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Is Chess a Game of Luck?

So now that we separated the luck from randomness. What is randomness?

Yes luck is the intersection of random and some evaluation. it is not only evaluation of any event. One does not say of an outcome that follows logically from the preceding half-move choice (say a mate in 1). I got lucky.

but there could be random events for which we would have no evaluation yet as we subjectively would not be able to evaluate its consequences on whatever goal we had with regard to such event. That would be a random event. If someone were to have assigned some positive value (win) or negative value (lose) to that event, then good luck and badluck (or degree of those, if having some clues upstream a sequence of such events).

so now homing on agnostic random event (no belief about the value of the event for any subsequent goal).

what is that "random" word doing there....? Does it just mean random.. so the definition of random, is that it is random? not satisfying I would say.. And don't go back to luck. Already dissected.

We all know what random is.... yes? so can anyone explain it? (I made a post going into probability root of the word, where random or stochastic seems to be a placeholder for absence of point mass a priori knowledge, in other word uncertainty, assign a space of functions to knowledge, in my words, and only worrying about what is controllable and knowable about that). But otherwise, how does one define random?

So now that we separated the luck from randomness. What is randomness? Yes luck is the intersection of random and some evaluation. it is not only evaluation of any event. One does not say of an outcome that follows logically from the preceding half-move choice (say a mate in 1). I got lucky. but there could be random events for which we would have no evaluation yet as we subjectively would not be able to evaluate its consequences on whatever goal we had with regard to such event. That would be a random event. If someone were to have assigned some positive value (win) or negative value (lose) to that event, then good luck and badluck (or degree of those, if having some clues upstream a sequence of such events). so now homing on agnostic random event (no belief about the value of the event for any subsequent goal). what is that "random" word doing there....? Does it just mean random.. so the definition of random, is that it is random? not satisfying I would say.. And don't go back to luck. Already dissected. We all know what random is.... yes? so can anyone explain it? (I made a post going into probability root of the word, where random or stochastic seems to be a placeholder for absence of point mass a priori knowledge, in other word uncertainty, assign a space of functions to knowledge, in my words, and only worrying about what is controllable and knowable about that). But otherwise, how does one define random?

If the universe is "deterministic", does "randomness" physically exist? Or should we relax randomness to "practically random"? Then, randomness to a player of a game (e.g. dice rolls, poker, chess, etc) is merely the most accurate modeling probability distribution (i.e. minimum KL-divergence w.r.t. the true distribution).

But then, by such a definition, chess is effectively random to the player, with the randomness modeled by probability distribution dependent on candidate moves, which are weighted via a pruned tree search to some depth. (With the typical assumption that the opposing player is trying to win, and will look at the expected candidate moves.)

If the universe is "deterministic", does "randomness" physically exist? Or should we relax randomness to "practically random"? Then, randomness to a player of a game (e.g. dice rolls, poker, chess, etc) is merely the most accurate modeling probability distribution (i.e. minimum KL-divergence w.r.t. the true distribution). But then, by such a definition, chess is effectively random to the player, with the randomness modeled by probability distribution dependent on candidate moves, which are weighted via a pruned tree search to some depth. (With the typical assumption that the opposing player is trying to win, and will look at the expected candidate moves.)

Fun related thought experiment:

Make two identical copies of the player that behave in some "deterministic" manner. (e.g. single-threaded Stockfish.) Make the exact same small variation (e.g. bishop_material_weight from 3.50 -> 3.49) for both players, and play another game.

The resulting games may be vastly different with vastly different outcomes.

Does this not demonstrate chaos and complexity, and ergo, practical randomness?

Fun related thought experiment: Make two identical copies of the player that behave in some "deterministic" manner. (e.g. single-threaded Stockfish.) Make the exact same small variation (e.g. bishop_material_weight from 3.50 -> 3.49) for both players, and play another game. The resulting games may be vastly different with vastly different outcomes. Does this not demonstrate chaos and complexity, and ergo, practical randomness?

@sicariusnoctis said in #82:

But then, by such a definition, chess is effectively random to the player, with the randomness modeled by probability distribution dependent on candidate moves, which are weighted via a pruned tree search to some depth. (With the typical assumption that the opposing player is trying to win, and will look at the expected candidate moves.)

Or you could start your point of view from the mathematical framework A0 and Lc0 were built on, which does not rely on heuristics of evaluation from positions that are not terminal positions.

It has a full position information lossless model, through all the layers. And uses core ruleset mobility rules and termination rules. no other evaluation posited criteria (AFAI understand or understood once).

make for more seamless thinking about randomness in chess.

