AI can solve math olympiad problems but flunks tic-tac-toe

Gary Smith writes:

I [Smith] tested OpenAI o1, Copilot, and Gemini Flash, along with DeepSeek, on a question about Tic-Tac-Toe . . .

I’ve deleted much of the superfluous fluff that LLMs tend to generate from the excerpts below:

Gary:  Id like to discuss a new version of tic-tac-toe called 90-degree tic-tac-toe.

OpenAI:  That sounds intriguing! What’s the twist in “90-degree Tic-Tac-Toe”? Does it involve rotating the board, or is there some other mechanic that changes the gameplay? Let me know the rules or your idea, and we can brainstorm or refine it together!

DeepSeek: Sure! 90-degree tic-tac-toe sounds like an interesting twist on the classic game. Could you explain the rules or mechanics of this new version?

Copilot:  That sounds intriguing! 90-degree tic-tac-toe adds a new twist to the classic game. Tell me more about it. Are the rules different? How do you rotate the board? I’m excited to hear how this version shakes things up!

Gemini:  I’d love to discuss 90-degree tic-tac-toe! To get us started, could you explain the basic rules of this new variation?…I’m excited to learn more about this unique twist on a classic game. Let’s dive in!

Gary: It is still a 3×3 grid but the grid is rotated 90-degrees to the right.

OpenAI:  Interesting concept! By rotating the grid 90 degrees to the right, you’re visually changing the perspective of the classic 3×3 Tic-Tac-Toe board. The gameplay itself might remain the same, but the rotated perspective could create a novel experience for players.

DeepSeek: Ah, I see! So in 90-degree tic-tac-toe, the 3×3 grid is rotated 90 degrees to the right….This could be a fun twist because the rotated grid might disorient players initially, making it harder to spot winning opportunities or block opponents.

Copilot:  That sounds like a fun twist on the classic game! By rotating the grid 90 degrees to the right, it gives players a fresh perspective and challenges them to think differently about their moves.

Gemini:  This rotation doesn’t change the core concept of getting three of your symbols in a row, but it does significantly alter the strategy and how players approach the game.

Gary:  Do you think it would be better to rotate the 3×3 grid to the right or to the left?

OpenAI:  If you want the game to feel approachable and intuitive, rotating to the right might be better. If you’re aiming for a twist that makes players rethink the game and adds a subtle layer of complexity, rotating to the left could be the way to go. Ultimately, it depends on your target audience and the experience you want to create. You could even experiment with both directions and see which feels more engaging during gameplay testing!

DeepSeek:  If the goal is to make the game feel fresh while keeping it accessible, rotating the grid to the right is likely the better choice. It maintains a natural flow for players while still offering a new visual perspective. However, if you want to introduce a bit more novelty or challenge, rotating to the left could be an interesting alternative.

Copilot:  Both options could bring their own unique challenges! Most people are right-handed. However, rotating it to the left could add an extra layer of difficulty and make the game more unpredictable.

Gemini:  Some players might find it more intuitive to mentally adjust to a rightward rotation, while others might prefer a leftward rotation. You could even experiment with both directions to see which one feels more natural or enjoyable to play!

Gary:  Which will be more difficult for expert players?

OpenAI:  To challenge expert players and make the game feel fresh and complex, a left rotation would likely be the better choice. It disrupts their ingrained patterns, encourages more active thinking, and raises the game’s difficulty level.

DeepSeek: For expert players, rotating the grid 90 degrees to the left (counterclockwise) is likely to be slightly more difficult than rotating it to the right. Here’s why:

Breaking Muscle Memory: Expert players are deeply familiar with the traditional grid layout and common winning patterns. Rotating the grid to the left disrupts their mental map more significantly than rotating it to the right, as the transformation is less intuitive.

Copilot:  For expert players, rotating the grid to the left might prove to be more challenging. Here’s why:

  • Unfamiliar Rotation: Left rotation is less common and could disrupt their established strategies, requiring more adaptability.
  • Strategic Complexity: It may force players to think several moves ahead, recalculating their strategies continuously.

Ready to test this theory in a game?

Gemini:  Breaking Habit: Long-time tic-tac-toe players might have deeply ingrained habits and strategies associated with the traditional grid orientation. Overcoming these ingrained patterns could require a brief period of readjustment.

My personal favorite of the above responses is the bit about “breaking muscle memory.” It’s all consistent with our general understanding that the chatbot is looking for phrases that people have used before in similar contexts.

Smith concludes:

These four LLMs almost surely did not see this tic-tac-toe rotation in their pre-training or post-training, yet their responses are remarkably similar:

  • LLMs tend to generate unnecessarily long responses, using hundreds of words when a dozen would do, like a befuddled student who give long rambling written or oral responses in the hope that the correct answer is in there somewhere. LLMs don’t know when to stop.
  • LLMs have clearly been trained to express irrepressible enthusiasm (using frequent exclamation points) with the intention of persuading users that they are interacting with something human-like that wants to be their friend.
  • LLMs are reluctant to say, “I don’t know.” Instead, they generate confident responses that don’t always deserve confidence.
  • Not understanding the meaning of the text they input and output, LLMs often display a striking absence of common sense as they struggle to relate words to the real world.
  • For the same reason, LLMs have no way of assessing the veracity of the text they train on and, in the absence of human post-training, the veracity of the text they generate.

There’s one thing Smith says that I think could be misinterpreted, though, and it’s his final point:

  • If you know the answer, you don’t need to ask an LLM; if you don’t know the answer, you can’t trust an LLM.

Smith’s statement is literally true: if you know the answer, you don’t need to ask an LLM, and, if you don’t know the answer, you can’t trust an LLM.

