IS CHESS A GAME OF CHANCE? Classical vs Frequentist vs Bayesian Probability

[@BainesMkII]

Slightly off-topic, but you'd expect to have a roughly 50/50 win/lose rate against people of your skill level because that effectively is the definition of "people of your skill level".

[@OmneAurumNon]

Another point that I think is important to note here, cognition is probabilistic. I in 100 times you may make a blunder you wouldn't have made the other 99, because you got distracted, were focused on a different part of the board, or just made a visualization error. The whole point of the elo system is understanding that players have a "standard deviation" of playing strength. If playing strength wasn't variable, there wouldn't be any other players "of about your skill level". Everyone would either be better, worse, or identical in strength to you and you would win, lose, or draw deterministically.

[@ghmacd10]

yeah there's a little bit of a confounding variable in this line of reasoning about chess being probabilistic, because ELO rating is basically a Bayesian formulation -- you gain or lose some number of rating points based on the relative probabilities of you winning, drawing, or losing to an opponent, given the ELO gap between you. Also this formulation of chess skill as "how many moves ahead you can think" can't really say all that much about chess ability -- specific positions afford different possibilities for thinking ahead. Much more interesting I think is some kind of discussion of the relative chance of blundering in positions players are more or less familiar with -- I think often even at the highest levels chess is played in this way. Someone like Firouzja might play a line that is not engine approved because he thinks he has a better chance of understanding the complications in an unknown position than an opponent. Someone else may avoid complications that lead to a winning position because they come with a greater chance of a loss. A position may give you an advantage in 10 moves if you play perfectly, but come with greater risk of losing if you play imperfectly, and good players need to assess whether they are going to go for something like that or play something safer.

[@albertbatfinder5240]

Well said! An example of stepping back from what you’re being asked to accept, and having a quiet think instead. It’s also a bit like the theory of management that says we all advance to our natural level of incompetence. If we were better, we’d move up the ratings … until we weren’t.

[@Igor_054]

However, if people are on your skill level, the actual expectation would be a large percentage of draws, not 50-50 win-lose. This is better noticed on high levels with long time controls, where draws are enormously present. The lower the level (or the tighter the time control), however, the higher is the amount of mistakes, and eventually one of the mistakes is decisive. So there are fewer draws than we would expect.

[@BainesMkII]

@@Igor_054 The expected draw percentage is going to depend on both the likelihood of a draw to a win in general as well as how balanced the two sides (not the players themselves) are. The former both depends on the game's design and the skill levels of the players.

[@MiroslawHorbal]

I definitely take a Bayesian approach to chess. My prior probability of winning a game of chess is ~10%. Then conditional on my opponent, that probability is updated, generally, to reduce the probability of winning. Then during the game, we can see that indeed, there is a 0% chance of winning conditional on the moves I've made because I've lost my queen and rooks within a handful of moves.

[@DrTrefor]

lol

[@warmike]

Blundering all your major pieces IN THE OPENING takes a LOT of skill, I have to respect that.

[@JJ-ck9iy]

I'm surprised that Bayesian Probability is about the different amount of information in our minds. The Prior belief and the updated belief after receiving new information really surprises me. Never heard of this explanation before. In class, the professor in uni and teachers in high school just taught us the equations. Thanks!!!

[@letsmakeit110]

1.) Horizon effect. You have very little idea for example if 1. d4 or 1. e4 is better. At some point you have to make a guess. 2.) Opening preparation. If my opponent plays a strong move I haven't looked at in a while I might make mistakes but if he plays a strong move I just reviewed then he'll essentially be playing against an engine for a while.

[@MichaelRothwell1]

The part of the discussion of Bayesian probability where you can see the card but I can't see it yet, then the probability flips to 0 or 1 once I see it, strongly reminds me of the Schrödinger's cat paradox in Quantum Mechanics.

[@oniongingertomato2216]

I think what is called gut feeling in chess is derived off of probabilistic way in which subconscious mind is thinking. The ideas in game after many hours of practice have an abstract feel to them.

[@CulinoB2B]

I think its more pattern recognition there

[@BJ52091]

@@CulinoB2B A distinction without a difference, especially from a machine learning perspective

[@demr04]

You are thinking backwards. Probability is the formalization of gut feeling

[@abrahammekonnen]

I think part of the issue with chess (and other things) is that in order to get a clean number that measures your "skill" we throw out lots of information to get to that point. It seems like the reason why it's about 50/50 for you to win against someone of your rating is because that's what the rating system is designed to do. If we somehow had a system where there were multiple categories of types of skills, we could get better than 50/50 odds because we would have more information. And you could keep on adding categories to get to an arbitrary point of precision. TLDR: Chess is a game a skill, but how we measure the skill seems to make it probablistic. And a broader point would be that probablity emerges when you attempt to measure things because of the decsions we have to make when we measure things.

[@karannchew2534]

Notes for my future revision. -- Card. A given a new card. What is the probability it is a heart? Frequentist: Would not say that there's 1/4 probability. 6:28 The card is chosen. It's fixed. There's nothing probabilistic about the card. The card is either a heart or not heart. Either 1 or 0 probability. 6:37 "They might think that they might tempt to explain the world by suggesting that it was a heart is something that, in a frequentist approach, if you did this trial many over would be a correct prediction about this objectively right answer one quarter of the time."??? -- Bayesian: 6:49 is totally happy thinking that things depend on the amount of the information that is subjective, and it's not until you gained the information that this is a diamond that you update your belief that there's a zero percent chance that it is a heart. You have this prior believe and going to update them to a posterior belief as you gained more information about the world. --- Chess. What's the probability one will wins? Frequentist: Of all the games, I won 50-50 ?or 95%), so the probability is 50% (or 95%). Bayesian: Going into the game thinking i might win 50%, and then as you gained new information, you will always update your probabilistic view points wether or not you will win. -- Bounded rationality. Remove some possible options. -- 11:34 Frequentist approach: Imagine many things happen over many trial Bayesian: Update probability as new information comes in.

[@edwinwang5594]

Very helpful video. Just first learned about the Bayesian network and the belief network in class without learning Bayesian probability before. This video clarifies the difference between classical and Bayesian probability for me.

[@GeoffryGifari]

For the example of picking one card and hiding it from the viewer, asking the probability of the card being hearts, is it even possible to have the frequentist view though? The one card in your hand is either a heart or not, so when the experiment repeats (shuffle, take to hand) its no longer that one card.... the question changes If we look at it from the classical and bayesian probability view, we can directly answer the question when the card is picked just once (assuming the prior knowledge is the types of cards in a deck)

[@RikMaxSpeed]

Nice presentation, I think it’s worth mentioning that many people have used Bayes classifiers in chess engines to improve their evaluation function, or even to adapt to the player’s personal style.