Also, true distribution. My question was probably kind of circular.. But positing a distribution true or estimated by player limited experience and or knowledge, is what i think is the definition act for randomness.

It only means which function space are you maximally attributing to legal move set AND position to apply move to combined domain (input of said distribution or density if sloppy like me with words across finite versus continuum ambient spaces).

However it would be nice to be able to have a common big enough domain where we could interpret both hand-crafted and material counting borne engine species development, and the very late introduced more empiriical approach (minimal handcrafting of evaluation as function of non terminal position information).

I have stopped trying to do that.. with the hybridization that came with NNue... But the hand-crafting might still be present or filtered by NNue input feature reduction from the full complete information set preserving A0 and Lc0 input framework.

The big information flow loop for NNue which enables its tournament speed advantages, is however limiting such evolution from previously single parameter optimization history for all the potential features contained in the "repressed" classical evaluation function which I heard was meant to be frozen. I thought the plan was to keep using NNue to include possibly more features, if there would open the information flow loop to be not just about approximating the frozen classical eval SF moderate search output. sorry i am not doing such long sentences on purpose.. the whole loop is needed to understand where things got stuck in my opinion. (i blame tournament cultural inertia to some extent.... priority on speed over true accuracy).

sorry i diggressed. but what is randomness. i meant to say even the true distribution posit is the only meaning of randomness.

other than convention of some never defined perception of what random could mean..

normal distribution assumption or model. is just restricting the uncertainty placeholder function to a few parameter function space spanned by exponential familiy, and intergral operator... i think 2 parameters.

one can make lots of math linking various constraints of interacting random variables and differently characterized respective function spaces.

and yes.. increasing knowledge is about constraining even more the degree of ignorance left using metrics as you suggested... to figure out what is informative or not in the data to distribution shaping evoluation loop (for a0 lc0 that evoluation is whitin training, for SF and fishtest it is across SF versioning, that is where the simpler framework under A0 and lc0. has a hard time in my mind applying).

many levels of possible ignorance models.. choosing a metric also has some implications on how the knowldge ignorance debate evolves. Human opening theories might also have their effect on admissible function space.. but that seems to be part of chess for both humans and engines so far. thanks for bringing your compatible point of view..

engines have their own design constraints on those.. i understand well i think the A0 and lc0 basic learning plan. but i find it difficult to bathe SF evaluation into it.. (some ignorance about it top most functional skeleton, and internal position information data structure which has been ground in many meanders of partial informations to be saving on cost of computation at any code branching points.. over a long history or code amendements... using intricate efficient coding and execution cost tentacular data structures... etc... needs a translation back to math. exhausting to do from outside.

how can i chop this post into on topic and off topic but not that off.. autonomous readable chunks.. i do find all those topics to be related.. but i have a visuo spatial memory support and i am trying to make a path in that to protrude it in this linguistic stream.. but the multiple probably logical connections keep popping and i wonder, did I start from the most reader digestible way.. grab what you can... and dismiss the possible BS.

