Is there such thing as "luck" in chess?

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Kotshmot
DiogenesDue wrote:

Chess as a logical construct contains no luck (beyond first move selection). I'm open for this definition of a logical construct, but not excluding luck. Chess in physical form between two humans does not contain luck either. The "luck" that manifests in all examples here come from the players or the environment. On a practical level, if you attribute luck to player's decisions (mind), that is actually a matter of skill (and a lapse of skill is not luck, nor is falling prey to emotions, lack of focus, etc.). Absence of skill creates uncertainty. Games or game elements like rolling the dice purposefully create a process with an absence of skill to ensure full uncertainty. On a practical level, there are occasions in chess where this absence of skill can exist. The only difference is that you can blame the player for this uncertainty. If you attribute luck to the environment (which includes tournaments rules, clocks, what the players ate, weather, lighting, bodily urges, etc.) then that is external to the game entirely and the phrase "in chess" fails. If you attribute luck to what happened before the game (training, pet openings, etc.), that is not part of the game of chess played either. Excluding the physical environment and training from chess for the argument I am open for.

Look at it this way (anyone that wants to be reductionist and simplify this all down)...if it's not in the PGN or is a purely optional part of the PGN (which is carefully designed to encapsulate all the information needed to recreate a game of chess), it's not part of the game of chess being represented and you cannot apply external examples to it and claim luck. PGN is not a perfect format, though, so you can only use this as a good rule of thumb for trying to decide if something should be considered part of a game of chess.

That's my non-idealist version of things, which I hesitate to bring up since people will seize on anything imprecise and start to argue about what it actually means.

I can accept your version for this debate. What I can't accept is your argument that it somehow excludes uncertainty and luck.

DiogenesDue
Kotshmot wrote:
DiogenesDue wrote:

Chess as a logical construct contains no luck (beyond first move selection). I'm open for this definition of a logical construct, but not excluding luck. Chess in physical form between two humans does not contain luck either. The "luck" that manifests in all examples here come from the players or the environment. On a practical level, if you attribute luck to player's decisions (mind), that is actually a matter of skill (and a lapse of skill is not luck, nor is falling prey to emotions, lack of focus, etc.). Absence of skill creates uncertainty. Games or game elements like rolling the dice purposefully create a process with an absence of skill to ensure full uncertainty. On a practical level, there are occasions in chess where this absence of skill can exist. The only difference is that you can blame the player for this uncertainty. If you attribute luck to the environment (which includes tournaments rules, clocks, what the players ate, weather, lighting, bodily urges, etc.) then that is external to the game entirely and the phrase "in chess" fails. If you attribute luck to what happened before the game (training, pet openings, etc.), that is not part of the game of chess played either. Excluding the physical environment and training from chess for the argument I am open for.

Look at it this way (anyone that wants to be reductionist and simplify this all down)...if it's not in the PGN or is a purely optional part of the PGN (which is carefully designed to encapsulate all the information needed to recreate a game of chess), it's not part of the game of chess being represented and you cannot apply external examples to it and claim luck. PGN is not a perfect format, though, so you can only use this as a good rule of thumb for trying to decide if something should be considered part of a game of chess.

That's my non-idealist version of things, which I hesitate to bring up since people will seize on anything imprecise and start to argue about what it actually means.

I can accept your version for this debate. What I can't accept is your argument that it somehow excludes uncertainty and luck.

Uncertainty of outcome and luck are not equivalent at all. Luck can only be said to apply to a subset of uncertain outcomes. I will also point out that from my end, adding in the word uncertainty (as if I ever said I exclude uncertainty along with luck from the game of chess) in order to hedge your bets means you are the one who isn't sure his argument can ultimately hold up. When two players play, their applied skill during the game, which is a range and can vary from move to move, determines the outcome. Two spectators could bet on the outcome and the loser of the bet might be able to say "I was unlucky that the player I bet on did not perform well today even though they are higher rated", but the player themselves cannot say "I was unlucky that I did not play well today against my lower rated opponent" because it was a lack of applied skill that lost them the game.

