There are lots of situations where a promotion to a queen would result in stalemate (draw) so a promotion to rook or other piece gets away form this. I'd say Rook would be most common, but some special (problem?) positions a knight or bishop could solve the problem with a mate or a nice fork. E.g. promote to a night with check and an attack on the opponents queen.

It's interesting that all these positions are called "common", but the actual board position might happen zero to one times in a lifetime, and I suspect it's usually zero times.

I noticed something similar when I played contract bridge at a competitive level. A top bridge player might play very roughly on the order of 10,000 hands a year, and vividly recall something that happens on the order of once a year as "oh yeah that's common". Of course I wasn't remotely close to them. But there is something about competitive games that seem to amplify the memory for certain kinds of unusual situations.

(Some people are commenting about under promoting to avoid stalemate traps down the line. I've always been a weak chess player, but... trying to set a stalemate trap after being down a queen, in a non-contrived position, is, like, adult chess players shouldn't do that. In my limited experience.)

Nowadays there are tournament matches with no resignations allowed, so setting stalemate traps may be more common from now on.

> vividly recall something that happens on the order of once a year as "oh yeah that's common".

I mean, think of how many times a typical person has sex in their life. Hopefully they and their partner aren't getting pregnant more than roughly once per year. But somebody getting pregnant after having sex is reasonably defined as common. Certainly common enough that it's something you would consider and take precautions to prevent if you didn't want it to happen.

In ranked chess games, underpromotion happens about 1 in 1000ish games. I imagine it would be more common in high level unranked play. If you play one chess game per day, that's once every 3 years on average. It's not frequent, but I'd describe that as common.

Knight promotion because it's the best piece in the situation happens often. Rook promotion because Queen promotion would be stalemate happens occasionally. Bishop promotion is a theoretical curiosity only.

This post ends with a situation in a real tournament game where a bishop promotion is the only winning move

https://timkr.home.xs4all.nl/chess2/minor.htm

Well, maybe. There's no full record of the game, it's not even clear which year it supposedly took place in. It could have been a real tournament game, but I don't think there's enough evidence to reasonably conclude that it was.

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Just to pile on, a common trick is to sac a queen for say a minor piece, then after king takes queen, a pawn is promoted to a knight with check and a fork on the queen. After the dust settles, a player is up a minor piece.

A knight will attack different squares than a queen so promoting to a knight of course makes obvious sense in situations that warrant.

A rook or a bishop attack a subset of squares that a queen does, so why would you ever pick one of them instead of a queen? To avoid the stalemate where your opponent is not in check but has no legal moves.

For not proffesional players (i.e. me) when there are only one or two pawn and the kings, it's better to get a rock.

With a queen it's too easy to make a mistake and get a draw because the other player can't move.

I’ve done this too often, now I always get rook unless the board is nearly empty.

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The juiciest one is the Albin Counter-gambit. If you follow the "ideal line" where white blunders and takes the bishop bait, there's a neat knight underpromotion to win a queen.

From my own play, I typically see knight f3 from white on move 4, which still results in interesting games.

> There are lots of situations where a promotion to a queen would result in stalemate

You disagree with their 'rare' then where is your analysis?

You gave zero numbers or evidence, you're just saying stuff that pops into your head.

This analysis is a 35 to 1 for queens, knights arethe most popular alternative but I don't believe they played out the opponent resigns which most people do before the promotion to queen or analysised shit/fun playing -

https://blog.ebemunk.com/visual-look-at-2-million-chess-game...

Lichess has a series of puzzles you can try where underpromotion is the theme (which is unfortunately a major giveaway to solving these puzzles, since they otherwise be rather hard to solve)

https://lichess.org/training/underPromotion

Tim Krabbés blog is recommended for this type of question and in general: https://timkr.home.xs4all.nl/chess2/minor.htm

There is also nice discussion of the beautiful and practically relevant "Saavedra position", which does have an under promotion to a rook. https://timkr.home.xs4all.nl/chess/saavedra.htm

I had known of stalemate (both causing and preventing it), but there are others as they mention there.

One other I think I have read about (I do not entirely remember) is that someone promoted to rook because promotion to queen would have taken more time due to not having a extra queen to promote to so they would have to go to another table to borrow it (or ask the tournament officials for it).