@sicariusnoctis said in #82: > But then, by such a definition, chess is effectively random to the player, with the randomness modeled by probability distribution dependent on candidate moves, which are weighted via a pruned tree search to some depth. (With the typical assumption that the opposing player is trying to win, and will look at the expected candidate moves.) Or you could start your point of view from the mathematical framework A0 and Lc0 were built on, which does not rely on heuristics of evaluation from positions that are not terminal positions. It has a full position information lossless model, through all the layers. And uses core ruleset mobility rules and termination rules. no other evaluation posited criteria (AFAI understand or understood once). make for more seamless thinking about randomness in chess. Also, true distribution. My question was probably kind of circular.. But positing a distribution true or estimated by player limited experience and or knowledge, is what i think is the definition act for randomness. It only means which function space are you maximally attributing to legal move set AND position to apply move to combined domain (input of said distribution or density if sloppy like me with words across finite versus continuum ambient spaces). However it would be nice to be able to have a common big enough domain where we could interpret both hand-crafted and material counting borne engine species development, and the very late introduced more empiriical approach (minimal handcrafting of evaluation as function of non terminal position information). I have stopped trying to do that.. with the hybridization that came with NNue... But the hand-crafting might still be present or filtered by NNue input feature reduction from the full complete information set preserving A0 and Lc0 input framework. The big information flow loop for NNue which enables its tournament speed advantages, is however limiting such evolution from previously single parameter optimization history for all the potential features contained in the "repressed" classical evaluation function which I heard was meant to be frozen. I thought the plan was to keep using NNue to include possibly more features, if there would open the information flow loop to be not just about approximating the frozen classical eval SF moderate search output. sorry i am not doing such long sentences on purpose.. the whole loop is needed to understand where things got stuck in my opinion. (i blame tournament cultural inertia to some extent.... priority on speed over true accuracy). sorry i diggressed. but what is randomness. i meant to say even the true distribution posit is the only meaning of randomness. other than convention of some never defined perception of what random could mean.. normal distribution assumption or model. is just restricting the uncertainty placeholder function to a few parameter function space spanned by exponential familiy, and intergral operator... i think 2 parameters. one can make lots of math linking various constraints of interacting random variables and differently characterized respective function spaces. and yes.. increasing knowledge is about constraining even more the degree of ignorance left using metrics as you suggested... to figure out what is informative or not in the data to distribution shaping evoluation loop (for a0 lc0 that evoluation is whitin training, for SF and fishtest it is across SF versioning, that is where the simpler framework under A0 and lc0. has a hard time in my mind applying). many levels of possible ignorance models.. choosing a metric also has some implications on how the knowldge ignorance debate evolves. Human opening theories might also have their effect on admissible function space.. but that seems to be part of chess for both humans and engines so far. thanks for bringing your compatible point of view.. engines have their own design constraints on those.. i understand well i think the A0 and lc0 basic learning plan. but i find it difficult to bathe SF evaluation into it.. (some ignorance about it top most functional skeleton, and internal position information data structure which has been ground in many meanders of partial informations to be saving on cost of computation at any code branching points.. over a long history or code amendements... using intricate efficient coding and execution cost tentacular data structures... etc... needs a translation back to math. exhausting to do from outside. how can i chop this post into on topic and off topic but not that off.. autonomous readable chunks.. i do find all those topics to be related.. but i have a visuo spatial memory support and i am trying to make a path in that to protrude it in this linguistic stream.. but the multiple probably logical connections keep popping and i wonder, did I start from the most reader digestible way.. grab what you can... and dismiss the possible BS.

@sicariusnoctis said in #83:

Fun related thought experiment:

Make two identical copies of the player that behave in some "deterministic" manner. (e.g. single-threaded Stockfish.) Make the exact same small variation (e.g. bishop_material_weight from 3.50 -> 3.49) for both players, and play another game.

The resulting games may be vastly different with vastly different outcomes.

Does this not demonstrate chaos and complexity, and ergo, practical randomness?

good practical thought experiments. might be more helpful than my babble.

but i wonder if the reproducibility of SF executable is well documented... not just safe PV depth for lichess to share with trusting lichess engine analysis users (Trust your engine!), but the underlying "instability" apparent assessment from SF development community (i can't read all, or know the confidence level of data analysis behind the statements i might have read).

Is it hand-crafted based on board borne flat profile and low SF scoring resolution combination (speed again, hypothesis). if PV profile too flat with some threshold, if there design pseudo random choice. How could it not be hard code.. i was going to find a counter point. but it boils down to either the exploration of many PVs exploring actually very similar evaluation landscapes. and some resolution limit makes some instability down the depths.. (would not know how, without source code insight, painful endeavor from outside) .. or long time known that scoring float or integer built around original material counts type of differences and speed gain constraint synergizing toward limiting the discerning power among many PVs at deep enough search parameters... that pseudo random early flat PV landscape heuristic might be saving the day...

@sicariusnoctis said in #83: > Fun related thought experiment: > > Make two identical copies of the player that behave in some "deterministic" manner. (e.g. single-threaded Stockfish.) Make the exact same small variation (e.g. bishop_material_weight from 3.50 -> 3.49) for both players, and play another game. > > The resulting games may be vastly different with vastly different outcomes. > > Does this not demonstrate chaos and complexity, and ergo, practical randomness? good practical thought experiments. might be more helpful than my babble. but i wonder if the reproducibility of SF executable is well documented... not just safe PV depth for lichess to share with trusting lichess engine analysis users (Trust your engine!), but the underlying "instability" apparent assessment from SF development community (i can't read all, or know the confidence level of data analysis behind the statements i might have read). Is it hand-crafted based on board borne flat profile and low SF scoring resolution combination (speed again, hypothesis). if PV profile too flat with some threshold, if there design pseudo random choice. How could it not be hard code.. i was going to find a counter point. but it boils down to either the exploration of many PVs exploring actually very similar evaluation landscapes. and some resolution limit makes some instability down the depths.. (would not know how, without source code insight, painful endeavor from outside) .. or long time known that scoring float or integer built around original material counts type of differences and speed gain constraint synergizing toward limiting the discerning power among many PVs at deep enough search parameters... that pseudo random early flat PV landscape heuristic might be saving the day...