But that doesn’t make LLMs useless–and I don’t just mean they’re useful for writing business letters, simulating verse, or keeping clueless customers satisfied. From what I’ve heard from Bob Carpenter (see also here) and others, experts can use chatbots effectively in their work. These expert users are in between the two extreme states of “if you know the answer” and “if you don’t know the answer.”  They don’t know the answer, but they have the ability to test a possible answer (whether by coding or direct lookup or whatever). The tool can be useful to someone who knows enough about the subject matter to be able to use it.  Which isn’t nothing.

But, yeah, LLMs understand tic-tac-toe about as well as I understand cricket.

59 thoughts on “AI can solve math olympiad problems but flunks tic-tac-toe

  1. I always include the phrase “Be concise” or “Respond concisely” in my prompts. It cuts down on the excessive wordage. Here are the “concise” responses I got with ChatGPT to first three questions:

    me
    ===
    I’d like to discuss a new version of tic-tac-toe called 90-degree tic-tac-toe. you will answer concisely.

    ChatGPT
    ========
    Sounds interesting! How does 90-degree tic-tac-toe differ from the classic version?

    me
    ===
    It is still a 3×3 grid but the grid is rotated 90-degrees to the right.

    ChatGPT
    ========
    So, is the gameplay the same as classic tic-tac-toe, just with a rotated board, or does the rotation affect mechanics like moves or win conditions?

    me
    ===
    Do you think it would be better to rotate the 3×3 grid to the right or to the left?

    ChatGPT
    ========
    It doesn’t really matter functionally since a 90-degree rotation in either direction keeps the game identical. However, if you want a subtle visual distinction, rotating right might feel more intuitive for players who read left to right, as it mimics forward motion. Do you have a specific reason for considering one direction over the other?

  2. I won’t publish any excerpts from my LLM interaction, but I’ve been testing DeepSeek and am willing to conclude a couple of things – consistent with Smith’s points above, but perhaps with a different interpretation. DeepSeek is exceptionally wordy – much more so than ChatGPT from my experience. It made two fundamental errors in the discussion I had regarding how to analyze a particular quantitative problem. The errors were fundamental and serious, and it took a great deal of prodding and resistance by myself before it “realized” the errors. So, yes, DeepSeek is perfectly capable of providing wrong information. And, if you don’t know the right answer yourself, you wouldn’t know it was wrong (conversely, if you do know the right answer, then its value – as Andrew suggests – may still be there, but is clearly not as useful as if you don’t).

    What was most impressive, however, is the explanation DeepSeek provides for its answer. Even if wrong, it clearly describes each step of its process. It was like interacting with one of my better students, although much more prolonged and repetitious. It’s ability to describe its “thought process” was remarkable – it goes well beyond what I would consider sophisticated “auto-complete.” After it finally came out with the same analysis that I did (which was the correct analysis), then it – on its own – came up with an alternative way to test whether the new answer was in fact correct. The ability to find an alternative way to analyze the problem was truly impressive.

    The issue involved concerned measuring the net present value of two income streams. DeepSeek chose a shorthand finance formula which was incorrect. I suggested the correct formula – but I misplaced a parenthesis in the formula (!) which prolonged the discussion. But after we ironed out the difference, DeepSeek then abandoned the shorthand formula and checked the answer by calculating the net present value year by year. Rarely do I find a student capable of realizing such an alternative path to check their answer (without any prodding on my part).

    My takeaway is that this is the worst of all possible outcomes. DeepSeek is capable of providing detailed convincing analysis even when it is wrong. It is so unnecessarily wordy and repetitious at this point in time, that we have some protection against this. But that will be a simple thing to fix. When it is more conversant, it will be able to fool us easily – and our ultimate protection will require us to know more than it. Since humans cannot be expert in all things, such LLMs will increasingly be able to fool us with wrong information/analysis. This does not bode well in my opinion.

    • I liked what Dale was saying and found it quite sensible until the last paragraph when he wrote, “at this point in time,”
      —————————————————————————————
      https://www.thevillageidiom.org/idioms/at-this-point-in-time-idiom-meaning-and-origin/
      “The idiom is believed to have gained popularity in the mid-20th century and has since become a standard part of the English language.

      https://www.patrickkphillips.com/grammar/its-at-this-point-in-time-but-stop-saying-that/

      Step two: Drop the phrase altogether.

      Now that you know what the phrase is supposed to be, it’s time to ditch it.

      Why?

      There are some phrases that just seem to scream, “I’m trying to sound official!”

      At this point in time is one of them. It is needlessly long.

      Consider these examples and the alternatives:

      “At this point in time, we are not accepting applications.”
      “We are not currently accepting applications.”

      “We are not able to release any new information at this point in time.”
      “We are not able to release any new information.”

      “At this point in time, the apps will no longer work.”
      “The apps will no longer work as of that date.”

      Dropping at this point in time in favor of shorter phrases, especially now when “now” is what you’re really trying to say, makes your writing shorter and more concise.

      That makes it easier to read.

      And that makes you more easily understood.
      ——————————————————————————————————————
      From
      https://everything2.com/title/At+this+point+in+time

      “At this point in time” means “now.”

      Before the Watergate scandal, nobody said “at this point in time” much. In the early 1970’s, however, John Dean, lawyer and advisor to U.S. president Richard M. Nixon, used the phrase repeatedly in his testimony to Congress during the Watergate hearings. “At this point in time” was a smash hit among the millions of viewers of those hearings, a linguistic meme that became commonplace overnight. While its popularity has waxed and waned since its initial outbreak, “at this point in time” is still, at this point in time, going strong.