Are upside down rooks not allowed to substitute as queens?

As far as I know, it doesn't count. But, I looked it up. Apparently, it is allowed in USCF but not FIDE.

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I've promoted to rook several times in over-the-board tournaments.

It's easier and quieter than stopping the clock and searching for a free queen piece if your position is decisive and your opponent stubborn. Or your piece to be captured immediately. So not necessarily "cocky" as the answers suggest but rather "mindful to other players".

Conversely, I could see a situation where a queen is available but will be captured right away, so you under-promote to a piece that is not immediately available so you can stop the clock while the arbiter finds the piece you need. If you are in time trouble this could give you some much needed time to reassess the position.

Why would you need to search for a queen piece when yours is already captured? No doubt promoting to multiple queens happens in casual games between very weak players, but extremely rarely in tournament play (where you also don't see "stubborn" players playing on in "decisive" positions unless the winning side has very little time on the clock).

Also, for in-person games, an upside down rook can be used as a queen in a pinch.

It's more common than you think in queen and pawn endgames. It might even end in a dear with two queens in one side: It wasn't on the board because there were other fighting alternatives, but it was pretty close to happening just last week in the Grand Chess Tour finals, where Caruana saw that a second queen wouldn't stop MVL from getting a perpetual.

I'd not say it happens in every tournament, but many active tournament players will see it every year or two. It just happens that at the higher levels, chances are the set came with two queens, as upside down rooks are not great indicators for DGT boards.

The stubborn player situation will happen in real tournaments too, just not those full of GMs. It will happen in your typical rated weekly tournament in the St Louis chess club, where your top tables might not be IMs, or in scholastic tournaments.

Tournaments doesn’t necessarily mean strong tournaments. There are tons of tournaments full of random kids and amateurs.

Btw, the upside-down-rook trick is illegal in serious play.

Can you explain why that is? I'd like to believe there's a reasonable explanation.

Using a proxy piece seems like an expedient, reasonable solution. A small square of paper with a Q on it?

As stated it's wrong--there aren't special rules for "serious play" as opposed to non-serious play. However, it's illegal under FIDE rules, but allowed under USCF rules (which cover many "serious" tournaments).

And I'm amused by another response that says that it's more common than I think and then cited a case where it "almost" happened, and says "many active tournament players will see it every year or two", as if that's not "extremely rare".

> there aren't special rules for "serious play" as opposed to non-serious play

Of course there are. We don’t follow every rule in the FIDE handbook when I play at Christmas with my brother in law.

For example, I would bet that in 99% of home games, touch-move is not enforced.

> allowed under USCF rules

interesting, I didn’t know that.

The discussion was about tournament rules, not what you do at Christmas, where the FIDE rules have no jurisdiction. And even if they did, what are these "special rules"? I don't think that you made a serious attempt to engage with what I wrote but instead were intent on naysaying, so I won't comment further.

> As stated it's wrong

Restatement of the premise is not an explanation. I asked "why."

> However, it's illegal under FIDE rules

Under which rule[1]? I anticipate the argument being one of identity, such as "a rook is a rook whether it is right side up or upside down." This is an argument of convention. I don't see a CAD model that describes a rook's physical representation. If both players were to agree that for the sake of a promotion that an overturned rook would in fact be played like a queen the piece identity requirement would be satisfied and no descriptive rule would be violated. Or perhaps a coin, or a stone, or anything of suitable size and ergonomics.

[1] https://www.fide.com/FIDE/handbook/LawsOfChess.pdf

FIDE arbiter guidelines, page 17:

> When a player places an inverted (upside–down) Rook on the promotion square and continues the game, the piece is considered as a Rook, even if he names it as a “Queen” or any other piece. If he moves the upside-down rook diagonally, it becomes an illegal move.

Link: https://arbiters.fide.com/wp-content/uploads/Publications/Ma...

This is not a philosophical question about metaphysics, where the rook’s true essence can be converted to that of a queen because really, what are the queens and rooks anyway but abstract symbols? The rook is the physical object that everyone in the tournament hall recognizes as a rook, which nobody has a problem identifying in practice.