[@richielavey1565]

Cool video! There’s an awesome book called the master algorithm that talks a lot about this sort of thing, it has a whole chapter dedicated to Bayesian inference and goes over several other algorithms as well and how they’re implemented into modern compuers

[@Primitarian]

Or in Star Wars terms: Han Solo, frequentist ("I just call it luck"), Obi Wan Kenobi, classicist ("In my experience, there is no such thing as luck") as well as a Bayesian ("Use the Force, Luke.")

[@andst4]

I've stumbled upon this channel by accident, but I have to say it's really top-tier popular science channel on KZbin. I hope you get much bigger audience as you deserve! Interesting, original topic, good explanation, helpful graphics, well done editing. Nice job!

[@DrTrefor]

Thank you!

[@srikanthtupurani6316]

Learning a skill has lot to do with the amount of time we spend. It is similar to this example. The amount of money some business organization makes is directly proportional to total assets of the company. This thing is true in case of learning any new skill. The more time someone spends on learning some skill the more he will be developing connections in the brain related to that skill. The more the connections the more quickly he can master it. People who don't work hard will suffer because they don't develop the connections in the brain. We cannot deny the role of inborn instincts. But inborn instincts are not sufficient to acquire some skill.

[@Baekstrom]

That was a great introduction to some interesting math that didn’t go too deep into the details. Just enough to make you interested enough to want to learn more.

[@wybren]

I think there are 2 decision points in playing chess that are more or less a guess. That might be based on a gut feeling or experience (human) or a mathematical approach of scoring the state of the chess board for that moment (computer). Those 2 decisions are made on what to prune and on how to rate the expected chess board after the expected outcome of a couple of moves. For a computer a Bayesian approach for rating the states might be out of reach because there are simply to many variables to take into account. I strongly believe Bayesian would be the superior choice if possible. However a frequentist approach would be more likely feasible. You could research what kind of statistics are important to keep track off and let a computer play millions of virtual chess games to fill in the stats. That way it might be possible to rate a situation based on a frequentist approach. That frequentists approach should be considered 'non-stationary' and trained continuously. Otherwise it would eventually start to loose games if the opponent figures out the general strategy.

[@benjaminshropshire2900]

Practically the best current solutions seem to be ML via NN, which mostly just ignores the "research what kind of statistics are important" and lets a computer figure out what works. As I understand it (I think it was actually Alph *Go* I heard described), that amounts to "playing a bunch of games", logging everything and then training hundreds or thousands of parameters on a back-box function to match board states as input to if black or white won as output. (At the training stage you know who won each game so the training values are 0 or 1, but the function returns a real value.) Once you have a first crop of modals, you have them play each other to get a second generation of training data and then train a (set of) gen-2 model(s) from that... lather rinse repeat until you run out of compute budget or have to ship it.

[@wybren]

@@benjaminshropshire2900 NN's are superior these days. I am not fighting that claim. What I wanted to do is use probability calculations in a fantasy algorithm to answer the question where you might want to use it in a chess computer. In my not so humble opinion the video starts to talk about this subject but does not fully explain a way to use probability in a chess game. Just that there seems to be a factor of probability and how it works for card games. I tried to improve that a little with a plausable strategy.

[@thatchapthere]

@@wybren I think this sort of question is discussed on the chess programming wiki, there might be some answers there.

[@ricardobautista-garcia8492]

@@thatchapthere I had no idea this website existed.

[@GeoffryGifari]

Hmmm it seems like going from Frequentist -> Bayesian -> Classical probability is like starting with no prior knowledge -> partial knowledge -> complete knowledge

[@stephenpuryear]

Doctor, thanks for adding a little bit of clarity to an interesting area!

[@lgl_137noname6]

5:19 Well, I finally learned how to properlysay that word "BAYESIAN". Thank You.

[@michaeldunkerton3805]

Rolling a die is, strictly speaking, not random. If we had perfect information and understanding of the imperfections of the die and the spin we impart to it and the air pressure changes and tremors on the table, etc etc etc....but of course we don't so it's far more practical to treat it as evenly random. I like the explanation that choosing a probability method is like choosing a philosophical approach. I had considered this notion when someone was explaining to me that StarCraft was a game without randomness (as in, no random damage values or hit chances, the only randomness that could be considered baked into the game is pathing). Somewhat cheekily I responded that your opponent's behavior is functionally random because there are simply far too many possible moves for you to consider, so you have to treat them as random possibilities weighted based on what you expect them to do. I'm glad to see I wasn't totally off track.

[@androkguz]

It's also worth mentioning that games of hidden information are basically games with randomness, even if nothing is chosen at random by any computer or dice. If you play rock, paper, scissors then you better model your opponent's behavior as a random choice generator. (of course, a good player gets into the enemy head enough to predict them better)

[@danishhussain7127]

Simply loved this video, subscribed

[@Darkev77]

A wonderful and a very intuitive insight to these topics, very well done

[@jacoboribilik3253]

It's a good time to recommend Keynes's book on the topic.

[@FishbrainMnt]

Good topic! I always gave chess as example for a game that there is no luck, but you've changed my mind a little bit. I say a little bit because it is still at the top of my list for games with least luck involved. In every sport the more skill/experience you have the less you have to rely on luck.

[@zyfryth]

I think what is important here is to establish the boundaries of the field we are thinking in. So for example. Without such boundaries we can say EVERYTHING is probabilistic. For example we play a game of chess, but there is a chance I will be feeling better at the moment of the game and thus - perform better. Or I could be feeling worse, maybe I have a headache, thus performing worse. Without established boundaries of the sphere we think in - we will always engage in mish-mushy unclear conclusions. The good thing about chess is that it gives you the OPTION to not rely on chance, if you can seize it. You can always hope for the chance of the opponent missing a move, or making a blunder, but that is a very bad strategy which will lead you nowhere on the long run. So in my humble opinion the key element here is the POTENTIAL for the game to be fair, without chance involved, but the subjective human factor, can introduce chance, willingly or unwillingly.

[@ehrichweiss]

Nice DeLand deck you have there. It took till almost the end of the video for me to verify that's what it is. I have one still to this day though I don't use it at all.

[@DrTrefor]

ha nice! Wasn't sure someone would notice! That is vintage 1990s era:D

[@dertfert745]

If you flip a coin 15 times you will get a wide variance in the number of heads. Yet somehow the media forces basketball players to say oh this or that was happening in the game to explain the outcome (which often there is some truth to) but sometimes it's really just simple luck - the ball just didn't go in.

[@DrTrefor]

This is very true, society broadly underestimated the role of luck in sports.

[@steelmongoose4956]

@@DrTrefor But is there such a thing as luck? Wouldn’t a “lucky” person be one for whom probabilities and outcomes were different and more favorable? Wouldn’t such a quality be noticeable, and wouldn’t casinos be much harder to manage if individuals had an intrinsic quality that affected probability?

[@Lopfff]

When aliens arrive, what is the probability they will greet us with “All your Bayes are belong to us?”

[@meunomejaestavaemuso]

Close to zero but not zero so that it can be updated later on if it does happen

[@Lopfff]

@@meunomejaestavaemuso Haha nice!