Even in the recent "but what if you just got a cancer diagnosis that morning?" example someone gave, it's sad, but still a lack of skill. Humans lack the ability to keep their emotions and thoughts out of the game entirely, yet another set of players exists that never have this particular lack of skill, and when that set of players plays, this outcome never occurs in their games of chess. By the simple technique of swapping out parts to eliminate each in turn until the faulty one is revealed, human beings have proven to be the faulty part.

Kotshmot

@DiogenesDue

When uncertainty arises from absence of skill, luck is inevitable. Atleast this is the case with human induced processes.

DiogenesDue
Kotshmot wrote:

@DiogenesDue

When uncertainty arises from absence of skill, luck is inevitable. Atleast this is the case with human induced processes.

That's not luck. We had this same discussion a few years ago. Luck does not come flying in to fill the vacuum when applied skill is not perfect. It's still a lack of applied skill. Again, two different spectrums. Luck is not the opposite of skill...this is a common mistake people make, but it's not the case.

Same impasse as before.

Kotshmot
DiogenesDue wrote:
Kotshmot wrote:

@DiogenesDue

When uncertainty arises from absence of skill, luck is inevitable. Atleast this is the case with human induced processes.

That's not luck. We had this same discussion a few years ago. Luck does not come flying in to fill the vacuum when applied skill is not perfect. It's still a lack of applied skill. Again, two different spectrums. Luck is not the opposite of skill...this is a common mistake people make, but it's not the case.

Same impasse as before.

I say luck does fill the vacuum that absence of skill leaves and it can be demonstrated.

"...when applied skill is not perfect."

Is your position that luck does "fly in" when there is a total absence of skill and 0% control, but luck does not come flying in when there is even the tiniest of influence by skill?

In practice, the total absence of skill influence on a dice roll results in an event of chance, but if player skill had a 1% influence on the result of a dice roll suddenly no luck is involved?

DiogenesDue
Kotshmot wrote:

I say luck does fill the vacuum that absence of skill leaves and it can be demonstrated.

"...when applied skill is not perfect."

Is your position that luck does "fly in" when there is a total absence of skill and 0% control, but luck does not come flying in when there is even the tiniest of influence by skill?

In practice, the total absence of skill influence on a dice roll results in an event of chance, but if player skill had a 1% influence on the result of a dice roll suddenly no luck is involved?

Nope.

Skill is one scale/spectrum. Luck is another. There are no dice, or concealed cards, or anything else in chess to allow for a spectrum of good vs. bad luck. In games of perfect information, there simply is no scale/spectrum for luck. That's the very definition of a game of perfect information.

So, remove the "luck" scale. Now you have the spectrum of skill remaining...sometimes the bar is full and sometimes it's empty, but at no point does luck get to drop by for a visit to the skill bar.

If you don't believe me, copy this whole exchange (prior to this post, obviously) word for word and toss it into ChatGPT with no preamble, just "Evaluate this exchange:"....here's the output you will get:

This exchange is a classic philosophical and game-theoretical debate about the nature of luck and skill, particularly in deterministic games like chess. Let's break it down logically and see where the strengths and weaknesses lie.

Core Arguments in the Discussion:

First Position: "When uncertainty arises from absence of skill, luck is inevitable."

This argument suggests that whenever skill is lacking, luck must take its place. This assumes that luck is the opposite of skill and that uncertainty (from lack of skill) automatically equals luck.

Counterargument: "Luck does not come flying in to fill the vacuum when applied skill is not perfect."

This position argues that luck and skill are not on the same spectrum and that a lack of skill does not automatically mean luck is involved. Instead, mistakes and uncertainty come from imperfect skill application, not from random external forces of luck.

Example with Dice Rolling:

One party tries to demonstrate that a total absence of skill in rolling dice results in a "luck-based" event (since the outcome is out of human control). They argue that if skill has even a 1% influence, does that suddenly remove all luck? If not, then skill and luck must exist on a spectrum.