That's interesting, but I wonder if it's not more accurate to say "tradition doesn't support the use of an inverted rook as a promoted queen's proxy" or "FIDE would prefer not using inverted rooks as a promoted queen proxy" instead? Unfortunately neither explain why this is the preference, but avoiding ambiguity for observers seems obvious.

My thinking is that if we take "many active tournament players will see it every year or two" as the absence of a strict prohibition, and that this description of how it is illegal occurs in the "Arbiters' Manual," which self-describes as guidelines for arbiters and in the preface explains that rules can't cover every situation which is why the arbiters exist, but not in the actual rules document, it seems less "illegal" and more "unadvised."

I did not wax metaphysical, quite the opposite with the desire to find a definition for how one identifies a given piece. I imagine there are some other tournament organizational guidelines which outlines how chess sets are chosen for official events. These conventions taken in aggregate would provide some perspective, but still not answer the original question. I wager that everyone in your tournament hall would also recognize the use of an inverted rook as a promoted queen. So if it's not a question of avoiding ambiguity, then I wonder again, "why?"

There is a shorter version of this reply, which I will now include below:

At the end of the table of contents there is another interesting note in an offset grey box, just like the box which contains the note you quoted above:

> IMPORTANT:

> Throughout this manual, text which appears in a box such as this one is given as advice and is the opinion of a number of experienced arbiters. It does not form part of the Laws nor the Regulations in which it appears.

> That's interesting, but I wonder if it's not more accurate to say "tradition doesn't support the use of an inverted rook as a promoted queen's proxy" or "FIDE would prefer not using inverted rooks as a promoted queen proxy" instead?

No, it is against the FIDE rules. Both the official rules, and the unofficial explanatory text in the Arbiter's Manual. The official rules say that chess sets contain a piece called a queen, and a piece called a rook. They do not say anything about a piece other than a queen becoming a queen if it is turned in a different orientation, so it should be obvious that it doesn't do so.

But even for those for whom that wasn't obvious, there is additionally the arbiter's manual, explaining that yes, this is in fact the interpretation of the rules that FIDE and senior arbiters believe to be correct.

Despite all this you are refusing to believe it's actually against the rules. I am not sure what else I can cite to convince you. Google, ask your favorite LLM, or ask a FIDE arbiter if you want -- everyone will agree that if you promote to a rook, it is a rook, regardless of whether it's upside down or not.

Nobody has written a formal definition of which piece in a chess set is "the rook" and which one is "the queen", because the FIDE rules were not written by formal logicians, and so it probably never occurred to them that this was necessary.

This simply never comes up. You are probably the only person in history from the founding of FIDE until now who has pretended not to know what a rook or a queen is.

> My thinking is that if we take "many active tournament players will see it every year or two" as the absence of a strict prohibition

I think you are misinterpreting that comment. They are saying those players will see a scenario with two queens of one color on the board every year or two, not that they'll see someone trying to use an upside-down rook to stand for one of them.

> They are saying those players will see a scenario with two queens of one color on the board every year or two

That makes sense.

It seems to me that you've used a lot of truism reasoning out of frustration. I tried to head these off with my original assumption that it was a question of identity.

>> I anticipate the argument being one of identity, such as "a rook is a rook whether it is right side up or upside down." This is an argument of convention.

Since the reliance is on convention, and an inverted rook is conventionally treated as a promoted queen, the FIDE Arbiters' Manual describes a policy of not following this convention. I'm sure someone knows why this is the guidance. I was curious about that reasoning. It seemed interesting and worthy of discussion.

> You are probably the only person in history from the founding of FIDE until now who has pretended not to know what a rook or a queen is.

You ascribe to pretend ignorance what is in fact interest in the history of a thing. This seems unreasonably antagonistic.

I believe you've misunderstood my original comment and I do not know why, but I think I will be done with this thread. If you find out why this was the adopted guidance for the FIDE Arbiters' Manual I'd enjoy reading about it and I imagine others may too, but it should be put under the original question, not here.

> Since the reliance is on convention, and an inverted rook is conventionally treated as a promoted queen

I think that convention is much less strong than the conventional meaning of the piece shapes. I have only seen it in casual games, and I’m not sure if it exists in every country.

I don’t know why this rule was adopted, but I gave a few plausible reasons off the top of my head in another post on this thread.