[@erikmartin2]

There's certainly some probability, but making a chess move is a mixture of intuition and calculation. Even if both players can only calculate 3 moves ahead, at every level the intuitive element of discerning which move leads to a more sound position can dominate at the highest levels of chess as well as lower levels. So it's hard to say that it was chance that the move I selected ended up leading to an advantage that I couldn't calculate all the way to, because even though I couldn't calculate my way there the move itself wasn't random but based on some pattern recognition about what makes a better position on the board.

[@DrTrefor]

I agree, but I think this just sort of pushes it back a level. Two similar elo players don't necessarily have the identical strengths, one might have better intuition and pattern recognition in some situations and not others, but it is hard to predict ahead of a game whether you are going to find yourself in comfortable territory or not.

[@birendrachhotaray2263]

such a nice explanation!

[@StanislavMudrets]

There's also noise and bias attributable to each person. For example, daily differences in whether you are mentally more or less efficient due to what you ate for breakfast, whether you slept, etc., can make a big difference in how well you practice your skill. Same goes for whether you are hungry, or in a hurry.

[@DrTrefor]

I’ve noticed these really effect me! Recently lost back to back against two rare pairs against someone ~200 elo below me, I think I was asleep at the wheel

[@la-la-code]

I'm curious what is your ELO is? And if this thinking about probability could improve your chess skill? For example, when I assume that my opponent calculates equal moves ahead as I do, it motivates me to think longer/more focused.

[@DragonBank]

Probability won't make your skill as an individual any better. Your skill is based on your ability to find the best move. Best doesn't mean computer move. It just means the move that will create positions you win. What that means is hard to determine and is what makes such a simple game so complex.

[@samuelfalk8438]

My guess is that you already do think that of your opponents, even if you hope they don't - it would be kinda weird to assume otherwise. Besides, both you and your opponent probably have similar amount of resources when it comes to calculating depth.

[@69nites]

Every game of chess starts as a draw. Winning is making less mistakes or less important mistakes than your opponent.

[@MannISNOR]

Wow, the card examples are very clever. Great stuff!

[@zahidhasan7052]

The video and audio quality of your videos have got significantly better. I'm sure it'll affect the algorithm positively.

[@kennythegamer1]

6:51 or you could use Bayesian Probability and Philosophically say that these updates are merely for our subjective, Epistemological use and that the card is, in actuality, either a heart or it isn't

[@jeronimo196]

His explanation of Bayesian probability sucks. The update is not on B (card is hearts), the update is on A (some hypothesis about the deck). For example, if A is (there are no hearts in the deck), seeing B disproves it. And using your logic, all probability is 50/50 - I'll either see a T-Rex today, or I won't.

[@nastyavicodin6229]

Thanks for the great explanation!

[@mtaur4113]

In the abstract, every chess position is winning, losing, or drawn. But in practice, the amount of computation power needed to decide which scenario it is and what the best moves are is beyond prohibitive. In theory you could just click the "best move" button for days and it would be boring, but at the moment, we can't do that, we can just make AI that crushes humans the vast majority of the time (with the occasional super-strong player stumbling across a blind spot once in a blue moon) So in practice, yeah, you end up branching into families of opening moves (theory) which are unknown whether to be "won" or "lost" or "drawn", and if you have some rough idea which positions you and your opponent understand better... it starts to get rather head-gamey and probabilistic. Or just modeling player behavior as essentially random with a sort of quirky and unknowable "algorithm" makes the outcome sort of random from that point of view too. It actually looks kind of hard to make an AI make "human" mistakes. To some AIs, it seems like they view a bad move as just a bad move, and blundering a piece in one move for poor compensation might be "no worse" than blundering a three-move tactic or something, but the lowest difficulty-level AIs don't even recapture losing trades half the time, which... is just not human at all. Also, chess is just hard. lulz.

[@ramit7]

thank you for this trefor

[@guillemperdigooliveras5351]

I love everything about this video!

[@Scatter_Guy]

I love the topic and example! Thank you for the contribution! :)

[@lgl_137noname6]

6:30 Would it be safe to assume that "frequentists", in general , loath Schrödinger's cat thought experiment ?

[@DrTrefor]

Not necessarily. They might say that over a large number of trials, half the time there is a cat, and so the probability is 0.5.

[@lgl_137noname6]

@@DrTrefor Okay then. Where does Einstein's quote about God not playing dice put him in the classical/frequentist/bayesian spectrum ?

[@bomboid]

@@lgl_137noname6 He couldn't be bothered less

[@all_so_frivolous]

@@lgl_137noname6 Einstein’s quote is more about determinism which is compatible with both interpretations (I ignore classical since it’s mostly of historic value). However, i think Bayesian probability is much closer in spirit to this quote.

[@jeronimo196]

@@lgl_137noname6 this quote isn't about probabilities, it's an objection to the Classical Interpretation of Quantum Mechanics. Even if we live in a deterministic universe, we still need probabilities due to our limitations of knowledge and computing power.

[@Neweraa]

From Whole Newera Family, I really like your videos! Thanks, Newera

[@carlossegura403]

Frequentist probability is based on the long-run frequency of events observed in repeated trials. In contrast, Bayesian probability represents a subjective degree of belief, incorporating prior information and updating with new data.

[@OrcaChess]

Great explanations of the three statistical perspectives! Thank you for this fresh and hands-on video. Do you play 1.e4 or 1.d4?

[@DrTrefor]

e4! Lots of italians and alapin Sicilians

[@OrcaChess]

@@DrTrefor Classical Chess ♟- solid choice 👍🏼

[@daviddempsey8721]

Die: one die, 2 dice. DnD play uses 4,6,10,20 etc sided dice. One of the important parts of it is checking that dice are fair, as turns out many dice sets on the market are biased. We float them in saltwater and keep pushing them under to see what side shows up. It is a quick check if biased.

[@Nik-qh7cq]

There is 52!/(13!*39!) sets of 13 cards that can be chosen. If we calculate the probability of choosing a heart out of the remaining 39 cards for every set of 13 cards been taken and then combine these probabilities together can we calculate the probability of choosing a heart out of 49 cards in a classical way? So suppose A1 is a set of 13 cards, A2 another...and so on P(❤️) = P(A1 selected out of the deck) *P(❤️|A1 is selected) + P(A2 selected out of the deck) *P(❤️|A2 is selected)+....+P(An selected out of the deck) *P(❤️|An is selected), where n = 52!/(13!39!)

[@fturla___156]

Classical probability should always be modified by the increased frequency of what current and past outcomes have resulted because you are never given complete assurances that the data points and elements within a game environment have stayed the same. The trend is your friend until you sense something is different or changed then your reliance on past outcomes no longer applies.

[@griffinbur1118]

This mash-up is 🔥.

[@xiangzhang5717]

For the frequentist probability, I really like the way of presenting. But I am not sure if I agree with the shuffling part is only shuffling the selected cards. I think the process is 1. reshuffle the entire cards 2. draw the same number of the cards as the first time as the subsample 3. randomly draw a card from the subsample. 4. repeat 1000 times

[@RMOB362]

What is the difference between probability and statistics? Are frequentist and Bayesian statistics?