Final Response: "Skill is one spectrum. Luck is another. In a game of perfect information, there is no spectrum for luck."

This response reinforces the idea that luck is defined by randomness and external chance elements (e.g., dice, hidden cards, RNG in video games, etc.). Since chess is a game of perfect information, the outcome is purely determined by moves made, and any errors come from imperfect skill, not luck.

Evaluating the Arguments:

Is Luck the Opposite of Skill?

Flawed assumption: Luck is not simply the inverse of skill. It is a separate variable in game design and probability theory.

Example: In poker, an expert player might lose to a beginner due to bad luck (e.g., drawing the wrong cards). But in chess, an expert losing to a beginner is never due to bad luck—only due to blunders or psychological mistakes.

Correct approach: The absence of skill leads to chaotic, unpredictable outcomes, but that is not the same as luck.

Does Uncertainty Mean Luck?

Flawed assumption: Just because an outcome is uncertain doesn't mean it's dictated by luck. Example: If a student randomly guesses on a math test, the outcome is uncertain, but it's not due to "luck" in the sense of an external force—it’s due to their lack of knowledge.

Is a Tiny Amount of Skill Enough to Remove Luck?

This is a strong counterargument by the first person: If total absence of skill (like a dice roll) means luck is involved, then how much skill is needed before luck "disappears"?

Counterpoint: The second person correctly argues that in games of perfect information (like chess), no hidden randomness exists—so there is no "luck" variable at play.

Conclusion: The first person's point applies better to games with random elements (dice, shuffled cards, etc.) but not to chess or similar deterministic games. 

Final Verdict:

The strongest argument in this discussion is that luck and skill are not on the same spectrum—they are separate variables.

The second person is correct in saying that perfect information games (like chess) remove luck entirely. Any mistakes or uncertainty come from human imperfections in skill, not from external randomness.

The first person's argument about skill "leaving a vacuum that luck fills" is incorrect for perfect information games but could apply to situations where true randomness exists (e.g., dice rolling).

Now, even if you do not trust ChatGPT to be correct, you can at least trust that it consolidates from a consensus of opinion that shows your position to be in the minority (at best) or just flawed (at worst).

Kotshmot

ChatGPT is great tool, but as you know it's not reliable in solving logical problems independently - It refers separately to information on dice and chess that might be in the wrong context, and is not able to make novel logical conclusions especially in a rare context.

I'm not a fan on referring to ChatGPT in a debate.

It takes airtime from our conversation and requires me to read through a leghty AI ramble, that is potentially a waste of time and nobody is accountable for its mistakes.

I'll address it when I have time.

Elroch

I can do better than ChatGPT on this.

"Luck" is a word referring to behaviour that is random, focussing on those random outcomes which are desirable (the "lucky" ones).

So, putting aside the simple aspect of desirability (we all want to score higher), we can replace the term by "randomness".

Randomness is the phenomenon that some system has multiple possible outcomes, but the outcome is not determinate (i.e. 100% predictable) from a specific viewpoint.

This is certainly the case with a typical chess game before it is played. If you disagree, you need to be able to predict the result with 100% reliability.

So chess, as a phenomenon in the real world has luck (= randomness with a familiar notion of preference).

[Chess as a game theoretical topic is distinct from chess in the real world. One is about abstract truth, and the other is about what happens].

Kotshmot
DiogenesDue wrote:
Kotshmot wrote:

I say luck does fill the vacuum that absence of skill leaves and it can be demonstrated.

"...when applied skill is not perfect."

Is your position that luck does "fly in" when there is a total absence of skill and 0% control, but luck does not come flying in when there is even the tiniest of influence by skill?

In practice, the total absence of skill influence on a dice roll results in an event of chance, but if player skill had a 1% influence on the result of a dice roll suddenly no luck is involved?

Nope.