I didn't "restate the premise", I said it was wrong, and added information. Since I wasn't present when the FIDE hammered out their rules, I don't know why they decided that upside down rooks can't be used as queens, and any speculation on my part would be no more authoritative than your own imagination.

I tried to be helpful and I got an aggressively hostile response. (And I see that the same happened to others here.) I won't make that mistake again.

> I didn't "restate the premise", I said it was wrong, and added information.

You originally wrote:

> Btw, the upside-down-rook trick is illegal in serious play.

You followed up to my asking for an explanation why with:

> As stated it's wrong

It seems like a very low effort restatement to say "illegal" and then "wrong." Your additional details were about the FIDE rules, which do not seem to forbid using an inverted rook as a proxy for a promoted queen. If they do, please tell me which rule[1]. The pivot from "illegal" to "wrong" adds a moral aspect to the evaluation which seems bizarre.

> I tried to be helpful and I got an aggressively hostile response.

I'm sorry if my spinning of a hypothetical yarn about the argument being one of identity of the piece in question came across as "aggressively hostile." It was not my intention in the least.

> And I see that the same happened to others here.

I grant you the other thread got more antagonistic and that's disappointing. I will defend that I think that if you want to claim the rules forbid this act, you should be able to cite a rule, and not a guideline about general consensus. The former is clear, the latter is something more akin to "tradition."

I'm also, across both of these descendant threads, annoyed with responses not readily engaging with my legitimate inquiry about why forbidding the use of the inverted rook as a promoted queen proxy may be the case. It's a neat quirk or curiosity to me. And I'm barely a casual player. It seems like an elegant solution to piece availability and actually preserves game pace -- those are aspects of the elegance that seem obvious to me.

[1] https://www.fide.com/FIDE/handbook/LawsOfChess.pdf

> You followed up to my asking for an explanation why with:

>> As stated it's wrong

You misunderstood that comment. He was saying that my claim (that using an upside-down rook is illegal in serious play) is wrong as stated, because it's only true for FIDE rules, not USCF rules. He wasn't saying the act of using a rook that way is wrong (morally or otherwise).

> if you want to claim the rules forbid this act, you should be able to cite a rule

No, this isn't how rules work. The rules of a board game describe all the ways you're allowed to move the pieces, under what circumstances pieces can become other pieces, and so on. If some piece transformation isn't discussed in the rules, then it's not allowed. Otherwise, I could on a random turn say "I declare all my pawns to now be queens". There's no specific rule that says you can't do that, but nevertheless, the rules forbid it implicitly by not mentioning it. Similarly, the fact that they never mention that a rook can become a queen means that in fact, it can't.

So in fact the rule you're looking for is on page 7 of the PDF you linked:

> If a player having the move [...] promotes a pawn, the choice of the piece is finalised, when the piece has touched the square of promotion.

"The piece". Not a different piece having been turned upside down.

Let's take an analogy to real-world laws. Imagine you live in a country that says apples are taxed at 1 cent per apple. Now, imagine a shop turns all the apples upside-down, and declares that they consider upside-down apples to actually be bananas, so they don't have to pay the tax. Is this legal? No! Even though the law doesn't mention anything about whether you can or can't do that, nor does it give a mathematically precise definition of what an apple or banana is. Even though it's not explicitly forbidden, it is still not allowed.

> I'm also, across both of these descendant threads, annoyed with responses not readily engaging with my legitimate inquiry about why forbidding the use of the inverted rook as a promoted queen proxy may be the case. It's a neat quirk or curiosity to me

In another subthread I gave five plausible reasons why it makes sense not to allow it. Link: https://news.ycombinator.com/item?id=45512086

> You misunderstood that comment.

You are absolutely right, I misread that entirely. Thanks. I also misattributed the original comment and the follow-up to the same author.

The problem with pursuing "identity" is that these rules don't anchor the identity of pieces so far as I can tell. If the players agree that for expediency the inverted rook is a queen, the move notation would call it a queen, it would in fact be a queen for the purposes of that game. The only way anyone could tell which token was used in place of a normative queen shaped piece would be if there were video or photographs of the actual board at that phase of the game. And it doesn't affect those other people. In a formal setting it seems like an arbiter or judge or proctor or whomever should also be informed for accurate record keeping.