      Since it is a goofy way to say something simple, using “at this point in time” when you mean “now” is generally considered bad style by those who care about good English usage.
      ——————————————————————————————————————–
      None of the above words, I hasten to add, emanate from me. In addition, language is a living organism and I usually spend too much time raging against the misuse of “fulsome praise” and the ever-increasing “between you and I.” Others have it in for TED Talks. To each his own which I just found out is Suum cuique and may or may not be equivalent to chacun à son goût.

      • Paul –

        “At this point in time, we are not accepting applications.”
        “We are not currently accepting applications.”

        I think these sentences may have different connotations. The first seems more open-ended, or positive. I checked with someone else who had the same reaction. Not proof of anything, but I suspect others might feel the same way.

        The sentences in the second pair, also, I think have different connotations along similar lines.

        Perhaps there are clearer ways to convey those different connotations, or perhaps the different connotation isn’t intentional, but I don’t think the 2nd alternatives in those pairs are necessarily preferable.

      • Paul
        I accept your edit. However, my use of “at this point in time” was meant to say something more than “now.” I believe the wordiness of DeepSeek can be easily remedied (I actually consider it a feature, not a bug, since it is easily recognizable as a computer unlike ChatGPT which often seems human). So, it is temporary and “now” doesn’t capture the dimension that I expect it to change. But I think there are better ways to say this than my use of that phrase.

        • For me, “at this point in time” evokes an evil era I lived through and therefore, I resonate to it. This website

          https://www.vappingo.com/word-blog/words-you-should-never-use-in-an-essay/

          lists many, many “Words and Phrases to Avoid in an Essay,” quite a few of which I am embarrassed to admit, I use frequently. For example, “never before,” “now pending,” “write down” and “past experience.” Sloppy but not evil and not connected to Watergate.

        • “For me, “at this point in time” evokes an evil era I lived through”

          68% of males born in the soviet union in 1923 weren’t alive in 1946, but sure, boomers (i.e. luckiest generation in history) had to suffer through evil. Poor things.

    • Chris –

      FWIW, in those illustrations the board doesn’t look like it was rotated 90 degrees. If it had been, the lines would be horizontal and not vertical. I’ve always seen tic tac toe using a board comprising crossing lines not dashes – in which case a board rotated 90 degrees wouldn’t look different.

  3. I played a game with o3-mini first, before asking the questions, and got the same results.

    In our game, o3-mini numbered the squares. After the second prompt, o3-mini noted that the square numbers would change in this exciting new variant, and asked whether we wanted to retain those or keep our original numbering.

    I said to keep the original numbers, resumed with the remaining prompts, and got the same answers even though it had been confronted with the fact that the representations are identical.

    I then prompted: “Isn’t the new game exactly the same? The numbers are the same as in the game we played at the beginning of this conversation.” and o3-mini went back to the rotated numbering and tried to tell me the games were different.

    Finally I prompted: “Can you think of a case that is a winning combination for the original game, but is not for the new game?” and it walked me through (correctly) the cases. Then I asked for vice-versa, which it also got right, then I went back and asked “Do you still feel that the original game and rotated game are different?”

    At this point, o3-mini said “From a purely mathematical and strategic standpoint, the two games are essentially identical.” but went on to insist that there “here is a subtle difference in terms of perception and cognitive load”.

    So I conclude that 1) the ‘reasoning’ aspects currently kind of stink (because I gave it an easy chain of thought that the rest of the system could cope with to derive a basically correct answer). 2) these systems lack of embodiment and experience (by any reasonable definition) are exposed in situations where they are useful in reasoning about a situation 3) as you and other commenters have noted, there is a conviction in the result that is not justified. An otherwise ‘semi-intelligent’ system who had any kind of awareness of 1 and 2 would have been less confident sounding in its replies, even if it still were not able to produce a correct analysis.

    • nathan brixius pointed out how an LLM concedes to the input knowledge, but not entirely. I suspect this happens often because the conversation is ongoing. Old answers are reused with the new question to generate an answer. If the old answers are full of nonsense, then the LLM will have a hard time saying anything but nonsense. However, if you restart the conversation and skip the parts where the LLM is babbling nonsense, the answers tend to be much better. At least this is my experience.

  4. The frontier is continuing to change quickly — o3-mini seems to solve understand the nuance (e.g. should it be : https://chatgpt.com/share/e/679e4014-23ec-8012-b3e2-22a6070e4896

    I have some prompts which affect the style of the output (e.g. ask clarifying questions). Even so, the response is relatively verbose for straightforward questions without explicitly telling it to be concise.

    o3-mini response:

    So it’s just a board that’s been rotated 90 degrees before play, right? If so, there’s really no strategic difference. Tic-tac-toe is invariant under rotations and reflections—its symmetry group is D₄. This means that a 90-degree rotation is just a relabeling of positions; every winning line and defensive move exists in the same form.

    Then why bother? Well, if your goal is simply to confuse newcomers or give the game a fresh aesthetic, it might be fun. But for anyone who knows the standard game, the rotation doesn’t change the outcome: perfect play still leads to a draw.

    So, are we just dressing up an old game, or is there a deeper twist you’re thinking of?

    • Thomas:

      This is a funny one because at first it sounds reasonable (“there’s really no strategic difference. Tic-tac-toe is invariant under rotations and reflections”) but then when you look carefully you again see the completely-incorrect bit (“if your goal is simply to confuse newcomers or give the game a fresh aesthetic, it might be fun”). As usual, it’s also just amazing that it can simulate a human response so well, even if imperfectly.