[@Lemaat2]

I believe there are five possibilities here that are inherent to the game of chess per se (considering an ideal situation where both players never fail and the rules of chess remain in its current standard). 1st it's the possibility that who starts (the white) has the victorious advantage, so the whites always win. The 2nd possibility is that the player who responds to the 1st move has a victorious advantage, so the blacks always win. The 3rd and 4th possibilities just add more depth to.the first two possibilities. The 3rd possibility is that who begins first is not influential to the victory, however as the distribution of the armies in the board is not perfectly simetrical, working as the reverse/mirror image of the other, the army whose pieces occupy that sector of the board where the respective king occupies the black house (the whites) always wins, regardless if the whites begin 1st or not. The 4th possibility is that the black army always wins because their pieces occupy houses with reverse colors to the white (the black king is in the white house), and that's the victorious advantage. And finally the order of who makes the 1st move, and the initial positions of the armies on the board have no influence in the outcome, and both armies are equally powerful, meaning that the chess game is no more than a hyper tic tac toe game, faded to stalemate unless one of the players fail. As the chess game is so complex we don't know if thr initial position of the pieces, or who makes the 1st move is influential or not to the victory, so we can't know (till now) if the chess game is the hyper tic tac toe game or not. Which leads us to another question, would be all known skill games hyper tic tac toe games whose winners are just harvesting the opponent's errors? That means in a skill game between same skill level opponents the real winner is the biorithm of the winner.

[@Lemaat2]

Exploiting more the 3rd and 4th possibilities, the whites would always win because their pieces are on the right sector of the board (their king in the white house) And they make the 1st move. Or, on the contrary, it's the blacks who always wins because their king is on the white house And they play after the whites.

[@seeker.8785]

Statistics do not tell us whether a thing will happen, they only tell us how frequently the thing would happen, given multiple trials. The proper use for this conceptual tool is to help ourselves decide how much to prepare for uncertain outcomes. If an outcome is likely, then you will, more often than not, be better off having prepared. If you prepare according to the likelihood of events, then you will waste less resources preparing for things that don't happen, and you will more often be prepared for what does end up happening. That is what statistics are useful for, and NOTHING ELSE.

[@PopeGoliath]

I was expecting this to dive deeper into how to measure probabilities at the edge of deterministic prediction. Maybe quantify why and how a slight edge in player skill effects the odds of winning.

[@DrTrefor]

I do think a follow up video that takes a slightly more sophisticated view than the intro to the basics I did here is probably due:D

[@PopeGoliath]

@@DrTrefor that would be great! Maybe dive into the "odds" chess engines give when evaluating boards, and how their certainty is calculated. Also how that can be applied to human players. The border between perfect information and probability is really hooking into my brain now.

[@HomeBologn]

Do more chess videos!!!!!!!!! I REPEAT DO. MORE. CHESS VIDEOS.

[@michaeltellurian825]

You and most of the commenters here don't understand chess. This has nothing to do with skill level. Steinitz, almost 200 years ago, discovered chess theory that holds true to this day. Lasker, elaborated on those ideas in 1906 in his book "Struggle" (English edition) and then expanded even further in 1913 with "Das Begreifren der Welt" (I think only the German edition exists) and later "Die Philosophie des Unvollendbar" in 1918. And then there is Game Theory, ..."the study of mathematical models of strategic interactions among RATIONAL agents", [wikipedia]. Random dealings of cards are nothing like rational agents. Chess has zero elements of chance.

[@Killua2001]

You're missing the point. Chess is a game of skill, but it's a game where the 'skill' is 'selecting from a uncountably (to a human, or even computer right now) large set of possible choices'. That 'skill' has a variance. How 'deeply' one person can see varies based on a whole host of conditions, humans aren't 'rational' agents. If they were, Nepo wouldn't have made that b5 pawn push with a tactic even I could see. And once we're talking about words like 'variance', probability comes naturally.

[@michaeltellurian825]

@@Killua2001 Texas Hold 'Em is also a game of skill...but with elements of chance, that is random distribution of cards AND partial indeterminacy, meaning some information is unknowable regardless of the intelligence of the agent (some cards are still in the deck and 2 cards for each player are known only to that player). In chess, the starting position is not random and is known by both players. Each move is known by both players. The game proceeds by reducing possible moves (legal moves) until the king of one of the players MUST move but has no legal move (checkmate). There is at no point an element of chance. Ignorance does not constitute chance. Faulty reasoning, and this applies to your comment about Nepo, does not constitute chance.

[@madg891015]

These are actually the frequentist and Bayesian approaches to STATISTICS. Probability has no paradigms, its approach is through measure theory and its foundations are well established, which by the way, entail the "frequentist approach to statistics" (e.g. Central Limit Theorem, Law of Large Numbers, Ergodic type Theorems).

[@karannchew2534]

What does this mean please??? 6:37 "They might think that they might tempt to explain the world by suggesting that it was a heart is something that, in a frequentist approach, if you did this trial many over would be a correct prediction about this objectively right answer one quarter of the time."???

[@Loots1]

E4, your move Doc!

[@DrTrefor]

You are getting some form of Sicilian!

[@Loots1]

@@DrTrefor look forward to it :)

[@merdishakki]

@KingZlatan ...d6

[@sayso2135]

@@merdishakki 3. d4

[@merdishakki]

@@sayso2135 cxd4

[@ETBrooD]

What distinguishes a better player from a worse one is of course their greater insight and intelligence, but that's not the whole story. Relentlessness and consistency are among the greatest predictors of success. That means even if you're technically more proficient than someone else, they can still outcompete you in the long run if they push themselves significantly harder. In a chess competition that's like turning a losing game into a win by continuously building threats, while the opponent ignores the problem until it's too late.

[@jeronimo196]

Your explanation of Bayes is terrible, if not wrong altogether. The point is not to update our belief B (card is hearts) to 100%. After seeing B (card is hearts), we update our belief in A (some hypothesis about the deck) to A|B - our belief in hypothesis A after seeing B. If A is "there are no hearts in the deck", seeing B disproves it. If A is "there are only hearts in the deck", B supports it - but B also supports "1/4 of the cards are hearts", etc. The Bayes theorem tells us exactly how much we should increase our confidence in hypothesis A after seeing evidence B. And the answer is (how much hypothesis A predicted B)*(how likely hypothesis A was) divided by (how likely B was in general). P(A|B) = P(B|A)*P(A) / P(B) If event B is predicted only by hypothesis A (novel prediction), seeing B is strong evidence for A. If B is predicted by many different hypotheses, seeing B is weak evidence for A and cannot be used to distinguish between hypotheses. If there are events B, not predicted by hypothesis A, A is falsifiable (there are no hearts in the deck, but then we draw a heart - A is wrong). If hypothesis A can explain every outcome we can think of, it can never be proven wrong, but it is also useless - it cannot restrict our expectations for the future. So, a Bayesian approach to chess would be saying the Spanish defense is a good strategy and playing a game (or 100) using it. If you win, you increase your confidence in the Spanish Defense, while acknowledging that maybe you lucked out and your opponent was weaker than you. It is said that all learning is Bayesian in nature. For the ones still reading - you might enjoy lesswrong.com - the blog community of Eliezer Yudkowsky, the guy who coined the phrase Friendly AI, among other things. You might enjoy "Harry Potter and the Methods of Rationality" ( hpmor.com ) even more.

