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Why is this club lead suspicious when partner has two small hearts?
Follow-up question to Why is the King of Spades the best opening lead with this hand?
In the next example cited by the website, the board and auction is:

What would you lead with the North hand?
It’s not the most challenging lead, and I would guess 99 out of 100 experts would lead the jack or ten of hearts depending on the honour lead agreements. Ron Schwartz led a club, which I still haven’t found any other expert to do. If partner had heart honour, I would say that Ron was number 57 in that line of 100 experts and just made a creative lead. When partner turns out to have two small hearts I get suspicious.

I can understand why most players lead the Jack or 10 of Hearts from the answer to the linked question. However, I cannot understand the last few sentences. Why would anyone lead a Club, and why is a Club lead especially effective if partner has two small hearts (and creative if partner has heart honors)?
I have no knowledge about Bridge except for the rules & the strategy from the answers in the linked question, so I'd appreciate an elementary explanation.

Observations:
East-West have failed to make a game try. Even Non-Vulnerable (risk-reward in team play says bid games aggressively Vulnerable and passively Non-Vulnerable) they are limited to the combined 23 HCP they actually hold. Further, West is limited to 14 points as he would have opened 1NT with 15 or more and distribution such as his bidding showed. Therefore partner has anywhere from the 10 actually held up to perhaps a so-so 12; almost as good a hand as Declarer.
This means South has entries, in addition to the possible Club Q entry in North's hand. If Partner has at least 3 Hearts (more likely a priori than his actual 2) or a doubleton honour then there is a chance of getting at least 6 defensive tricks on a Heart lead by establishing:

3 Heart tricks in North;
3 more tricks (outside Hearts) between North's Club Q and South's honours;
possibly a heart trick in South; and
possibly even a Spade T trick, also providing an entry to North's  established Hearts.

Wander into virtually any Bridge club in the World, and at least the top 1/4 of those players will give you the same analysis. To be regarded as a strong intermediate or better Bridge player, one simply must lead a Heart (either J, T, or 9 depending on lead agreements with partner).
Further, even in the absence of his own Heart suit, North will be considering a Heart lead because of its absence from mention in the bidding by East-West. There is a strong reward for finding playable Major suit contracts in preference to Notrump. When he knows, as here, that South holds the majority of the partnership assets, it is highly likely that North will lead a heart from any holding of even 3 small.
Analysis:
So the only reason to not lead a Heart here is: unauthorized information.
If North knows that South has only 2 small Hearts he can try to avoid giving away a trick to West's Q by looking for another suit where North-South might hold 7 or more cards. He can take a flyer.
But since East-West have bid Spades and Diamonds, that really only leaves Clubs for this - to avoid attracting too much attention to his unauthorized information. As pointed out in later episodes of the saga, there is a burden borne by cheaters at Bridge: They must work to avoid being too obvious. They cannot always use the information they have, as on occasion it would be too obvious.

Thanks for great answer. By "doubleton honour" do you mean two honours in Hearts? If so wouldn't that be very ambitious since North is holding two Heart honours? Also, why would South holding more Hearts improve the odds of taking Heart tricks? Wouldn't all the Heart tricks come from North leading Hearts when nobody else has them?

@Allure: No; the phrase "doubleton honour" refers to a two-card (ie doubleton) holding headed by one honour. South holding 3 Hearts significantly increases the chance that there is a Heart entry back to North's hand, by having the Heart ace doubleton in East, while South having doubleton honour means the single stopper in the suit can be removed by leading and continuing the suit at tricks 1, 2, and if needed 3. Finally: honours are the Ace through Ten in each suit; so North startde with three Heart Honours plus the 9.

Thanks for answer. Can I clarify the second sentence: are you saying that if East had a "doubleton honor" (Ace + x of Hearts), and South also had doubleton honors (Q + x of Hearts) then North/South can play around the Ace stopper by "continuing the suit at tricks 1, 2, and if needed 3"? If so, how would this work? Presumably once East wins with the Ace, they would not play another Heart (?)

@Allure: What part of "... means the single stopper in the suit can be removed by leading and continuing the suit at tricks 1, 2, and if needed 3" was unclear? Surely it's clear that the Defense cannot continue leading Hearts on the trick immediately following that on which Declarer won his Heart Ace - and that my statement does not claim otherwise?