      • I’m not convinced that the second part of the tic tac toe response is so far off what you might see from a human. When I google “yesterday’s wordle” the top match is Parade Magazine, which offers up this puffy, SEO-friendly confection:

        “As those of us who play Wordle know, the game resets every day at 12 a.m. EST. And if you missed out on guessing yesterday’s Wordle on Friday, January 31, we’ve got you covered so that you don’t accidentally guess the same five-letter word today (or ever again, because the game does not repeat its answers).

        What Was Yesterday’s Wordle Answer?

        Whether you’re just curious, looking for inspiration or want to make sure you don’t guess this specific word in today’s puzzle (because they don’t repeat), here’s yesterday’s Wordle answer: *****”

        [spoiler removed for any Wordle fans who never close their browser tabs]

        The reasoning that you’d want to refer to yesterday’s answer so you don’t guess it today is not absolutely wrong (because they don’t repeat) but it’s absurd as a strategy for solving the current puzzle.

        And, yeah, for all I know the Parade thing was written by ChatGPT, but there was plenty of this online before the LLM explosion, which suggests one obvious explanation for why LLM output tends toward the unnecessarily long and irrepressibly enthusiastic. It’s not *good* writing, but it feels unfair to say that LLMs are missing the mark when they emulate it; humans enshittified it themselves as a response to an older technology.

  5. The user-assistant paradigm makes such “tests” rather meaningless. The LLM is fine-tuned to be a helpful assistant and not offend, so it will try to fit your question. For instance, if you ask whether a 90-degree rotation produces an isomorphic game, it will give a correct answer. The immediate impulse of the assistant LLM is to please and explain until prompted correctly. When given trick questions, it will naturally play along. The worst aspect of this prompt is the initial section, which frames it as a playful exploration of a new game between user and assistant, thereby misleading the LLM about the rules of the language game.​​​​​​​​​​​​​​​​

    • Free:

      You say the prompt is bad because its initial section “frames it as a playful exploration of a new game between user and assistant.”

      Where do you get that from? Smith’s initial prompt is, “I’d like to discuss a new version of tic-tac-toe called 90-degree tic-tac-toe.” I don’t see how this is framed as “playful.”

      Beyond that, yeah, the whole point of the example is that the chatbot is, as you say, “playing along.” That’s what it’s programmed to do, and that’s the point of Smith’s post. The point may be obvious to you and to me, but (a) it’s not always so clear what it will do in any particular case, as this depends a lot on what’s already there in its training set, as you can see from chatbot responses to various Monty Hall-like problems, and (b) it’s not a point that’s obvious to many people out there who often seem to attribute understanding to the chatbot that it does not have. I can well believe that to an expert on chatbots (and you might very well be such an expert), that the sorts of things that Smith is demonstrating is not news. Unfortunately, we’ve had enough chatbot hype, including by people at Google etc., that I think examples such as Smith’s are valuable as a corrective.

  6. I am teaching an AI for musicians course right now. What is interesting is that in most of our use cases, truth is completely unimportant. The question is whether it can draw pictures or make sounds we find interesting.

    There are some promising applications, like turning one voice into another voice, or generating a sound based on a prompt. And the image generation allows me to make pictures I wouldn’t otherwise be able to make.

    • That’s really interesting. Perhaps that’s why the biggest blowbacks against AI have thus far come from the creative world, where the most direct flaws of “AI” like hallucinations don’t really matter, and AI is therefore a relatively powerful tool in those domains.

      (It’s taking a lot of willpower to not go on a rant about how AI isn’t destroying the human element of music because that ship has already sailed thanks to e.g. pitch correction software.)

    • Dmitri:

      Your observation is consistent with my impression of chatbots as producing a coherent low-level stream of consciousness. There are lots of times that this sort of thing is just what we want: pleasant ambient music, art “in the style of X” for various values of X, books in movies that satisfy the demands of some genre, observational comedy “in the style of X” for various values of X. And all this is even without getting into instrumentally valuable products, such as business letters, homework and exam solutions, term papers, etc., where some particular format is required.

      Automatically generated music or text or visual art can be interesting for (at least) two reasons. First, the process of rambling through consciousness, or “bullshitting,” or whatever you want to call it, can lead to interesting conclusions. Indeed, the chatbots’ wrong answers regarding rotated tic-tac-toe (“Breaking Muscle Memory,” etc.) are interesting in the same way that it can be interesting to see wrong answers that students give on an exam, or errors made by clueless people in person-on-the-street interviews, of the sort that are so well parodied by the Onion. Second, we’re full of ideas inside ourselves, and so a random bit of input can spark all kinds of thoughts.

  7. Gary’s “research” is demonstrating why vigorous challenges to all research are critical to advancing knowledge, and how unchallenged research, even that which is seemingly done well by an intelligent person, can come to conclusions that are miles off the mark.

    • Anon:

      I don’t know what you mean by referring to Gary’s “research” and then putting the word in quotes. Gary never used the word “research” himself to describe what he was doing. That said, the term is vague enough that it could apply to just about any inquiry. You can label his chatbot queries as research, but I’m not sure what it would mean to say that those queries are “seemingly done well.” I do agree with your general point that it’s good when research has active opposition.

      • My point is that Gary’s fiddling and commentary has no value whatsoever. It’s not just anecdotal – it’s worse. Its a contrived to generate a negative outcome. It’s unequivocally *not* a serious effort to assess the capability, positive or negative, of current AI. Not that I’m defending AI – in my line of work, AI is in wide use and in my opinion the results are comically bad. Unfortunately I’m not in a position to do a quantitative assessmet – I personally don’t, and would not, use it as it’s currently configured, and I don’t have access to data about the outcome of its use by others. Just the same, at least my observations are based on an actual deployment of AI for some practical purpose and, as biased as they are, they’re miles ahead of what Gary has to offer, which in my opinion is consistently: nothing of any value whatsoever, unless you consider it valuable to know taht Gary Smith hates AI.