[@uropinionistrash4461]

Thanks

[@cgoodm]

I feel like I just read this chapter in Nate Silver's book "The Signal and the Noise."

[@kylelee3043]

glad i came across this video, where did you get your chess set from if i may ask

[@gymnasiematematikmedigor5035]

Great video! As an experienced chess player, I can only say that when it comes to a game between two more or less equal opponents, then chess really feels like a game of chance :) Chance and psychology…

[@mexicano7926]

Bud, not evrything you read in he internet is true. There is NOTHING of chance in chess. If you train harder study more then you play better moves closer to what the engine would say if you dont you get destroyed. That you can try to predict something from the outside looking in does not make it a game of chance.

[@crimfan]

@@mexicano7926 How would you deal with the fact that human players are imperfect, for example suffering momentary and essentially unpredictable lapses in concentration that might induce them to make a mistake?

[@mexicano7926]

@@crimfan The better you are the more you calculate the better the results. How is that chance? Misstakes would be a random factor in a prediction model, same for any other sport or anything really. That doesnt mean football, soccer or any other thing is a game of chance. If i make my moves at random i am going to get smoked by anyone who has a working knowledge of the rules of chess. Simple as that. CHESS IS NOT A GAME OF CHANCE. The guy even if he has a doctorate has to make videos with interesting titles and does not value his content

[@crimfan]

@@mexicano7926 I think you are using "game of chance" in a very narrow way. I totally agree that chess is not a "game of chance" the way that, say, dice or roulette is. It's absolutely not that as it clearly features no randomizer. So if you're defining "game of chance" as requiring a randomizer, you're right. Thinking more broadly about what probability represents, though, there are a lot of elements that can be modeled or thought of as random variables, such as players' "trembling hands" or the cognitive limitations. And in that sense, a deterministic system can be modeled or understood as involving chance elements. Even a randomizer like a well-shaken die isn't really random the way that, say, Brownian motion or nuclear decay appears to be. It's subject to complicated equations of motion that are simply too difficult to figure out due to sensitivity of initial conditions.

[@ApiolJoe]

@@mexicano7926 The very best chess players in the world agree that there is chance involved in the game. There must be something up, you know? Maybe you play an opening and you run into a specific opening preparation by your opponent which makes the game way harder for you than him. You had no control over what his preparation was, and yet your chances of winning the game were impacted by this. No chance in the game? that's a hard thing to argue. Maybe you and your opponent are in a complicated position and both of you need to calculate a very long sequence. Sequence so long it's impossible or a human to have a perfect evaluation of the position. Say both you and your opponent calculate the line, and agree to play according to it. And then, it appears that 40 moves down the line there is a small tactical thing that was missed by both players and which gives a definite advantage to one of the two players. None of them had any control over this, and they both took their decisions based on the same assumptions and information. No chance involved in being one or the other player? Are you really ready to support the fact that one of the two players played better than the other even though they both had the same evaluation and agreed to the same sequence of moves as being best for both players? that's a very tough position to hold. Maybe you'll even disagree with that last part, but for your information, this is the argument that most very highly rated chess players use to describe why there is chance involved in playing a game of chess. And I think that they know better than us. The game doesn't involve throwing dices, but the game forces players to choose actions based on imperfect information because players never can have access to everything. In an ideal world where chess players are omniscient beings, there is no chance in playing a game of chess. However we live in reality, and in reality there is chance involved in the result of a game of chess. Also note that a game of dice also doesn't involve chance if omniscient beings play it, as omniscient players would have access to all the information about velocity, angular velocity...etc... of the dices and therefore would be able to calculate which number would come out. Conceptually (or abstractly), chess isn't different from a game where someone throws a die and both players have to tell which number will come out before the die hits the table. In reality, one of the two games is much more interesting and rewards skill much more, but that's it.

[@mdfakhrudin7039]

Sirr, when will the exam prep video come?

[@DrTrefor]

Tuesday!

[@mdfakhrudin7039]

@@DrTrefor thank you for that lie 😔

[@kck9542]

I also wanted to know the same.

[@lilggs4813]

10:21 That’s a very good point (and 10:55)

[@davidbellamy1388]

Chess is not a game of chance by strict standards. It is a finite state, deterministic, fully observable game. Every game of chess must have the same single outcome by perfect play on both sides - we just don’t know what that one outcome is because we can’t minimax optimize over the full game tree (too big like you said). But when it comes to imperfect players competing in chess, then sure, you can think about moves and game outcomes probabilistically. But it is important to note that the probabilistic aspect in chess only arises due to imperfect players on both sides. Tic-tac-toe is a good counter example when the game tree is not too large to minimax over.

[@robharwood3538]

"we just don’t know what that one outcome is" This is the fundamental difference between a Frequentist/Classical definition of 'probability' and a Bayesian definition of 'probability'. The Bayesian definition is *based* on what we 'know' or 'don't know', and it is actually a way of accurately *quantifying* that level of certainty or uncertainty in a way that is in accordance with the universally accepted laws of probability (all camps agree on the basic laws; it's the interpretation and application where they differ). If we "just don’t know" what the outcome of "perfect play on both sides" is, then there is a level of uncertainty (lack of knowledge) there. How do you quantify that? If your opponent is Magnus Carlsen, wouldn't you agree that you should adjust your estimation of your 'probability' of winning the game away from 50/50? In effect, it really doesn't *matter* what 'perfect play' would dictate (say for example that perfect play would lead white to always win, and you happen to be playing white), since you personally don't have that information available to you. All you can really reason about is what you 'know' and 'don't know' (including your level of certainty/uncertainty of that knowledge). The Bayesians simply say: That quantity, whatever it happens to be (and it is dependent on context and observer), *is* what is meant by 'probability'. To a Bayesian, virtually everything a person makes judgments about is a matter of probability, and so even the concept of 'perfect play' in chess could be considered still to have some level of uncertainty associated with it: I mean, how do you *know* that your 'perfect play' oracle is actually correct? Maybe it has a 'bug' in it. It's possible, right? Maybe Magnus has Perfect Play version 2.0 with the bug fixed, and he'll exploit the bug to win despite your (premature) confidence that you're making the perfect moves. 100% certainty is almost never justified. Hence even with 'perfect play', chess could still be considered a 'game of chance' (i.e. involving probabilities). And in any case, it turns out that *even absolute certainty,* such as in the ideal case of 100% pure logic, you can *still* treat 'true' as a probability value of exactly 1 and 'false' as a probability value of exactly 0, and Bayesian probability becomes Boolean logic in this special case. In other words, even pure logic can still be interpreted as Bayesian probabilities! So, 'technically', even 100% pure logic is still a 'game of chance'! Cheers! 😃