I think it's probable that what you've written is clear to bridge players but not to people unfamiliar with the terminology like me - in my case, it seems to me like the Defense is the side that is removing the stopper (I assume the Ace is the stopper), and then they are continuing the suit (i.e. continuing to lead the suit). The 1, 2 and 3 would then be the tricks they win by continuing the suit.

I'll try a different way to phrase the same thing.  A stopper is the card that "stops" the opponents from running the suit - a trick for your side.  Declarer wants to hang on to her stopper until one opponent doesn't have cards in the suit any more - so if they get in, they can't lead them to the other hand. The opponents want declarer to take their stopper so that they can run the suit later.  Here, it is obvious (reasoning elided) that you want to not play the ace the first two times it is led.  So let them win the first two tricks - and yes, they'll keep leading Hearts "tricks 1, 2 and 3".

Absolutely a matter of scale.  This is much less obvious than the other example - but that's because the other example was deliberately designed to be 1 in a million to make it screamingly obvious.  As I said in my answer to that other question, in order to show anything with "less obvious" cases that will happen in real life, you have to show a pattern of "lucky guesses".  This is the first link (only) in the pattern.
There are two basic styles of defence, active and passive.  Part of the skill of the game, especially on the opening lead, is to work out which one is best for this hand.  Again, as I mentioned in the other question, the best of the best make a trick-conceding mistake here one time in 5; if someone could somehow get that down to one time in 8, say, just that could vault an ordinary world-class player into a multiple world-champion.
Active defence means "pushing declarer around to set up tricks you're entitled to before she sets up hers".  Passive defence means "play as safely as possible, avoid giving declarer a trick she wouldn't get without help, and force her to generate the tricks she needs on her own".
The time for active defence is when declarer might be able to set up her tricks and not have to give you yours if you don't set them up in time.  The risk of active defence is giving declarer a trick she isn't entitled to.  The time for passive defence is when declarer likely doesn't have enough tricks on her own, provided you don't give her any.  The risk is that you may have enough tricks to set the contract, but you don't get to them in time.
There is no single right solution, but the auction gives hints (and seeing dummy gives more hints, and partner's signals help, and declarer's play pattern also helps.  But by then it might be too late to switch).
Here, the fact that they have stopped low (especially in 1NT, for reasons too complicated to get into here) and the fact that your hand isn't especially good, means that partner is marked with some cards, but the opponents likely have more between them than your side does.  It is likely that partner will have "honour doubleton" (Qx or Ax) in hearts, just because he'll have "some cards" (as opposed to if the contract was 6NT, needing 12 tricks instead of 7, where if the opponents are to be believed, partner will have no card higher than a ten). If he does have honour doubleton, then leading a heart will set up the rest of the suit as soon as declarer is forced to take the other honour.  That's 4 of the 7 tricks your side has to take to set 1NT, and you have cards in the other suits that will get you in to take them.
So that, in itself, leans the balance in favour of the active lead.  The downside, of course, is when partner has two small and the declaring side has both A and Q.  Now, you're giving them two tricks where, if declarer had to lead hearts, she would only get one.  Which is right?  There's no way to know on this hand; you just have to play the odds.
If you're going to go passive instead, best to lead a club (the other suit the opponents haven't explicitly stated they have some of).  It still has risks, but that's the least likely lead to give up a trick.  It is not likely to develop any for your side, of course, you're just hoping declarer can't find a way to 7.
Now that you have your options, what do you do?  Well, now we go to the quote in your question - he thinks that 99/100 would go with the heart.  So does Forget... I might be a bit less secure here - there are reasons beyond the scope of this question that I'm more likely to lead passively - but I'd still guess that maybe 80/100 would choose the active lead.  The chance of success is high, and the reward of success is also high; and the cost when it's wrong is acceptable (details of the Risk-Reward analysis is fascinating, but well beyond "non-bridge audience").
This time, the opening leader led passively.  And this time, it turned out that the active defence would cost.  That in itself doesn't say anything obvious - it's an unusual lead that was right this time.  I'm sure I make tens of those a month, and even experts who are much better at opening leads than I likely make "not normal" leads 5ish% of the time - and 40% of the time the 40% play is right (and the 60% play is wrong)!
But if we can show 20 hands, say, where there were unusual actions taken, and 17 of them were "right", and the other 3 it didn't matter, but would have with a different lie of the opponents' cards, then - well, maybe that's suspicious.
Again, the defence to this is "look at all these 'unusual' leads we made that did cost us!  We're just differently aggressive to 'standard expert', it's our style, and it works for us."  So this is enough to set suspicion - only by analyzing every hand can we move from suspicion to "nobody gets it right that often without help".
Note: The other answers (especially Forget...'s last paragraph) explain why a spade or a diamond, even if they knew it was the right lead "somehow", would be too suspicious even to attempt.