If that is not your position on the dice example, what is?

Skill is one scale/spectrum. Luck is another. There are no dice, or concealed cards, or anything else in chess to allow for a spectrum of good vs. bad luck. In games of perfect information, there simply is no scale/spectrum for luck. That's the very definition of a game of perfect information.

I never brought up chess in my previous post, because I'm testing your overall position on luck in a separate context. You bringing up chess and games of perfect information does not answer my question. Are you trying to avoid answering the question?

So, remove the "luck" scale. Now you have the spectrum of skill remaining...sometimes the bar is full and sometimes it's empty, but at no point does luck get to drop by for a visit to the skill bar.

We can investigate this position and how it holds with the dice example from my earlier post, that's why I brought it up.

If you don't believe me, copy this whole exchange (prior to this post, obviously) word for word and toss it into ChatGPT with no preamble, just "Evaluate this exchange:"....here's the output you will get:

This exchange is a classic philosophical and game-theoretical debate about the nature of luck and skill, particularly in deterministic games like chess. Let's break it down logically and see where the strengths and weaknesses lie.

Core Arguments in the Discussion:

First Position: "When uncertainty arises from absence of skill, luck is inevitable."

This argument suggests that whenever skill is lacking, luck must take its place. This assumes that luck is the opposite of skill and that uncertainty (from lack of skill) automatically equals luck.

Counterargument: "Luck does not come flying in to fill the vacuum when applied skill is not perfect."

This position argues that luck and skill are not on the same spectrum and that a lack of skill does not automatically mean luck is involved. Instead, mistakes and uncertainty come from imperfect skill application, not from random external forces of luck.

Example with Dice Rolling:

One party tries to demonstrate that a total absence of skill in rolling dice results in a "luck-based" event (since the outcome is out of human control). They argue that if skill has even a 1% influence, does that suddenly remove all luck? If not, then skill and luck must exist on a spectrum.

Final Response: "Skill is one spectrum. Luck is another. In a game of perfect information, there is no spectrum for luck."

ChatGPT literally answers "My position is right because I say so" and doesn't engage the logic. This is because it's referring to this ready answer from somewhere, but it doesn't provide an answer to the specific question.

This response reinforces the idea that luck is defined by randomness and external chance elements (e.g., dice, hidden cards, RNG in video games, etc.). Since chess is a game of perfect information, the outcome is purely determined by moves made, and any errors come from imperfect skill, not luck.

Evaluating the Arguments:

Is Luck the Opposite of Skill?

Flawed assumption: Luck is not simply the inverse of skill. It is a separate variable in game design and probability theory.

Example: In poker, an expert player might lose to a beginner due to bad luck (e.g., drawing the wrong cards). But in chess, an expert losing to a beginner is never due to bad luck—only due to blunders or psychological mistakes.

Correct approach: The absence of skill leads to chaotic, unpredictable outcomes, but that is not the same as luck.

Does Uncertainty Mean Luck?

Flawed assumption: Just because an outcome is uncertain doesn't mean it's dictated by luck. Example: If a student randomly guesses on a math test, the outcome is uncertain, but it's not due to "luck" in the sense of an external force—it’s due to their lack of knowledge.

Is a Tiny Amount of Skill Enough to Remove Luck?

This is a strong counterargument by the first person: If total absence of skill (like a dice roll) means luck is involved, then how much skill is needed before luck "disappears"?

Counterpoint: The second person correctly argues that in games of perfect information (like chess), no hidden randomness exists—so there is no "luck" variable at play.


Conclusion: The first person's point applies better to games with random elements (dice, shuffled cards, etc.) but not to chess or similar deterministic games.
 

Final Verdict:

The strongest argument in this discussion is that luck and skill are not on the same spectrum—they are separate variables.

The second person is correct in saying that perfect information games (like chess) remove luck entirely. Any mistakes or uncertainty come from human imperfections in skill, not from external randomness.