[@zak3744]

​@@robharwood3538 It seems to me that to characterise the Bayesian approach as dealing with levels of knowledge relies entirely on how you label things. And that the difference between the two approaches is therefore solely linguistic. Let's say you have drawn a card from a deck 9 times. Let's say you draw a card from the deck once more. You're trying to name a probability, whichever "school" you subscribe to. You could say: "I can calculate my best estimate of the probability in situation A (9 cards drawn). I can also calculate my best estimate of the probability in situation B (10 cards drawn). Each of these is a probability for a separate scenario. If I want to know something about this deck of cards then given the choice, I'll use the latter of the two parameters that I have access to that relate to this particular deck (the 10-card draw scenario rather than the 9-card draw one), since it's the more informative." Or you might say: "I am calculating one single thing about this deck, and I'll change, or 'update', that single parameter when I get more data. I can track my updating progresses and that tells me about my knowledge and confidence in this one single calculation and how it changes over time. But it remains the same calculation all throughout the process, honest. I just get a different number each time." Isn't that basically the distinction? Do you view the probability as one single entity (your personal knowledge of the probability) that changes throughout your life and "inherits" something from your previous guess as you include more data. Or each time you get new data, are you calculating a brand new probability for a new scenario (one that has more information than some previous separate but similar scenario you calculated once before). And when you want to know something about a thing in the world, you'll use the most informative of multiple discrete scenarios available to you that relate to that thing. Basically, as far as I understand it, a frequentist would say to a Bayesian: "No, you're not 'updating' one single calculation, you're doing a whole new calculation because you're considering a new scenario, with different data (however similar it may or may not be to some other calculations you've done in the past)." And apart from that, all the numbers come out the same whichever method you use. And in terms of the difference between the two that's ...it? A difference of linguistic definition? And one definition might be more aligned with the way people intuitively think in particular situations, but there isn't any more fundamental distinction between the two is there? Anything mathematical rather than simply linguistic? (I've tried to sit down and understand the Bayesian/frequentist fight on a few occasions, and every time I've come away being unable to see any difference beyond a difference in terminology. But people seem to get very heated about the whole thing, so I keep wondering if I've missed something more fundamental!)

[@sriramb5703]

@@zak3744 That's not even close to what the heart of the conflict is. In your example, everything is well understood and both camps will give the same answer. The differences really becomes clear when it comes to assigning probabilities to non-repeatable events, which frequentists think is meaningless.

[@robharwood3538]

@@zak3744 Hi Zak! Before I get into my reply, I should mention that I'm feeling a bit 'fuzzy' right now (not sure why), so I may not give as clearly-thought-out a reply as I would hope. Also, I'm going to try to 'simplify' the scenarios you laid out, in order to try to get at (what seems to be) your main question, which I interpret as, "What, if anything at all, is really at the heart of the Freq/Bayes disagreement?" "It seems to me that to characterise the Bayesian approach as dealing with levels of knowledge relies entirely on how you label things. And that the difference between the two approaches is therefore solely linguistic." Hehe, I have a hunch that you (perhaps without quite understanding why at the moment) are already more or less a Bayesian, in your interpretation of probability. (BTW, I'm not an expert Bayesian, but I've read quite a bit from some who are.) I believe that most Bayesians do indeed see the differences as largely (maybe not 'solely') linguistic, and that Bayesians are definitely 'concerned with' how one 'labels' things. Indeed, all of Frequentist statistics can be interpreted in a Bayesian framework. The reverse, however, is not true. When I was trying to understand the difference myself, I got a huge insight when I realized how much importance Bayesians put on Conditional Probability (i.e. expressions like this: P(A|B), read "the probability of A, given that we know/assume that B is true"), so that might be a key concept to pay close attention to as you explore the topic(s) further. Indeed, one Bayesian perspective is to *_start_* with conditional probability as the main quantity of interest, because everything that follows the conditional 'bar' (the '|' character) *should* ideally represent "all of the relevant assumptions that go into determining the 'probability' of whatever appears before the 'bar'". This is where there is a big gap between what a Frequentist will consider versus what a Bayesian will consider. From the perspective of a Bayesian, the Frequentist is 'leaving out' a lot of their implicit assumptions, not including them in 'the model'. From a Frequentist perspective, they believe that they have an _a priori_ 'objective' definition of 'probability', and thus they would 'disqualify' a lot of the things Bayesians consider 'probabilities' as valid 'probability' expressions in the first place. So, for example, a Frequentist might write, in English (or whatever natural language): "Assuming a biased coin with probability (long term frequency average) of heads, p, then let random variable X be the number of heads observed in n independent tosses of the coin. This is the definition of a Binomial distribution, Bin(n, p), and so the probability that we will observe k heads is therefore:" Now switching to math/probability 'language', they would write the 'probability' like so [NB: where nCk means 'n choose k', which is equal to the binomial coefficient for (n, k)]: "P(X=k) = nCk * p^k * (1-p)^(n-k)" A *_hardcore_* Bayesian might write (closer to the language of logic, defining logical propositions in terms of English): "Let C(p) be the logical propositional statement 'The coin has a probability, p, of landing heads on a single toss, independent of any other toss'. Let T(n) be the proposition 'The coin is tossed n times'. Let VarX(n, p) be the proposition 'X is a random variable representing the number of heads observed in n tosses of a coin with probability p'. Let BinVar(X, n, p) be the proposition 'Variable X is distributed according to the Binomial distribution, Bin(n, p) = nCk * p^k * (1-p)^(n-k)'. Finally, let M (for 'model') be the logical conjunction, 'C(p) and T(n) and VarX(n, p) and BinVar(X, n, p)'. Therefore, the probability we will observe k heads is:" Now switching to math/probability 'language': "P(X=k | M) = nCk * p^k * (1-p)^(n-k)" They look quite similar, right? "P(X=k) = nCk * p^k * (1-p)^(n-k)" vs. "P(X=k | M) = nCk * p^k * (1-p)^(n-k)" But you can see that the Bayesian has added "| M", meaning "given that we know/assume that M (the 'model') is true". In other words, the Bayesian has spelled out all of their assumptions explicitly, their entire probabilistic model. The Frequentist wouldn't 'see' that they are making exactly the same assumptions, because they don't *have* a complete 'model': They are implicitly *assuming* that 'probability' means "long term frequency average". The Bayesian is not assuming that! The Bayesian only assumes that 'probability' is a number between 0

[@bunkerputt]

Chess is not a game of probabilities. Playing lots of chess games is though. When we say we have "winning chances", we mean the opponents position is hard to play for a human and he might mess up.