low dimension random versus high dimension random might come out of looking at chaos or (transient complexity like die throw) throught the random goggles. rather than practical randomness. (as there is not other type of random in my "what is random, truly, tangent subthread). it is always for practical reason that a studied set of phenomena.

typical normal distribution about some testable variable of unknown full system dimensionality (the universe, or a population trait from non-invasive measure protocols, e.g. out of the blue of my exhausted typing self).

if there are only a few factors behing the visible measure being sampled and binned, that are being ignored, and they have large effect on that visible dimension, the normal distribution might have a hard time being found a good model ..

typically one can prove the normal distribution as the limiting distribution of a high dimension system of interacting variables each with small additive effect on the one visible dimension... i am basing my reasoning on that.. one would need to check with true statistician about the converse (?, sorry my logic on vacation, speaking from memory of past reasonable thoughts).

what is remarkable of "chaotic" systems is that their local divergence (yet local deterministic dynamics, local in time steps) is a sort of mixer when the state evolution is also know to be bounded (not finite, but bounded, although finite is also bounded).

the divergence is everywhere apply to subset of simply connected or even nice round potatoes of initial condition neighborhoods, and one will have a hard time following the pairs within such evolving intial "interval" through large times... like a bread dough being returned upon itsrelf many many times... the initial set of probes one could have put near each other at the start would end up travelling from the dough in mysterious ways... that is mixing (and egodicity, somehow i think of poincarré and reccurence but ergodic it what i can find on wikipedias these days).

but on right track. your experiments. in my opinion.

low dimension random versus high dimension random might come out of looking at chaos or (transient complexity like die throw) throught the random goggles. rather than practical randomness. (as there is not other type of random in my "what is random, truly, tangent subthread). it is always for practical reason that a studied set of phenomena. typical normal distribution about some testable variable of unknown full system dimensionality (the universe, or a population trait from non-invasive measure protocols, e.g. out of the blue of my exhausted typing self). if there are only a few factors behing the visible measure being sampled and binned, that are being ignored, and they have large effect on that visible dimension, the normal distribution might have a hard time being found a good model .. typically one can prove the normal distribution as the limiting distribution of a high dimension system of interacting variables each with small additive effect on the one visible dimension... i am basing my reasoning on that.. one would need to check with true statistician about the converse (?, sorry my logic on vacation, speaking from memory of past reasonable thoughts). what is remarkable of "chaotic" systems is that their local divergence (yet local deterministic dynamics, local in time steps) is a sort of mixer when the state evolution is also know to be bounded (not finite, but bounded, although finite is also bounded). the divergence is everywhere apply to subset of simply connected or even nice round potatoes of initial condition neighborhoods, and one will have a hard time following the pairs within such evolving intial "interval" through large times... like a bread dough being returned upon itsrelf many many times... the initial set of probes one could have put near each other at the start would end up travelling from the dough in mysterious ways... that is mixing (and egodicity, somehow i think of poincarré and reccurence but ergodic it what i can find on wikipedias these days). but on right track. your experiments. in my opinion.

sorry for the convolutions.. that is all i can do right now..

sorry for the convolutions.. that is all i can do right now..

I see that the user @dboing is discussing the topic of randomness in chess and the different ways it can be defined and understood. In the first message, they suggest starting from the mathematical framework of A0 and Lc0, which does not rely on heuristics of evaluation from non-terminal positions. They also discuss the idea of a true distribution and how increasing knowledge can help constrain the degree of ignorance left.

In the second message, @dboing responds to a thought experiment regarding chaos and complexity in chess. They question the reproducibility of the Stockfish executable and suggest that the "instability" apparent in its assessment might be due to the exploration of many PVs exploring similar evaluation landscapes. They also discuss the idea of low dimension random versus high dimension random and the limitations of the normal distribution as a model for complex systems.

Overall, it seems that @dboing is interested in exploring the different ways that randomness can be understood in chess, and the limitations of current models and frameworks in capturing its complexity.