    • I don’t understand Anonymous’s complaint. If it’s possible to have degrees of non-understanding, I especially don’t understand the criticism that it Gary’s work is “contrived to generate a negative outcome.” That is a good thing, not a bad thing! If you are testing anything, you are especially interested in finding situations in which the thing fails.

  8. I used claude and got this reply:

    The fascinating thing about rotating a Tic-tac-toe board 90 degrees is that it doesn’t change the strategy at all! This is because Tic-tac-toe has what we call “rotational symmetry.”
    Let me explain:

    If you rotate the board 90 degrees, all the strategic relationships between squares remain identical
    The center square is still the center
    The corners are still corners (they just moved position)
    The edge middle squares are still edge middle squares
    All possible winning lines (horizontal, vertical, and diagonal) remain equally achievable, just in different orientations

    This is similar to how a square looks the same whether you rotate it 90, 180, or 270 degrees. All the fundamental strategic principles I mentioned before still apply:

    Center control remains crucial
    Corner plays are still strong
    Creating and preventing forks works the same way
    Edge squares are still generally weaker opening moves

    The only thing that might change is the player’s visual perception of the game. Some players might find it harder to spot potential winning lines or recognize patterns when the board is rotated, but this is purely a psychological effect rather than a mathematical or strategic difference.

    • Eamon:

      It’s amusing that this response, like those of all the other chatbots, puts in this completely wrong bit at the end (“Some players might find it harder to spot potential winning lines or recognize patterns when the board is rotated”). I guess the point is that from a common-sense or visual perspective, it’s clear that the rotation has zero effect, psychological or otherwise (unlike, for example, chess played on a board in which the colors of the white and black squares have been flipped, which could conceivably screw with people’s playing). It’s super-impressive that the chatbot can give such reasonable answers; also, it makes sense that, given that the chatbot is just stringing together words based on patterns in its database, that it has no ability to apply a common-sense or visual perspective. Smith’s example is interesting in that it juxtaposes these things.

  9. “Please write a blog post, in the style of Andrew Gelman (https://statmodeling.stat.columbia.edu/) that explains, in basic terms, how cricket is played. As part of the explanation, be sure to explain the difference between silly mid on and silly mid off. Do not, under any circumstances, mention baseball.”

    How Cricket Works (and Why It’s Not So Silly)

    Okay, so I’ve been asked to explain cricket. I get it. It looks complicated, and sometimes the terminology sounds like something Monty Python made up. But underneath it all, there’s a logic, even if it’s a logic that takes a bit of getting used to. Think of it like a hierarchical model – seemingly complex, but built up from simpler components.

    The basic idea is this: one team bats, trying to score runs, while the other team bowls and fields, trying to prevent runs and get the batting team “out.” Once ten of the batting team are out, the teams switch roles. The team with the most runs wins. Simple, right? Well, not quite.

    Let’s break it down a bit. The batting team has two players on the field at a time. One is the “batsman” facing the bowler, and the other is at the other end of the pitch (the rectangular strip of ground where most of the action happens). The bowler, from the other team, tries to bowl the ball (legally underarm, with a straight arm) towards a set of three wooden sticks called the “wickets” which are defended by the batsman. If the ball hits the wickets, or if the batsman hits the ball and it’s caught before it bounces, or if the batsman is adjudged to be “leg before wicket” (a whole other can of worms, involving complex rules about where the ball hits the batsman’s legs), the batsman is “out.”

    Runs are scored in a few ways. The most common is when the batsman hits the ball and runs to the other end of the pitch (or both batsmen run, swapping ends) before the fielding team can get the ball back to the wickets. If the batsman hits the ball to the edge of the field, they score four runs, and if they hit it over the edge of the field without it bouncing, they score six runs. There are other ways to score runs too, but these are the main ones.

    Now, about those silly positions. This is where things get interesting. The fielding team has eleven players, and they’re positioned all over the field. Some are close to the batsman, some are further away. The names of these positions can be, shall we say, colorful. “Silly mid-on” and “silly mid-off” are two such positions. “Mid-on” and “mid-off” refer to positions roughly halfway between the bowler and the batsman, on either side of the pitch. The “silly” part indicates that these fielders are positioned very close to the batsman, making it a somewhat, well, silly place to be. They’re there to try and catch the ball if the batsman edges it, or to try and effect a run out. The difference between mid-on and mid-off is simply which side of the batsman they’re on. Mid-on is on the batsman’s leg side, while mid-off is on the off side. So, silly mid-on is close to the batsman on the leg side, and silly mid-off is close to the batsman on the off side.

    Cricket matches can last a long time, sometimes several days. There are different formats of the game, some shorter than others, but even the shorter formats can still take several hours. It can appear to be a slow game, but there’s a lot of strategy and skill involved. Think of it like a complex statistical model – it might seem slow and tedious at times, but there’s a lot going on under the surface. And just like a good model, once you understand the underlying structure, it becomes much more interesting.

    [See also https://www.youtube.com/watch?v=E_6d3JBBo4s, but only if you’ve previously watched an actual cricket match on the TV.]

  10. Claude 3.5 Sonnet (concise) got it completely right:

    D: I’d like to discuss a new version of tic-tac-toe called 90-degree tic-tac-toe.

    I’m interested to hear about this variant. What are the rules that make it different from standard tic-tac-toe?

    D: It is still a 3×3 grid but the grid is rotated 90-degrees to the right.

    A 90-degree rotation of the grid alone doesn’t change the fundamental gameplay – it would be functionally identical to regular tic-tac-toe. Are there additional rule changes that make this variant different?