[@crimfan]

Once again, nice video. I often think about probability in an information-theoretic or even game-theoretic sense, where we have uncertainty of different forms. In the case of a game like chess, there is a lot of strategic uncertainty and probability essentially induced by combinatorial explosion and the players' "trembling hands". We can understand it probabilisitcally, but can't actually understand it deterministically, even if, in principle, it could be. One thing I always emphasized with students is that probability is about information, and we can have markedly different information states. It's very Bayesian to say that probability depends on our state of knowledge, for example a coin flipped behind a screen. For a hardcore frequentist the coin has been flipped and isn't random anymore. For a Bayesian still on the other side of the screen, the information set still makes it random until the screen is removed. Frequentism isn't dead, though: It's very hard to think of concepts such as a biased estimator in a Bayesian manner, but having seriously biased estimators is very bad for a Bayesian hierarchical model or meta-analysis, where many estimates are pooled and bias can, therefore, accumulate. You're 100% right about the fact that we as humans like to minimize luck. As an example, genetics are probabilistic and influence our lives massively. We literally had nothing to do with the genes we inherit. Kathryn Paige Harden's book The Genetic Lottery discusses this quite a bit.

[@FranFerioli]

I was so hoping that you would do a magic trick in the video!

[@johnsavard7583]

I think I'd begin a discussion of this issue with describing the game rock-paper-scissors, to explain how chance could enter a game like Chess.

[@wesleywashington4568]

Dude I've been thinking this too

[@bmmmburns]

Dr. Bazett, I think probability i.e., luck had everything to do with the discovery of the MRB constant.

[@brockobama257]

There’s a chance that someone plays a REALLY bad move or misses a REALLY good move. The distribution, over all your moves, of your chosen move relative to the best move, is a normal distribution. An average player will most often choose a move that isn’t the best, but is not detrimental. The distribution skews toward the lower or latter ends dependent on skill level. That’s speculation but I’m pretty sure it’s true and I’d bet it’s a normal distribution because of the central limit theorem.

[@letsmakeit110]

I think you want a binomial distribution. In 32-piece tablebase land there's only accurate moves and blunders, and a player will pick from either pool with a probability corresponding to their rating.

[@vasanthraj5572]

thanks sir.

[@tomas387]

'Chess,' said the Dutch grandmaster, Jan Hein Donner, 'is as much a game of chance as blackjack; or tossing cards into a top hat.' There was a pained silence, then a polite babel of disagreement: it was a game of the utmost skill; a conflict between disciplined minds in which victory would inexorably go to the more perceptive, the more analytical player; a duel of the intellect in which luck played no part. Donner shrugged, lit another cigarette and said: 'Believe that if you like.' Bent Larsen smiled the smile of a man who had heard his friend air such iconoclastic arguments in the past but was quite happy to contest them again, when the score of the fifth game of the World Championship match between Karpov and Korchnoi was brought in. Both men pulled out of their inside pockets the wallet sets all grandmasters seem to carry at all times and began to skim through the moves. It happened that the teleprinter tape had been torn off after Karpov's 54th move as Black [...]. They studied the position for a few moments, mated Karpov in four moves and were surprised when another whole sheet of moves was brought from the teleprinter. When they saw Korchnoi's 55th move - Be4+ - Larsen's eyebrows went up. 'There you are,' Donner said, quietly and without triumph as though some self-evident truth had been revealed, 'pure luck'.

[@ac4740]

I don't see how classical probability fails to analyze the situation where we've removed N cards from the deck. Can't we just construct the set of all decks with N cards removed, and calculate the number of possible scenarios where we flip one card from the 52-N cards, and then count the number of situations where that card is a heart, and divide as usual?

[@owensthethird]

The myth of meritocracy is more like a legend-- effort and ability play a major role, but somewhere down the line we forgot that randomness/chance/probability play a lesser, yet ever present role in outcome. I believe societies benefit from pushing the "bound of rationality" for individuals, allowing those willing to see further into their potential future.

[@steelmongoose4956]

The idea of meritocracy isn’t a measurement of potential, effort, or even personal virtue-it’s a measure of result toward an intended goal. Meritocracy doesn’t concern itself so much with *why* a person can accomplish something as the simple fact that it was accomplished. The problem with attempting to govern a society under such a model is that those is power may tend to value maintaining their own power, wealth, and status, rather than the original perceived goal for society. In that case, the results that maintain someone’s political career may be those that maximize power for politicians at the expense of the people they rule. It could still be a meritocracy, but not the one the people thought they were getting. In the United States, there don’t appear to be any multi-term legislators whose personal wealth doesn’t increase considerably faster than their salary would seem to allow. Many who want to claim accomplishments “for the people” are doing very well for themselves, while “the people” are simply suffering through problems largely caused by problems that the government purports to solve in some self-serving way. It’s a sort of meritocracy, but only for those in the club.

[@Archonsx]

somehow you both managed to write so many words yet say nothing of value

[@jaybingham3711]

One's effort and ability are hugely a factor of luck. Having no role in your genetics or manner of upbringing, it's not hard to imagine the results of only making a few tweaks.

[@Primitarian]

The more I have succeeded the more I have realized that luck is a huge factor. That having been said, I would also say meritocracy has points in its favor, just as classicist probability does. So we should continue to pursue meritocracy, but we should also admit to ourselves that it is often not attained and even unattainable.

[@gowrissshanker9109]

Respect sir ,how to visualise inner product of complex vector space?

[@stevo-dx5rr]

My initial reaction to this video is that it's a bait-and-switch. "Is chess a game of chance?" No...It's absolutely a game of perfect information, and I don't see why it matters that the state-space is unfathomably large for a human to grasp. The reason I say it's a bait-and-switch is that I think the Dr. is actually asking a different question: "When humans play chess, are outcomes probabilistic?". To this, I 100% agree; that's why we still play it. It's a skill based game, but given two similarly rated opponents, anyone can win. That's why chess tournaments aren't settled with a best-of-one format. Philosophically, we can toy with the idea that game of chess is probabilistic because the state space is, at least for now, incalculably large, and therefore we humans that play it have no choice but to imitate a random walk through that state space. However, I don't see it as a particularly fruitful line of thought.

[@DrTrefor]

You are right I mean it as a bait and switch, but I think somewhat differently than you suggest. My real goal is to think, what exactly is probability? And I think whether chess is considered probabilistic or not depends on the exact way you view what probability means. Under the classical approach you are using, then no, but that isn't the only approach.

[@santiagoacosta6614]

Why is "game of skill" contrasted with "game of chance"? A game can clearly be both at the same time.

[@stevo-dx5rr]

@@santiagoacosta6614 The reason it is being discussed this way in the video is because chess is classically thought of purely as a game of “perfect information” (in a sense, all skill, no luck).

[@androkguz]

5:48 "The point here is that it's subjective" No, I think you are wrong. The word you are looking for is "relative" not "subjective" For instance, position and distance are relative to the frame of reference, but they are not subjective. There's no opinion.