The fruit analogy raises the stakes to fraud while the use in a game, unless a player tried to cheat, is inconsequential to those players.

> The problem with pursuing "identity" is that these rules don't anchor the identity of pieces so far as I can tell.

Again, the identity of objects is assumed in all sets of rules or laws, as the apple/banana example was intended to show. When you write the rules for board games, you do not need to re-derive the entire foundations of metaphysics and discuss what it really means for an object to have identity. You assume these words have the normal meanings commonly associated with them.

> The only way anyone could tell which token was used in place of a normative queen shaped piece would be if there were video or photographs of the actual board at that phase of the game.

Whether people can tell that a rule was violated has no bearing on whether or not it was actually violated. I thought we were talking about what the rules say, not how easy or difficult they are to enforce. Of course if you are by yourself and there are no spectators or official arbiters then you can do whatever you want; nobody is going to stop you.

> In a formal setting it seems like an arbiter or judge or proctor or whomever should also be informed for accurate record keeping.

But if you're already pausing the clock to inform the arbiter anyway, why can't the arbiter just give you another queen? I thought the entire point of this whole rook-as-queen exercise was to avoid having to stop the game and talk to the arbiter?

> The fruit analogy raises the stakes to fraud while the use in a game, unless a player tried to cheat, is inconsequential to those players.

We're not talking about the stakes or importance. I agree that what token chess players use as the queen is less meaningful than actual crimes, but that wasn't the point of the analogy.

> You originally wrote:

>> Btw, the upside-down-rook trick is illegal in serious play.

No I didn't. I won't engage in conversation with someone who doesn't even track who said what.

https://news.ycombinator.com/item?id=45520037

I was mistaken and ultimately recognized that as well as being told I misidentified the antecedent of your "As stated it's wrong."

Apparently it’s allowed under USCF (US Chess Federation) rules, according to my sibling comment, just not under FIDE (international) rules.

Anyway, I’ve never stopped and thought about why it’s not allowed — it just seems like it obviously shouldn’t be, in serious competition. If at an NBA game they ran out of basketballs, they’d stop the game until they got one, not use a soccer ball instead.

It’s hard to imagine that at an actual FIDE-rated tournament with arbiters, etc., they would be unable to find a queen piece to use.

> it just seems like it obviously shouldn’t be, in serious competition

Why does it seem obvious? Out of some sense of accessibility to third party observers?

> If at an NBA game they ran out of basketballs, they’d stop the game until they got one, not use a soccer ball instead.

This is an unreasonable straw man because basketballs and soccer balls behave quite differently. A marble would be less suitable than an overturned rook because it may roll away, but both are similarly graspable with similar dexterity.

> Why does it seem obvious? Out of some sense of accessibility to third party observers?

I can think of lots of reasons.

1. It looks cheesy and unprofessional to use random objects instead of the pieces the game is supposed to be played with; you might not think this is a good reason but keep in mind we are talking about a game that until recently everyone played wearing a suit and tie.

2. It is distracting and impedes comprehension and calculation if the design of the actual pieces is burned into your pattern recognition — not only for observers, but for the players themselves. A lot of official chess rules, e.g. the touch-move rule, are just about not annoying your opponent.

3. It opens up ambiguity about what was actually intended. What if later the player tries to claim they really did mean a rook? What if a player accidentally turns one of their actual rooks upside down during the course of a game — is it still a rook, or are they trying to cheat by turning it into a queen? Etc.

4. It does not work with high-end electronic chessboards that automatically record moves (DGT).

5. Last but not least: there is absolutely no reason to allow this, because it’s impossible to imagine that at a serious tournament the arbiter wouldn’t be able to find an extra queen. And stopping the clock and asking for an arbiter, while still a bit distracting to others, is surely less distracting than starting a discussion with the opponent about whether it’s okay to use an overturned rook or any other random object as the queen.

i can definitely see someone stalemating with the rook-queen then claiming its actually a rook so its not a stalemate.