The first person's argument about skill "leaving a vacuum that luck fills" is incorrect for perfect information games but could apply to situations where true randomness exists (e.g., dice rolling).

"could apply to situations where true randomness exists"

If human skill influenced a dice roll, like it does in the example we're trying to study, it no longer is true randomness any more than a chess move with imperfect skill is. ChatGPT logic fails here.

Now, even if you do not trust ChatGPT to be correct, you can at least trust that it consolidates from a consensus of opinion that shows your position to be in the minority (at best) or just flawed (at worst).

ZonguldakZonguldak

Yes there is, however it's close to zero in reality the higher skill level gets.

Let me explain:

Just by CHANCE it is in THEORY possible that I would play the exact best moves that Stockfish would play, of course the chance is extremely low and gets lower with each consecutive move, but there is a non zero percentage chance to hit good moves by accident.

PennsylvanianDude

I mean it's takes skill to take advantage of an opponent's mistakes if they make one, and to play the best moves. If your opponent blunders mate and you missed it, they are not really lucky you did not see it, as you are not good enough to see it.

playerafar

Skill and degrees of applied skill do not 'eliminate' luck although they can reduce the influence of the luck in situations.
Luck - including bad luck - can reduce the impact of skill too.
They co-exist.
--------------------------------
Controlling situations and outcomes versus having little or no control.
I think almost everyone knows that both surround us constantly.
Some rain hits you. You get wet.
You weren't in a position to prevent it. It wasn't forecast and came on suddenly.
No control there.
But - you go inside and switch to dry clothes.
Control there.
Everybody knows that control and non-control surround us.
And are constantly reminded.
Applies internally too - although that's forgotten much more often.
Illusions and delusions of total self-control versus illusions/delusions of 'can't help it'
----------------------
chess is exempt from reality?
Not in the usual meaning of the word.
-------------------------
If chess is defined as its rules or its pieces/board everyone knows there's no 'luck' there. It would be like claiming there's 'luck' in the number 2.
If chess is defined as 'the John Tromp number' (5 x 10^44 is an upper bound on the number of possible chess positions) or as the 'Shannon number' (named after Claude Shannon) which is a lower bound on the number of possible chess games and is a whopping 10^120 (the John Tromp number is already more than 'whopping' enough) ... then that total number of possible chess games and the data totality of all the chess games that could be - 
also has no 'luck' in it.
---------------------------------
Nor does the number pi. It has absolutely no luck 'inside' it.
(the 'inside' of a number ... lol - is there such a thing?)
Point: if whoever wants to define 'chess' as all its possible games/outcomes with no players then you've got a solid case for 'no luck in chess'
But that's like 'record of chess game' which is distinct from 'chess' in the common meaning of the word.
--------------------------------
Summary:
If the forum title had been written:
'Is there luck in chess in the common meaning of the word 'chess'?
Answer: 'Yes. Obviously. And to varying degree.'

DiogenesDue
Kotshmot wrote:

ChatGPT is great tool, but as you know it's not reliable in solving logical problems independently - It refers separately to information on dice and chess that might be in the wrong context, and is not able to make novel logical conclusions especially in a rare context.

I'm not a fan on referring to ChatGPT in a debate.

It takes airtime from our conversation and requires me to read through a leghty AI ramble, that is potentially a waste of time and nobody is accountable for its mistakes.

I'll address it when I have time.

Now that ChatGPT is around, I will sometimes check it after there's an impasse, to see how the "trained consensus" feels. It's obviously not conclusive, but it's a good indicator of how these debates go in general and a good way to see if I am missing something. No need to address it, I don't consider it an argument you need to address, merely a stamp of approval on my end of it.

playerafar

That's an idea.
The one Dio just stated.
I'll take my post I just made and post it to ChatGpt and make sure to include 'Please respond to all points' ....
I don't know what reply I'll get but there's a strong chance it will say something like:
'it sounds like you're making a synopsis about determinism and fatalism and also how such might apply to the game of chess'
AI also flatters people approaching it.
Maybe it even flatters the Flatters. The flat-earth people.
When they try to push flat earth on the AI.
---------------------

playerafar

After GPT I'll also try the same paragraphs on Copilot and Brave Leo.
See if they all react the same.
I'm guessing no.