[@benjaminshropshire2900]

If you don't like the Bayesian saying the probability of something depends on who you are and what you know, would it also be correct to frame it as "in situations like this, where I know what I know now, I expect this guess to be correct X% of the time"?

[@benjaminshropshire2900]

@Johann Sebastian Bach sure you can. You just need to invent interstellar travel and fin another star to spend a century or so explaining. 😁 The "other" cases can be hypothetical.

[@benjaminshropshire2900]

@Johann Sebastian Bach what meaningful difference is there between the one off case and a set of cases in different locations that each have the same evidence? The fact that one is concrete and the other hypothetical doesn't change anything about that statement that I care about. Talking about "if I were to encounter multiple situations" can be meaningful even if you have only so far encountered one.

[@benjaminshropshire2900]

@Johann Sebastian Bach But historical situations, by their nature, are also not hypothetical. As soon as you exclude the hypothetical, you are no longer able to address my argument because my argument take the hypothetical as axiomatic. I'm not asking for someone to consider the cases that do exist, but those that hypothetically *could* exist. -- Or to argue the point from another direction: what prevents a future World War N (and O, P and Q) from happening where all the attributes under consideration are the same as WW2? Include the infinity of space and time and you can't even say that hasn't already happened. In either case, your argument falls apart: if another example has or will happen (we just don't know about it yet) then there is the *possibility* of multiple observations, and considering that possibility is functionally the same thing as considering hypothetical examples without even bothering to assume they actual exits. The whole point is *presuming* the "if" is true, not that it actually *is* true.

[@benjaminshropshire2900]

@Johann Sebastian Bach I very carefully did NOT say "identical in all ways" but rather said the much weaker "all the attributes under consideration are the same". As long as the set of those attributes under consideration is finite, then they can be matched. -- Furthermore, given the whole point is the hypothetical, the only requirement for my argument is that such a war be *possible*. It being extremely *improbable* is not a problem. (If you don't mind dragging cosmology in, there is even an argument that an /exact/ match is not only possible but, given an infinite universe, inevitable. But that's at most tangentially relevant, and I'm not sure I buy it anyway, so I'll not press that point.)

[@benjaminshropshire2900]

@Johann Sebastian Bach If you want to craft the attributes under consideration with the specific intent of limiting it to a a single event, why be so subtle? Make the only attribute under consideration be that it's the singular even you want to limit to! Problem solved. (And that would also exclude an identical even happening simultaneously somewhere else in the universe.) Can you craft the question so that there is and can only be one event, that's already happened, that can be talked about? Sure, I won't even try to refute that. But with that sort of constraint restricting you to know historic events, the "knowing what I know now" from my original comment devolves to perfect knowledge, to factual statements rather than a probabilistic ones: "In the 1 of 1 cases where we know Germany lost WW2, what's the odds Germany will lose WW2?" Is that a pointless question? Sure, clearly it is. But I'm not, and never was, trying to talk about that sort of question. On the other hand, the kind of questions I am talking about, what I started this thread talking about, are the cases where the explicitly enumerated knowledge under consideration can be matched by more than one real or hypothetical event. And I think that covers most cases that people actually care about. If you want to talk about other questions than you are more then welcome to start your own thread, but this thread isn't about that.

[@itchykami]

I guess arguing bad luck is a way to rationalize consistent failure.

[@bradkevin6594]

Sir , please explain dynamic systems

[@Hakabas01]

Your Win/Lose rate might be almost 50/50 but that is not true with my winrate (13% more wins tha losses) and there are way more extreme examples. People with 2 to 1 win to loss rates etc.

[@DrTrefor]

I’m curious how that works in the long long run. As in, with a higher than 50 win rate, don’t you just raise elo until you are close to even? I feel for players with less games that have risen quickly in elo a big spread is possible

[@cu7695]

I knew I was Bayesian before this video

[@bhaveshsonalkar]

Wonderful

[@birdthompson]

just went 1-3 in a chess tournament, losing to lower rateds...elo onward!!!

[@inthebackwiththerabbish]

good ol’ chess, it’s a game of chess

[@mentilsoup]

but the board doesn't contain all the information in the system?

[@DrTrefor]

perhaps if you could calculate it all then yes

[@jon9103]

I suspect that more skilled chess players will more accurately predict the odds of success of each move even if they don't explicitly think in terms of probability.

[@afrye51]

And this is a large part of what makes chess interesting. If every chess game was the same, no one would play it. I'm often reminded of the futurama scene where two robots are playing, and on the first move one says to the other "mate in 143 moves", and his opponent gives up: kzbin.info/www/bejne/jqXKi36tgJt2abc.

[@vwlh8r]

High probability this man has done magic tricks before, or worked in Vegas. I lean toward magic.

[@vwlh8r]

I wrote before I finished the video. 🤦‍♂️

[@elltwo8393]

Some topics about probability and chess that could be interesting to cover in a video format would be random walks on a chessboard (of various sizes, maybe even an infinite grid). Both the king and the knight random walks have some interesting properties (what is the chance that a king returns to its original starting spot? If it does, what is the expected number of moves to do so? And similarly for the knight, though that is much harder). It could be neat to have some nice visualizations or animations of these kinds of walks.

[@jackhales6179]

Cool idea mate, I wrote up a sample for the king idea, but quickly noticed it had to be bounded by either a grid, or a max iteration for the sake of time. The king is possible for an infinite grid since the moves are static (+1/-1 for one coordinate) but like you said, knight would be hard (impossible? for the future to decide) on an infinite grid since picking a random number from 1->inf is... rough. Below are numbers for the king, on a couple different max iterations! My average result on the king moving home in under 10,000 moves with 100,000 samples was: 352.75 moves. From a much lower 1,000 samples it was 312.46 moves. When testing with a restricted 5,000 max moves on 100,000 samples, the average king move count to return home is: 207.02. So it becomes pretty fair that the average moves is based on "how much" of infinite you want to grant to the king... pretty cool thought. One single sample path could get so lost in the oblivious aether that it never returns home, or takes 1,000,000,000 iterations to return, of which you will blow out the average completely. Median would be better to measure. Can view the code I used at github.com/halesyy/probability-scmobability/blob/main/fun-simulations/ell-two-king-walk.py

[@thomaskember4628]

How can he play chess without the pawns? Tartakover used to say "I have never beaten a wholly well opponent". Does that mean his chances of winning were in part dependent on the probable state of health of his opponent?

[@louisvuittondonvg9040]

of coursethis is the case with every activity in which humans engage in ever. if I'm a three point shooter and am in a first to 10 3 point contest with another 3 point shooter with the exact same FG % as me, whoever wins is chance. its 50-50. that's the very definition of "opponent of equal skill" otherwise it'd be 60-40.

[@pedroteran5885]

I appreciate the positive aspects of the video but at one point it conflates 'Bayesian' and 'subjective', and it strongly implies that frequentists somehow reject the Bayes theorem.

[@themowgli123]

Feynman's path integrals

[@greccioporras]

5:09 But... you actually can Dr. Strange

[@epgui]

Easy, TSLA only goes up!