I see that the user @dboing is discussing the topic of randomness in chess and the different ways it can be defined and understood. In the first message, they suggest starting from the mathematical framework of A0 and Lc0, which does not rely on heuristics of evaluation from non-terminal positions. They also discuss the idea of a true distribution and how increasing knowledge can help constrain the degree of ignorance left. In the second message, @dboing responds to a thought experiment regarding chaos and complexity in chess. They question the reproducibility of the Stockfish executable and suggest that the "instability" apparent in its assessment might be due to the exploration of many PVs exploring similar evaluation landscapes. They also discuss the idea of low dimension random versus high dimension random and the limitations of the normal distribution as a model for complex systems. Overall, it seems that @dboing is interested in exploring the different ways that randomness can be understood in chess, and the limitations of current models and frameworks in capturing its complexity.

@dboing said in #6:

luck, random, surprise, uncertainty would need some defintion discussion.

does the board itself has uncertainty to it. for any level of human chess player.

is a pair of dice throw, truly random? or do we just don't care to map the conditions one would need to throw the dice to have it end up on some stationary orientation after some elastic sequnces of bouces and collisions, while loose kinectic energy, and finally not having enough bounce left to rotate into another face attractor. it is willfull ignorance of the intinial conditions partition to final resting state that allows us to call the process random. too much work to do that mapping.. but with proper elastic solid body and newton equations of motions together, this is still a deterministic system.

is chess also that way. locally deterministic (from position apply a move will determine the immediate next position complet information), but at least for human players, any, always has an outcome forecasting limit.

deleted my elaboration on that. better leave it as question

The depth of the analysis, the amount of knowledge and the calculations needed to rule out "luck" in any scenario from simple to complex is almost (you could directly say never on a certain priority of events) never available as needed and in particular the variable of time which in general has a decisive influence in the result of decision making.
Said this and considering the limitations of human nature to sort out puzzles by walking in the direction you have suggested ( rationalism ) you can conclude with a very solid logical reasoning that luck is very much present in almost all our activities.
Luck in itself is not bad, in fact it is necessary to equalize and smooth the edges except when it has become a challenge to a determined, rebel and naughty will willing to prevail
.Genius already face the problems with the answers in their pockets (intuition?!) which have been musitated by ... the Muses ... the answers bloom and reveal themselves before the privileged one in the form of sparks that escape the everlasting fire of the ruby stars only to dwell in the gaps of helpless ideas blinking on a hungry dark background prison, that rare kind of dancing stars have that colour from the enchanting moon that gave its blood for them to shine like gemstone beacons helping travelers in the ethernal night.

@dboing said in #6: > luck, random, surprise, uncertainty would need some defintion discussion. > > does the board itself has uncertainty to it. for any level of human chess player. > > is a pair of dice throw, truly random? or do we just don't care to map the conditions one would need to throw the dice to have it end up on some stationary orientation after some elastic sequnces of bouces and collisions, while loose kinectic energy, and finally not having enough bounce left to rotate into another face attractor. it is willfull ignorance of the intinial conditions partition to final resting state that allows us to call the process random. too much work to do that mapping.. but with proper elastic solid body and newton equations of motions together, this is still a deterministic system. > > is chess also that way. locally deterministic (from position apply a move will determine the immediate next position complet information), but at least for human players, any, always has an outcome forecasting limit. > > deleted my elaboration on that. better leave it as question The depth of the analysis, the amount of knowledge and the calculations needed to rule out "luck" in any scenario from simple to complex is almost (you could directly say never on a certain priority of events) never available as needed and in particular the variable of time which in general has a decisive influence in the result of decision making. Said this and considering the limitations of human nature to sort out puzzles by walking in the direction you have suggested ( rationalism ) you can conclude with a very solid logical reasoning that luck is very much present in almost all our activities. Luck in itself is not bad, in fact it is necessary to equalize and smooth the edges except when it has become a challenge to a determined, rebel and naughty will willing to prevail .Genius already face the problems with the answers in their pockets (intuition?!) which have been musitated by ... the Muses ... the answers bloom and reveal themselves before the privileged one in the form of sparks that escape the everlasting fire of the ruby stars only to dwell in the gaps of helpless ideas blinking on a hungry dark background prison, that rare kind of dancing stars have that colour from the enchanting moon that gave its blood for them to shine like gemstone beacons helping travelers in the ethernal night.

@Artem-Kozirev said in #89:

Nice last paragraph borrowing from many images. I admire sentences like that, long flowing and with meaning until the end (meanings).

@Artem-Kozirev said in #89: > Nice last paragraph borrowing from many images. I admire sentences like that, long flowing and with meaning until the end (meanings).