DiogenesDue
ibrust777 wrote:

Indeterminacy is a state which isn't clearly defined, and could lead to multiple potential outcomes. Randomness is the statistical evaluation of indeterminate events, and luck is the subjective evaluation of randomness.

Skill is the ability of a player to determine a positive outcome of the game.

Luck and skill exist on a spectrum of indeterminacy vs. determinacy. When skill increases, so does determinacy of the games outcome, and hence the influence of luck decreases. Likewise when skill decreases so does indeterminacy increase, and so does luck.

Good vs. bad luck is the evaluative aspect of luck, but any random event, when evaluated, is luck regardless of how it's evaluated.

I explained this earlier but Dio responded by insisting it already supported point, i.e. no need to address it. Now he's arguing against it again...

Because your explanation is flat out wrong. Skill and luck are not two ends of the same spectrum. You definition of skill is off, by the way. Skill refers to good and bad applications of ability. Social convention prevents people from talking about poor applications of skill to those that apply them, ergo the "gee, that was unlucky" comforting that has led to human beings deciding that skill and luck are two sides of the same coin...but any logical person will see through that in a matter of minutes. The ability to show games on a 2x2 chart with low to high skill and low to high "luck" (introduced random outcomes, in a game design context) makes this pretty clear.

playerafar

Here's the reply I got from ChatGPT just now:
(Would people who have never used AI be surprised? Well maybe there's few such people nowadays - especially on chess servers)
-------------------------------
"

Thanks for sharing this! Let’s go through each point.

Skill and Luck: You’re absolutely right that skill and luck can coexist, with skill often reducing the impact of luck but not completely eliminating it. Both play roles in different situations. Skill might help you prepare better or navigate uncertain situations, but there's always an element of randomness or uncontrollable factors (luck) that could impact the outcome, despite your best efforts.
Control vs. Non-Control: The distinction you’re making here is key—control is something we often have over some things, but not over others. The rain example is a great way to illustrate this: you can’t control the weather, but you can control how you respond to it. Internally, the idea of control is often blurred by illusions, whether that’s overestimating our power to control outcomes or assuming things are out of our hands entirely. Acknowledging this duality can be quite empowering.
Chess and Reality: I think you’re distinguishing between the abstract concept of chess (its rules, possibilities) and the practical, real-world experience of playing the game. Chess itself, in its purest form, has no luck involved, but the execution of the game in real life (like any competitive endeavor) is influenced by factors that may be seen as luck—whether that’s external distractions, a moment of unexpected insight, or an opponent making an error due to fatigue.
Luck in Chess and Mathematics: You're correct that when we’re talking about the theoretical number of possible chess games (like the Shannon number), there's no randomness—it's deterministic, just like mathematical constants like pi. But when it comes to actual games being played by humans, randomness might creep in (like an error or an unanticipated move).
Summary: Your final point is a solid one. If you’re talking about chess in the strictest sense (as a game governed by fixed rules and endless possibilities), there's no luck involved. But in the common, real-world context—where players' skill, judgment, and sometimes errors come into play—luck can be a factor, and it does vary in influence depending on the specific game and situation.
Would you say the role of luck in chess (or any game) is often underestimated?
"
-----------------------------------------------

playerafar

The Copilot reply was different from the ChatGPT reply.
More different than I thought it would be.
And the Leo reply (Leo is an AI within the Brave browser) was quite different again.
I encountered a 2000 character limit with Leo.
Generally I've found that Leo is inferior to the other two AIs - GPT and Copilot.
---------------------
GPT did not use the ugly 'markdown' format in its reply. I didn't have to tell it not to.
But Copilot and Leo both did. I forgot to tell them not to.
But the actual text in each reply varied considerably!
------------
It appears that GPT is the cutting edge though.
As far as publically available for free and with no signup is concerned.