Thanks for answer. When you write The downside, of course, is when partner has two small and the declaring side has both A and Q, does it matter that partner has two small? Would things change if they had three small or one small? Similarly, If he does have honour doubleton, then leading a heart will set up the rest of the suit as soon as declarer is forced to take the other honour -- if partner has three hearts headed by an honour, does this conclusion change?

Not really.  There are similar entry issues with three (not with 4, but that's not likely on this auction) as with two, either way; and it's "giving up the second heart trick" that's the risk (versus giving up the ability to run the suit that is the risk of not leading hearts.  And, in this case, potentially conceding another trick by underleading the club Q).

It's really about looking at the hand from South's perspective.
His best suit is diamonds but they have been bid on the left, so that
North would be leading into strength is forseeable. The spade length is on
the right, so that might work better (and is actually the best double dummy lead)
but the suit isn't that great. His best bet looks like hoping North has club length
and the ace will fill a gap.
The point isn't that a club lead is effective here (it isn't).
It's that North picked an offbeat lead that lined up with his partner's preference.

What do the hearts have to do with the lead, then? Also, what is "length" and "double dummy lead"?

@Allure: Thank you for the quality question. I may have time after work to contribute another answer. However Bridge is a deep and complicated game, with endless domain-specific terminology. One of the most elementary of those domain-specific terms is double-dummy: a call or play made as though from knowing locations of all 52 cards before those cards could reasonably be located from previous bidding and play. Comments are not really the place for this. Here is a Bridge Glossary by Wikipedia.

@Allure  "Length" in this context refers to the number of cards in a suit, and particularly to the player holding the most cards in that suit. When the answer says "the spade length is on his [south's] right" it means that east holds longer spades than west does (4 vs 2 here). In general a lead where the 2nd player to the trick has longer or especially stronger cards than the 4th player tends to work better than the other way around.  The saying is "Lead through strength into weakness." Of course there are plenty of cases where this very general advice does not work well.

If South had something like Qx in hearts and xx in clubs, the obvious lead of the heart would also be the one that is the most effective. A normal North player who lead a club runs the risk of it backfiring badly. So was North taking a risk, or did he know something he shouldn't? It's very far from conclusive evidence on its own but might cause one to think twice.

I think it is exactly like the other hand, except for a matter of scale.
In the other hand, you have:
S: KQJT9
H: xxx
D: Kx
C: xxx

Here you have 4 winners and an entry, against 3NT.  The primary way you defeat 3NT is by setting up 4 winners and an entry, right?  So you lead any of those spades (the K is the conventional lead, so you choose that, but it doesn't really matter).  Force out the A, then hope to win the K later to get back in.
In this hand, you have a lesser version of the same.  Instead of 5 straight spades, you have KJT9x of hearts; and instead of Kx diamonds, you have Qxxx clubs.  But otherwise you have, more or less, some winners and an entry.  You're only facing 1NT, also, but odds are your partner has more in this hand than they did in the other one by a good bit.
In NT, it's vital that you use your opportunities to set up your running suits: so doing anything other than leading away from your suit is a bad idea, on balance.  Even though this isn't a truly runnable suit - it's broken up slightly - it's sufficiently close to a sequence such that anyone would lead from that, barring any other information.
But what's worse here is the lead of the low club, leading away from your only entry.  Now, this isn't as wild as leading Kd from doubleton diamonds, which would be totally insane; but leading a low club does two things.

Makes it more likely that opponents will win with a lower card than the Q - finessing yourself!
Reducing the number of clubs in partner's hand by one, making it harder for partner to lead to your entry!