In most board games, proxy pieces are generally forbidden in official play. For say, a card game it's because the game store owns the cards and would really prefer it if you didn't dillute the value of the cards they're also selling to people, not to mention they also have the actual cards in stock anyway. On a similar note, chess tournaments and clubs will almost always have enough pieces to not need proxies since there's only 4 unique pieces that you'd potentially need to add for (all the officials minus the king, in practice it's usually only the Queen and the Knight though), so any extra/reserve chess set can provide the bonus piece.

In casual play outside of formal tournaments and chess clubs, proxy pieces exist because nobody is buying extra chess kits solely to cover for the event in which someone promotes a queen while another queen is on the board. (Also in very casual play, most players lose their Queen due to a mistake early on and if they promote a piece to Queen later, they just use the original Queen piece again.) Proxy pieces exist to cover people playing at home, not people playing professionally or at a hobby club. The same goes for card games; nobody cares if you're proxying a card during casual play - maybe they'd ask if you own the card, but that's about it.

Exactly. In my region there are multiple tournaments a month (in season) where players from no ELO to 2300 play. Swiss system means you're going to be paired up/down.

I'm ~1900 which means first two rounds are typically beginners.

Most recreational players have probably underpromoted to a rook at some point to avoid stalemate. I do it online as a matter of course if a rook underpromotion would be immediate checkmate because a rook is all you need so why ask for more.

Bishop is extremely rare but it does happen. For example there was the famous case in the US champs when Fabiano Caruana underpromoted to a bishop[1] vs Ray Robson and Robson immediaely resigned. https://youtu.be/umabaHAGmJQ?si=ETy1cAFw7ydH4MhH

[1] He didn’t have to- he just did it because he had never done it in his whole chess career

There are chess puzzlers I've seen where promoting to something besides a queen is necessary to prevent stalemate.

In a losing position, I prefer under promoting to a pawn and triggering an infinite loop, buying time for a hasty escape.

Underpromotions to rook or bishop certainly can happen in play to avoid stalemating the opponent and preserving the win. Other reasons don't exist in play (aside from extraneous reasons like not having a queen handy or weak players underpromoting just because they are afraid of stalemating even though promoting to a queen wins) but can in compositions. e.g., here's a position that is the other way around, where promotion to a bishop is stalemate regardless of where the opponent moves and any other promotion loses:

1n6/PP1p4/n1p5/8/7q/5pbr/5k1p/7K w - - 0 1

https://www.chess.com/analysis/game/pgn/5WfasZuA6A/analysis

P.S. https://timkr.home.xs4all.nl/chess2/minor.htm contradicts my "Other reasons don't exist in play", assuming that the game that he analyzes actually happened, which is questionable.

There is a program called CT-Art[1], that uses "motifs" to train tactical sight for these sorts of things. Instead of next-move type puzzles where the moves are obvious, it gives you a game position several moves out from the targeted tactic, so you learn to recognize the conditions to be able to steer the game toward the tactical position. I think in it's current iteration it's broken out into separate courses or something but the older programs (v2 or v3 that I can vouch for) were really great for improving in these kinds of areas.

[1]: https://chesskingtraining.com/ct-art/

I played chess for only a few years, at a low level, and I encountered situations where underpromotion to a bishop or rook was necessary to win. It's possible it is more common at the just-above-beginner level than at the elite level, because a player in a losing position will play on longer and try to set up stalemate traps that would be pointless in higher-level games.

The unspoken assumption here would be promoting to rook or bishop "instead of a queen" and as the post points out other than avoiding the stalemate situation there doesn't appear to be a logical reason for doing this.

It probably wouldn’t ever happen in a real game, but I think it’s possible to be in a situation where you’re still losing after promoting to a queen, but underpromoting to a bishop forces a stalemate by leaving you with no legal moves no matter what your opponent plays in response.

Indeed it wouldn't happen in a game but ... I easily created a position where promotion to a bishop is stalemate after any black move (confirmed by Stockfish):

White pawns on a7 and b7, king on h8. Black king on f2, bishop on g3, rook on h3, knights on a6 and b8, pawns on c6, d7, f3, and h2.

This position is a draw after a8=Q or axb8=Q but that is easily remedied by adding black pieces, e.g., a queen on h4.