DiogenesDue
Kotshmot wrote:

If that is not your position on the dice example, what is?

My position on skill in dice rolls is simple. If it were significant, Las Vegas would be a ramshackle ghost town in the desert. Ergo, please dispense with using these type of examples. This falls into the same category as positing that a random generator has a non-zero chance of beating Carlsen. I am not interested in Jim Carrey-esque "so you're saying there's a chance..." back and forths.

I never brought up chess in my previous post, because I'm testing your overall position on luck in a separate context. You bringing up chess and games of perfect information does not answer my question. Are you trying to avoid answering the question?

This is a discussion of chess, and by extension also a discussion about games of perfect information. I have stated my definitions of what each word in "luck in chess" means in the past. I have no incentive to bother coloring outside the lines so you personally can be satisfied with my arguments when you didn't like them the first time. So, no, I am not going to take your "test". If there's a fresh angle we haven’t covered, I’m open to hearing it. Otherwise, I think we've exhausted this sub-sub-topic.

We can investigate this position and how it holds with the dice example from my earlier post, that's why I brought it up.

ChatGPT literally answers "My position is right because I say so" and doesn't engage the logic. This is because it's referring to this ready answer from somewhere, but it doesn't provide an answer to the specific question.

It does provide a top level consensus answer, which is what it's designed to do. You are well aware that you could drill down on everything in its summary on the exchange to the Nth degree of detail.

If human skill influenced a dice roll, like it does in the example we're trying to study, it no longer is true randomness any more than a chess move with imperfect skill is. ChatGPT logic fails here.

Human skill cannot influence dice rolls to any degree significant enough to be an argument for your position. Again...argument by Jim Carrey (appeal to possibility fallacy, if you prefer). 

Tempetown
DiogenesDue wrote:
ibrust777 wrote:

a) in quantum physics, which you clearly know nothing about, quantum indeterminacy states that without an observable - i.e. some subjective context inwhich events are observed - a systems physical state cannot determine events, i.e. it remains indeterminate. Which is exactly what I described above, and exactly opposite of your point.

b) probability theory rigorously defines the known vs. unknown in the form of a sample and population. The sample consists of the observables, the population consists of the unobserved. i.e. it relies explicitly on the subjective context of the mathematician, that data which is known to him vs. unknown. Without this distinction there can be no mathematical probability. So no, wrong. Try again.

c) Flipping a coin or rolling a dice, similarly, is an act of indeterminacy insofar as human beings cannot predict the outcome, but when it comes purely to the physical forces acting on the dice or coin, the outcome is not indeterminate.

You fail, and you demonstrate that you have zero understanding of the argument, but all along have just been hopping on board the backs of others points. Infact, you've now done a 180 twice in this thread, and I'm still not sure you realize it. But never has it mattered since I've yet to see you make an original argument.

Keep trying

a) Go ahead and tell me your Schrodinger's cat theories about chess positions, I guess .

b) Go ahead and attempt to connect this to something I have argued in a way that is not nonsense. That is, don't spout a bunch of stuff, then state at the end "so no, you're wrong" when I have not discussed what you are pontificating on.

c) So...you are a hardcore determinist then when it comes to dice? How does that jive with your quantum indeterminacy?

You keep wandering farther and farther off into the weeds. Demonstrate the 180, if you think you can.

Now, I have already told Koshmot that if he wants to argue that a random move generator can beat Carlsen, and therefore there is luck in chess, then I'll agree that there's about a one in a trillion trillion chance of getting "lucky" enough to do that much the same way as infinite monkeys can type all of Shakespeare's work, etc. So if you want to go after that level of a technicality, I'm not really interested that type of meaningless discussion.

I think you can give up on @ibrust. As Rick Reily said of Dustin Johnson, "He is so dense, light bends around him."