Further, you fail to convey important information to partner - the existence of the sequence and length.  Since the standard is for you to lead from long sequences like this, parter will assume you don't have it.  This will totally mess up their ability to defend the hand - they'll think you have a totally different shape!  Maybe they'll think you have more diamonds than you do, for example.
All that together makes it a terrible lead.  The post's point is that terrible leads happen, sometimes people do odd things - but when the person is an expert, and that person benefits from the terrible lead, it makes them suspicious.

In this analysis, why does the number of hearts in partner's hand matter?

@Allure For the most part I'm not too worried about how many hearts partner has - this is bad for other reasons.  I'm not addressing why the heart lead at the table turns out bad - it's for the reason that partner has two low hearts (so your suit does not set up).  Partner needs either 3 hearts, or Qx/Ax, for the lead away from the KJT9x to work out.  That doesn't really matter to what you ought to do (that's ends-based thinking), but it does matter to why they might "cheat" here.

Are you saying that if South had either 3 hearts or Qx/Ax of hearts, then the club lead is incorrect because leading hearts would have been better, but since South has two small hearts the club lead is correct and that is why it is suspicious?

Right. If south has either of those, then the heart suit sets up. Only with two small does it not set up and leading it costs a trick.


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Should I tell opponent they can't draw a card if they try to cantrip when I have a "can't draw more than one card a turn" effect in play?
Say I have Spirit of the Labyrinth in play and opponent plays a Preordain.
Spirit stops them from drawing a card, but they might simply have forgotten about it. Or they might think they need to scry 2 anyway. If it's the latter and I tell them, it might come across as rude, but if it's the former and I don't tell them, then we'd have to call a judge with all its associated problems.
Should I tell them? If yes, when is the appropriate time - e.g. before the spell resolves, after they have scryed, etc?

You've tagged the question with several rules enforcement levels, but tags are supposed to describe the content of the question, not introduce new information not otherwise found in the quesiton. (Games tend to be an exception.) Generally people should be able to verify a tag should be present or not just by looking at the content of the question, but we can't do that here with those rules enforcement tags. Could you confirm for us which kind of tournament you're interested in, or that you are (apparently) just interested in the handling at literally every level of tournament?

@doppelgreener the question includes calling a judge, the circumstances & results of which should depend on REL.

In this situation, you're certainly not required to proactively tell your opponent that they can't draw a card. In other words, when they cast the Preordain, you don't need to remind them. When it starts resolving, you don't need to remind them. When they finish scrying, you don't need to remind them. Whether it's actually rude to tell them is a matter of opinion, not within the scope of the game rules, but personally I think most opponents who are not new to the game would be a teeny bit irritated at the reminder, because as players we're generally supposed to trust each other to act out the game correctly. (That being said, reasonable people would understand that you're just trying to make sure the game is played out appropriately, and would probably let it go if it's a one-time thing.)
After your opponent scrys, if they make a motion indicating they're about to draw a card, then you actually have a reason to think that they're about to violate the game rules. So if you do get a chance to interject at that point, it's probably a good idea to do so. But there's going to be a very short window of time where the opponent looks like they're about to draw a card but has not yet done so, so in practice it's probably unlikely that you'll get to do this.
Once your opponent has actually drawn the card they weren't supposed to draw, then it's a whole different story. That's a violation of the game rules and you must point it out if you catch it. From the tournament rules:

1.10 Players
Players are responsible for:

...
Calling attention to any rules or policy infraction they notice in their matches.

I'm surprised you don't find reminding opponent obviously rude. After all, if one is knowingly casting Preordain with Spirit of the Labyrinth in play, one is probably losing pretty badly, and do not need opponent to rub it in.

I don't think it necessarily means the player is losing pretty badly. It could very well be the case that out of the available plays, playing a spell to scry 2 is the best one, regardless of whether you're winning or losing. And I don't see reminding your opponent not to draw a card as rubbing it in.

@Allure Or they could just not have seen Spirit before and forgotten its effect after it's been in play for a while.

You do absolutely have to remind him. Accurate board states are both players responsibility.

@Neil That sounds like it should be an answer

@Allure Perceptions of what's rude differ wildly, both among different people and in different settings. It took me a few re-readings to figure out that we were considering whether reminding the opponent is rude. I frequently play games with novices, so I fully expect people to make mistakes, and I would consider not reminding them to be rude, as it would mean that I would rather let them make the mistake and perhaps profit from it, rather than help them make the game about good play and learning instead of about rules mistakes.