There are puzzles where only a bishop promotion wins. The others are either forced stalemate or forced draw by repitition. Finding a real game where that happens is unlikely

The definition of a "real game" gets extremely relaxed in a competitive situation between low-rated players. Between two grandmasters, they're going to stop the moment the outcome becomes clear. But when you have two just-above-beginners, there are other factors. They're going to keep playing in lost positions where there's a big material imbalance. They're going to miss a lot of mates in 3+ moves, and even simpler mates under time pressure. They end up in weird and "unrealistic" positions that aren't even interesting as puzzles, but have competitive significance to them because if the player with a big positional or material advantage loses on time or makes a blunder under time pressure, it will affect their rating and their standing in a tournament.

Theoretically you could devise a scenario where promoting to a bishop would forcefully draw an otherwise losing position.

It's super exciting when it does happen, just from the rarity aspect. Here's one: https://youtu.be/z6jKBaVSOLw

I had a rook under promotion happen in a real game on Lichess under time control. Queen would have stalemated, but rook was mate in 2.

I have read that underpromotion can reduce the risk of immediate capture: the opponent has a bigger incentive to take a queen than, say, a rook. Seems pretty marginal to me though.

It's better to force the opponent to capture than give him the choice of capturing or doing something else. If your opponent chooses not to capture the rook it's because he has found a move he thinks is even better than taking the rook. And that move is then something you should fear.

A big part of chess is maximizing your own choices and freedom while restricting your opponents choices.

Level 1, yes, this is the correct way of thinking. You should always take the highest scoring move.

However, Level 2, making a decision harder for your opponent, might force them to spent more time thinking about the decision. If for some reason there is an imbalance of pondering, this might be beneficial. Suppose that you knew X position would be reached before your opponent, so you had more time to study it, you know what the correct piece to take is, whether a promoted rook, or a previously existing rook, but your opponent doesn't yet, and crowning to a queen will force your opponent into a move without a thought.

The computer will sometimes do this, more because of randomness than strategy, but it is probably always the case that if they underpromote, you should take, it's like a tell of theirs. Perhaps there is a case for nash equilibirum where you must sometimes offer an underpromotion in a scenario where a queen would have been marginally better such that underpromoting doesn't signal to your opponent that they should take the piece (whichever it may be, I'm a bit dizzy)

Very theoretical, but not impossible that underpromoting in such scenarios might be beneficial, that said, very theoretical.

For sure it happens, just not the most common of scenarios. I see it far more often in puzzles and analysis than I do OTB.

Under-promotion is the sort of thing streamers like ChessBrah will do to opponents who refuse to resign, just to rub their nose in it.

Unexpected, I didn't think it might be worth to promote to a weaker piece. But I don't play chess since long ago.

I think it can happen. The big question, how often a player at a high level gets to a point where a promotion can happen ?

For highly rated players, I think a resignation would occur before a promotion happens. So in general, promotions themselves are rare.

Now me, the only way I would win is to promote 3 pawns to 3 queens, and even then ... :)

Stats I’ve seen are that around 2% of games between grandmasters include a promotion.

What you might be overlooking is that often the player that promotes might have temporarily given up material in order to get the promotion so it is may just be restoring approximate equality.

Or it could be that the second player will also promote soon.

Resignation is a signal that you know your opponent knows how to win so why waste everyone's time playing it out. For high level players you can be confident they know how to win but there might be more than 100 moves left in the game, so not wasting time playing out a losing game is the polite thing.

When playing someone low rated your opponent isn't good enough to think they can win unless there are less than 3 moves left so you may as well just play the rest of it out at that point. Even then, if you are in a simple (rook?) endgame if the low rated player makes a couple right moves you can assume they know the remaining moves so is it worth wasting your time to prove it?

That all depends on time control. If you watch Titled Tuesday for instance you'll see plenty of games where a player promotes and their opponent doesn't concede hoping to get a stalemate or a dirty flag.

There's a very chill streamer named Eric Rosen that does stalemate tricks at all levels, and it's surprising how often he gets them to work (even with super GMs from time to time).

How did this question even made it to the front page?

Why shouldn't it?

“On-Topic: Anything that good hackers would find interesting. That includes more than hacking and startups. If you had to reduce it to a sentence, the answer might be: anything that gratifies one's intellectual curiosity.” --https://news.ycombinator.com/newsguidelines.html

Just was not expecting that this question would gratify intellectual curiosity of this many good hackers.

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