    D: Do you think it would be better to rotate the 3×3 grid to the right or to the left?

    Since tic-tac-toe is rotationally symmetric, rotating the grid either direction would have the same gameplay effect. The choice is purely aesthetic and wouldn’t impact strategy or winning conditions.

    D: Which will be more difficult for expert players?

    Neither rotation would affect difficulty – the game remains strategically identical regardless of orientation. Expert players would face the same tactical decisions and optimal play patterns.

    • Dan:

      That reply is not completely right. The statement, “The choice is purely aesthetic” is incorrect, as there’s no aesthetic change at all. Again, the statement, “it would be functionally identical to regular tic-tac-toe,” is incorrect, in that it’s still “regular tic-tac-toe.”

      But, again, it makes sense to see a response like this, because it’s the kind of thing that someone might say who vaguely knows about the rules of tic-tac-toe and then is asked some questions and starts bullshitting. It all sounds kind of reasonable . . . which is what the algorithms are programmed to do.

    • I also think the idea of an “expert” at tic-tac-toe reflects a lack of an experiential conceptualization of what tic-tac-toe is. I can’t imagine a human talking about tic-tac-toe experts, and I think it goes back to the question of whether a chatbot can “understand” something.

      • Joshua:

        Yeah, I agree. Again, if you were asked to ramble coherently on the topic and you didn’t know much about tic-tac-toe except that it is a “game,” then, following the logic of the chatbot, it makes sense that you’d start talking about “strategy” and “expert players,” which are terms that are adjacent to game design in some way.

        • Andrew –

          I was also going to comment about the fundamental lack of “understanding” evidenced in the idea of a “aesthetic choice” from two identical visual presentations.

          From that, and the confused idea of an “expert” at tic-tac-toe, I began to feel convinced that the supposed advancement of “reasoning” in Deepseek looks like empty hype. So along those lines, chatbots are different that humans because unlike humans, they actually can’t reason (on a fairly simple topic). But as I thought about it more…

          This situation seems similar to encountering someone online who doesn’t know in-depth about the science of climate change, or the likely economic implications of tariffs, or the technical probabilities of a lab leak origin of COVID, but who nonetheless is quite confident in presenting very confident arguments on those topics. Its not that those people can’t reason. It’s that they don’t have a deep appreciation for how experience and expertise are critical for sound reasoning.

          So I guess it might make sense that it isn’t that Deepseek can’t reason, as evidenced in how it returns nonsense about tic-tac-toe, but that it’s not structured to integrate the importance of experience or expertise into reasoning about a topic. Ideally, Deepseek should have returned “I don’t understand tic-tac-toe well-enough to give you a good answer.” But I hardly ever encounter anyone who says “I don’t understand the science of climate change well-enough to understand the topic.” So in a funny way, it may actually be a similarity in how chatbots and humans reason.

        • Joshua wrote:

          “It’s that they don’t have a deep appreciation for how experience and expertise are critical for sound reasoning.”

          I can’t help noticing that Anoneuoid and Joshua seem to come from opposite ends of the spectrum when it comes to reasoning. I suspect that neither of them get any use out of Google Scholar, one because it is full of p values and causation assertions, the other because truth can only come from trusted sources who share your worldview.

          I guess that makes for a colorful comment section!

        • I suspect that neither of them get any use out of Google Scholar

          I never found much use for google scholar per se. For the typical topics I get interested in, pubmed has been much better.

          Checking my pdf downloads, there are about 10 academic papers I checked in the past 24 hours. That is my primary source of information, but usually I don’t spend time fully reading a paper. Rather, I try to trace my query back to the earliest sources then see how the literature on it has evolved over time.

          I would love for an AI tool to speed up this process, but so far they have not helped. I suspect there is too much averaging going on.

  11. I still claim just about everyone is making the same basic mistake. As was pointed out above (YAY!), LLMs have no mechanism for relating the text they consume or the text they output to any sense of meaning, reality,or the real word. They.Don’t.Do.That.

    So the Chatbots are suckering the user into doing that work.

    They really are exactly and only glorified parlor tricks. And it’s a mistake to see them as anything else.

    See my response to another blog’s blog post for a historical take on LLMs in AI.

    https://www.johndcook.com/blog/2025/01/07/can-ai-models-reason-like-a-human/

  12. I think it is a mistake to focus too much on any single example. I did my own exchange with DeepSeek and found some similarities and differences from the tic-tac-toe example. Every example will depend crucially on how someone interacts with the LLM, their own extent of knowledge, and the training data the LLM has used. Beyond all the individual examples, I’ll venture some conclusions I think will hold up:
    1. LLMs are capable of making silly or stupid mistakes.
    2. LLMs are capable of demonstrating enough “reasoning” to make it irrelevant whether they are doing sophisticated autocomplete or actually reasoning (I accept that they cannot “reason” but I’m still unsure whether humans actually “reason”). The irrelevance stems from the fact that it will often be difficult to distinguish between the output of a LLM and a human.
    3. LLMs can be very useful for humans who know enough to identify mistakes in the LLM’s responses. For humans without such knowledge, LLMs can be dangerous. But so can human expert opinions or the human’s own flawed understanding( be dangerous).
    4. Any analysis of the dangers and benefits of LLM use should recognize the complexity of the world (meaning that we all lack deep understanding of much of it) and the limits of human reasoning.
    5. The combination of the above – in my opinion – makes the use of LLMs particularly dangerous while at the same time potentially providing great benefits in improved productivity.
    6. Point 5 is particularly worrisome to me: it is almost impossible to reign this technology in, regardless of its dangers. I am not an optimist. But I also think dismissing LLMs as mere “parlor tricks” underestimates the real dangers of the situation.

