way to plug-in, and test, such an engine?

For example, A chess game could end in 4 ply, based on the following moves, which would be evaluated accordingly:

f3 (-0.5%), e5 (-5%)
g4 (-100%), Qh4# (-inf%).

So, +inf% = white wins. So, -inf% = black wins. So, +100% = White has a sure checkmate. So, -100% = Black has a sure checkmate.

-5% = 1 out of the next 20 moves white could make (g4), would allow a Black victory.
-0.5% = 2 out of the next 20 moves black can make (e6 or e5), would allow a -5% Black probability.

Also, in each position, it could give a % chance for both players, prospectively, and the % changes given the math at deeper ply.
In the long-run though, one of them could dominate (quicker or more forcing checkmate), or the % chances can approach that of a draw though = 0% (no seen checkmate).

The thought here is to have the Engine explore deeply per level of ply, giving the player an idea about his/her fighting chances in the chess game.

The tree can be pruned, too.

I'm wondering if an Engine could be programmed in such a way, where it would choose the Best move based on 'A Checkmate Evaluation Decision Tree' criteria. Is there a way to plug-in, and test, such an engine? For example, A chess game could end in 4 ply, based on the following moves, which would be evaluated accordingly: 1. f3 (-0.5%), e5 (-5%) 2. g4 (-100%), Qh4# (-inf%). So, +inf% = white wins. So, -inf% = black wins. So, +100% = White has a sure checkmate. So, -100% = Black has a sure checkmate. -5% = 1 out of the next 20 moves white could make (g4), would allow a Black victory. -0.5% = 2 out of the next 20 moves black can make (e6 or e5), would allow a -5% Black probability. Also, in each position, it could give a % chance for both players, prospectively, and the % changes given the math at deeper ply. In the long-run though, one of them could dominate (quicker or more forcing checkmate), or the % chances can approach that of a draw though = 0% (no seen checkmate). The thought here is to have the Engine explore deeply per level of ply, giving the player an idea about his/her fighting chances in the chess game. The tree can be pruned, too.

AsDaGo

Interesting idea, but I doubt this would give you very meaningful evaluations. Most positions would probably be 0% because there's no immediate checkmate, and many positions would be completely wrong because, for example, one side might have only one good move, but an obvious one (a recapture, say), and all other moves lose (and let's say they lead to a quick mate so your engine would know they are losing). Then it might evaluate it drastically in favor of one side, when the actual position is equal or even favorable for the opposite side.

Approximation

@AsDaGo said in #2:

Interesting idea, but I doubt this would give you very meaningful evaluations. Most positions would probably be 0% because there's no immediate checkmate, and many positions would be completely wrong because, for example, one side might have only one good move, but an obvious one (a recapture, say), and all other moves lose (and let's say they lead to a quick mate so your engine would know they are losing). Then it might evaluate it drastically in favor of one side, when the actual position is equal or even favorable for the opposite side.

Thank you, I believe this is an interesting idea too, because Chess is fundamentally about Checkmate. :)

My guess is most positions would probably have <1% of lines leading up to a checkmate. I don't think it would be exactly 0%, unless there were no winning lines for either side (a dead draw). A dead draw might certainly be the end result, given perfect play, but a lot of things can happen in the meantime. Especially true when the engine can look at this, prospectively at a very deep ply, maybe even a ply of 50, looking at how deep and long normal evaluation goes, when people have the computer run for long amount of times, just calculating.

In a position that had an obvious and only move to get out of checkmate would have possibly +/- >90% correlation, where after making the obvious move to get out of it, the otherside might have a weaker correlation, lets say <10%, until a forced mating line was found, where it would be 100% up to the point of mate, being inf%. So, you are right about my idea, in a way, which is Correlation isn't necessarily causation at any point in time. Also, to prove this point, there is a simple illustration (the 4 move). After 1. e4 e5 2. Qh5 Nf6? 3. Bc4?? ; Black should immediately make the 1 obvious move of 3. ...Nxh5, where most other moves loses to 4. Qxf7#. Although, I'd suspect that if the total %s from each side was added together, the side with the extra queen material would have the higher sum total in % for the entire game played, even though there might be some exceptions to my general thought.

So, I think this would be a meaningful indicator of correlation up to causation, generally, being different than ACPL. I think the Checkmate Evaluation decision tree would be a Fundamental Analysis of the position and there might even be a science to opening up probabilities smartly, even though the ACPL engine scoring method seems to do exceedingly well on its own.

Also, hypothetically, if the only hole in the correlation of the Checkmate Evaluation Decision Tree is where the ACPL changed in favor of the opponent, as a result of the move being a defense to the checkmate plan, like in the 4 move illustration I mentioned taking the queen - then those situations should be ruled out from playing them, as the top candidate move plan. Keep doing that for other candidate moves until there isn't an ACPL sacrifice, I think, and that line should be the most playable, I'd think.

@AsDaGo said in #2: > Interesting idea, but I doubt this would give you very meaningful evaluations. Most positions would probably be 0% because there's no immediate checkmate, and many positions would be completely wrong because, for example, one side might have only one good move, but an obvious one (a recapture, say), and all other moves lose (and let's say they lead to a quick mate so your engine would know they are losing). Then it might evaluate it drastically in favor of one side, when the actual position is equal or even favorable for the opposite side. Thank you, I believe this is an interesting idea too, because Chess is fundamentally about Checkmate. :) My guess is most positions would probably have <1% of lines leading up to a checkmate. I don't think it would be exactly 0%, unless there were no winning lines for either side (a dead draw). A dead draw might certainly be the end result, given perfect play, but a lot of things can happen in the meantime. Especially true when the engine can look at this, prospectively at a very deep ply, maybe even a ply of 50, looking at how deep and long normal evaluation goes, when people have the computer run for long amount of times, just calculating. In a position that had an obvious and only move to get out of checkmate would have possibly +/- >90% correlation, where after making the obvious move to get out of it, the otherside might have a weaker correlation, lets say <10%, until a forced mating line was found, where it would be 100% up to the point of mate, being inf%. So, you are right about my idea, in a way, which is Correlation isn't necessarily causation at any point in time. Also, to prove this point, there is a simple illustration (the 4 move). After 1. e4 e5 2. Qh5 Nf6? 3. Bc4?? ; Black should immediately make the 1 obvious move of 3. ...Nxh5, where most other moves loses to 4. Qxf7#. Although, I'd suspect that if the total %s from each side was added together, the side with the extra queen material would have the higher sum total in % for the entire game played, even though there might be some exceptions to my general thought. So, I think this would be a meaningful indicator of correlation up to causation, generally, being different than ACPL. I think the Checkmate Evaluation decision tree would be a Fundamental Analysis of the position and there might even be a science to opening up probabilities smartly, even though the ACPL engine scoring method seems to do exceedingly well on its own. Also, hypothetically, if the only hole in the correlation of the Checkmate Evaluation Decision Tree is where the ACPL changed in favor of the opponent, as a result of the move being a defense to the checkmate plan, like in the 4 move illustration I mentioned taking the queen - then those situations should be ruled out from playing them, as the top candidate move plan. Keep doing that for other candidate moves until there isn't an ACPL sacrifice, I think, and that line should be the most playable, I'd think.