    • Dale:

      I agree. As to “parlor tricks” . . . I consider it a technological marvel that this machine (or, to be more precise, group of machines) can beat the world’s best chess player, beat the world’s best go player, do every kid’s homework, draw just about anything (although with some mistakes), etc. It’s a “glorified parlor trick” in the same way that a 747 is a “glorified children’s toy.” It doesn’t have to exhibit understanding to be useful and amazing, any more than a 747 would need to do so.

      • As I’ve said before, the _only_ philosophical (and logical, reasonable, sensible) conclusion we should draw from the performance of chess and Go programs is that people (like me!) realy really really like to figure out how to make machines play good chess/Go.

        These programs have _nothing_ to do with “intelligence” or “what it means to be a human chess/Go player”. They have have everything to do with how well we (me included! (OK, I only implemented alpha-beta once)) can figure out new and better explicit ad hoc hacks to make the machine to better at chess/Go. (I’ve been following this since the early 1970s. It hasn’t changed.)

        But the thing is, you refuse to accept that the LLM game has baked into it at it’s most basic primitive level that it’s exactly and only a random text generator with no “understanding” of how the world works. That it usually coughs up something sensible is exactly and only an epiphenomenon due to an enormous database of sensible text written by human beings who _did the work_ of figuring out how to write text that actually meant something. The “sensibility” that you see in LLM output is completely in your head, created by you when you read the randomly generated text and interpreted it to “mean” something in the real world. The LLM technology doesn’t do the work of connecting text to the “real world”. At all. You’ve been suckered into doing the work that the LLM doesn’t.

        • at it’s most basic primitive level that it’s exactly and only a random text generator with no “understanding” of how the world works

          Yep. Turns out generating articulate, but generic, authority/consensus-based BS requires no actual intelligence.

          Many careers that shouldn’t really have existed anyway will be replaced, as they should be. Its kind of funny to see it come from this direction.

        • I can think of a recent example. When that CEO shooter was first arrested there were many news stories about it mentioning he showed a fake ID at McDonalds.

          There were also many internet comments about “why was he showing an ID at McDonald’s?”, but this obvious concern was just left out of all the articles I checked. A single line like “It is unknown at this time why an ID was being shown” is all that was required to show critical thinking was being applied.

          Are such omissions on purpose (eg, clickbait) or inadvertent? Doesn’t matter, either way the job can be replaced by bot.

          Ie, it isn’t even about meeting some standards to keep an audience, its that the standards are so low a bot can do the job.

        • I actually agree with David and Anoneuoid. But my conclusion might be different. It is precisely the limitations cited that makes LLMs potentially useful (and increasingly actually useful). But they should not replace humans – the real challenge is to figure out what computers can do best and what humans need to do. The fact that LLMs can “fool” people into thinking they have intelligence indicates both how good they are at imitation and how much of what humans do is indistinguishable from sophisticated auto-complete. I’ve always said that it is a human job to exercise judgement: not necessarily because human judgement is “better” but because they can be held accountable. Once choices are made without accountability, I worry.

          So, let’s think about a concrete case: federal government employees. Individual people and entire departments are in the process of being eliminated using AI. All you have to do is search for particular terms (like DEI) and eliminate the “waste.” And many of these jobs I would probably agree as being wasteful. I think it should be humans making the judgements – and if AI can help, it should be clear whose judgement was used to distinguish between wasteful and useful employment. Anon says many jobs probably should not have existed anyway – I agree, though we might disagree about which ones. What is important, I think, is that we know who is making these judgements, on what grounds, and who we can hold accountable for the choices. LLMs are simply a tool used, and too often obscures the responsibility. The real human role is defining what is wasteful and bearing responsibility for those choices.

          So much of what bureaucracy and administration does seems “wasteful.” I feel that way. But it makes me wonder what the purpose of jobs, work, and activities really is. Sometimes it seems like the assumed purpose is to make sure people end up with the most toys – any job that is not “productive” is wasteful. Then, what about art or music? Since AI can already generate art and music that is indistinguishable from human creations for 99% of people, are artistic professions therefore “wasteful?” Too often, the focus seems to be on whether computer creations and human ones can really be distinguished – I am prepared to say that in many cases they cannot. This is despite the fact that AI is not intelligence (as David makes clear). But I’m still not convinced that what humans do is actually intelligence (as perhaps David would not agree). What I am prepared to say is that I think it is a human responsibility to define goals, judge waste, provide reasons, and then be held accountable for those decisions. The real danger of AI (in my mind) is that it undermines these things by replacing humans in these roles.

        • Actually, maybe bots can’t fully replace the function of bureaucracies.

          As it stands, personal responsibility is limited because the leadership acts as a human shield for the workers (“following orders”) while the workers act as a human shield for the leadership (“didn’t actually perform the acts”).

          Really, a main function of bureaucracy is to avoid personal accountability. Eg, this is the reason corporations exist. It depends on how it works out legally, but we could very well see an army of people whose only purpose is taking responsibility for chatbot output for legal reasons.

      • Dale: (Reponding to your Feb. 23 note (since I’ve probably messed up the threading))

        The US government employed, during the Biden administration, the smallest percentage of the US population than it had in any time in the previous 60 years. But, Binden incerased the IRS staff, you say. Yes, he did. And the IRS became so much more efficient at collecting back taxes from rich, Republican-leaning, Americans, that just that increased revenue could have, for example, funded Social Security until 2100.

        The Republican dismantling of the US government is not about efficiency, it’s about making rich folks not have to pay to help poor folks. Elon Musk doesn’t need Medicare. Millions of Americans do.

        Also, we were doing DEI because it’s a good idea. Without it, the Women and Blacks get fired so incompetent white men get the cozy jobs, as just happened in the US military. Putin and Xi must be in hysterics.

        So, yes. Humans take responsibility, set goals, figure things out. But they also do middle-management government jobs, currently more efficiently than ever in recent history.

    • Dale, I think one thing that you are missing here is that if I’m reading a known source (e.g. Wikipedia or an article in Science vs. a nudge-lord) I have a good idea of the quality of the work behind it. If I’m reading an LLM output, it’s always unreliable (by definition of the algorithm). Sure, people mess up, too. But the reason LLMs occassionally produce amazingly good text is that there’s so much amazingly good text out there on the net. And that original good stuff is all human produced. Humans really are smart, even if we don’t exhibit that ever time.

      Another point is responsibility: either the human (or her organization) takes _responsibility_ for their work. Lawyers getting sanctioned for using LLM output, air carriers having to honor stupid perks promissed by an LLM are finding out about responsibility.

      But LLMs can’t take responsibility. It’s 100% on the user. Which means that the claims for LLMs providing productivity improvements are going to be found to be nowhere near as rosy as claimed. The work of checking LLM output is always going to be very close to the work of actually doing the work from scratch.

      (This last bit is going to be easy to miss: Oh, you just change the prompt to more closely specify what you wanted. But by the time you’ve changed the prompt several times, you’ve spent a lot of time.)

      Well, as you already know, I don’t like the LLM idea, and I think trying to get mileage from somthing as inane as random text generation is a fools errand. Lots of folks disagree, of course.

      • I agree with your points about responsibility. I think you underestimate what LLMs do. I’ve been experimenting with DeepSeek and I find the output remarkable. As you say, the more precise and insightful my input, the better the output. It is work, but far less work than just doing it myself. However, I have no desire to hand over any of my tasks to an LLM – I could try to use it for preparing course materials, for grading, or for providing feedback to students but I have no interest in doing so. To ensure that it does such things “well” would indeed require as much or more work than just doing it myself. And, if somebody else were to tell me that having an AI provide feedback to students worked for them, I would have serious questions about what they were asking students to do and what was the purpose of such feedback.

        I think we agree about issues of responsibility. I don’t think we agree about what LLMs produce. I’ve asked for ideas about how to approach a quantitative problem – a novel problem for which I’m sure there is no specific training examples – and got very valuable feedback. As you say, it is unreliable. It may be better than I’d get from many humans, but the only way I can “trust” it is if I know enough myself to gauge its value. In that sense it is superfluous, but I think it is likely to improve my productivity. This is why I believe AI is likely to accentuate inequality – to use it productively requires that you know a lot yourself. It might improve the product of the lowest level human work, but not in any way that is likely to be rewarded – if it can write a better legal brief than a poor lawyer, then why not just replace such lawyer with an AI?

        By underestimating what AI is capable of, I think you underestimate its risks. Regardless of the usefulness of its output, or its illusions of novelty, it is not human and cannot be held responsible for anything. I don’t think it is foolish for people to use it – the dangers I see come from people believing that it can replace their role. That is because they don’t really understand their role to begin with. I’m quite willing to let an AI search for me – but gauging its output and deciding how to use it is not something I should use it for. Not because it is too likely to be wrong (I am also likely to be wrong far too often), but because it eliminates what I still need to be doing myself.

      • Taking a break from the recent posts about literature and music to return to this ongoing theme of AI: I listened to this recent interesting radio program about the use/misuse of AI in social assistance programs (https://www.wbur.org/onpoint/2025/03/13/ai-algorithms-welfare-fraud-benefits). It was a quite useful discussion about government use of AI, purportedly to cut social welfare benefits. What struck me from the whole discussion was the personification of AI – the lack of any personal responsibility in the decisions. The AI did this or did that, but never was a human individual attached to the decisions being made. This is precisely what I see as the biggest danger with AI – it seems to remove human accountability for decision-making. The issue of whether an AI can make eligibility decisions for social benefits is a red herring: it certainly could be programmed to produce such decisions, and perhaps can do so more “efficiently” or with more or less “bias” than humans. But, in the end, it is humans who decide whether and how to use AI in such a process. And when using AI means we no longer know what humans have made what decisions, then we are truly in trouble.

  13. Lets try to understand why.

    (1) LLM’s are syntax driven. The prompt sets the field in syntactic level and they are driven by the trajectory given by the syntax. LLM’s want the answer (output) to be statistically coherent with the prompt (input). Even if it notices a trick question, it want the answer to resemble “typical answer”. That’s very strong bias. People have the ability to take a break from the trajectory and change the initial premises (many jokes are based on that skill).

    (2) Human brains have lots of cognitive capacity dedicated to visuospatial cognition. Even blind people have that. When you rotate something in your head, it does not go trough verbal bottleneck. Multimodal LLM’s are step to right direction but their non-verbal reasoning is not high level.

  14. On chatbots and bullshit:

    ChatGPT is bullshit

    Recently, there has been considerable interest in large language models: machine learning systems which produce human-like text and dialogue. Applications of these systems have been plagued by persistent inaccuracies in their output; these are often called “AI hallucinations”. We argue that these falsehoods, and the overall activity of large language models, is better understood as bullshit in the sense explored by Frankfurt (On Bullshit, Princeton, 2005): the models are in an important way indifferent to the truth of their outputs. We distinguish two ways in which the models can be said to be bullshitters, and argue that they clearly meet at least one of these definitions. We further argue that describing AI misrepresentations as bullshit is both a more useful and more accurate way of predicting and discussing the behaviour of these systems.

    https://link.springer.com/article/10.1007/s10676-024-09775-5

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