Depends on the REL status of the event. In high level play both players are expected to keep an accurate board state. You are not just required to keep your play accurate but ALL play should be correct. At the high-end tables it is expected that correct and better play should lead to wins not just the happenstance of who forgot what triggers. Remaining silent for a benefit when you see something illegal is basically cheating (at this level).
At pre release or fnm is more casual in nature so I guess you could probably get away with it there, but you risk alienating your whole store. For what exactly 3 packs more worth of prize support in a tournament that is not even reported half the time?

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Whatever happened to leading the 4th highest card of your longest suit?
Sort of a follow-up question to Why is this club lead suspicious when partner has two small hearts? and Why is the King of Spades the best opening lead with this hand?
In both those examples, the contract is No Trumps. I vaguely remember reading that in No Trumps, the 'standard' lead is the 4th highest card of your longest suit. That would mean leading with the 9 of Hearts in the first example and the 10 of Spades in the second example. However, the "expected" lead in both cases is a higher card (the J or 10 of Hearts in the first example, and the K of Spades in the second).
Whatever happened to leading with the 4th highest card? A first guess is that I remembered wrong, but a quick search reveals that leading the 4th highest card is still something that's taught (example).
Alternatively, leading a high card indicates you are not following the "4th highest" convention - for example if I lead the K, then I obviously can't be leading the 4th highest card since there is only one card higher than the K, and this indicates to partner that I am using an alternative convention. However, in this case the J or 10 of Hearts lead in the first example would be ambiguous, since I can conceivably have the AKQJ. A thought would be, if I did actually have the AKQJ, why didn't I bid Hearts? But even then there are lots of possibilities ... maybe my other suits are dismal, for example.
I'm looking for an explanation why the "4th highest" convention doesn't apply to these hands, especially since none of the answers to either question mentioned it so it is apparently not relevant.

You may want to get a copy of the Mike Lawrence book on Opening Leads. Also, there are two books from a few years ago: "Winning Notrump Leads" and "Winning Suit Leads" by Bird & Anthias; they used computer simulations to determine the best leads in many situations.

When selecting an opening lead, there are two decisions that you must make. First, which suit should you lead? Second, which card should you lead from that suit?
Most of the "rules" about leading address the second question. "Fourth highest from your longest and strongest" addresses both. It's an easy rule to remember, and it's usually not a terrible choice, so it is taught to beginners as something to do while they gain enough experience to learn when other choices are better.
In the particular cases you've linked to, leading from the longest and strongest suit is likely the best choice, but the standard lead is not fourth highest. Why is that? Experience has shown that, when leading against no trump from a suit with a (possibly broken) honor sequence, you are most likely to get your full share of tricks by leading one of those honors. Let's look at your examples.
From KQJT9 xxx Kx xxx, you are on lead against 3NT. You have an excellent 5-card suit and at least half (and likely more) of your side's high-card strength (opponents likely have 24-30 high card points combined based on the 1NT-3NT auction). Leading a spade means that you will defeat the contract if any of the following is true:

Partner has a stopper in a suit they need to play on and enough spades to play one back at that time.
Declarer has the diamond ace and needs to play on diamonds to get to nine tricks (the finesse into your hand will give you the DK and now you can enjoy the rest of your spades).
Partner started with the spade ace and at least one more spade.

Two of these depend on partner knowing what to do in whichever situation you find yourselves in. If they have Ax in spades, they have to know to go up with the A at trick one and continue another. If they win a trick in another suit, they have to know that continuing spades is correct. The way they know this is that you've played the SK, which shows a suit with a lot of honors. Leading the ten does not give this signal - you would have to lead the ten from Tx, T9x, QT9xx, etc (we'll see why next in the last case, but just trust me on the others) - so partner may decided that the best prospects for the defense are in another suit.
In the other example, you hold T87 KJT92 J Q852 and are on lead against 1NT. Even though your partner has the bulk of your partnership's high cards (opponents are limited to at most 24 points by their auction), you are most likely to defeat the contract if you can score some heart tricks. One way to make sure that partner knows this is to lead a heart. But which one? Well, let's think about some honor layouts. Let's ignore signaling for a moment, and just consider how many tricks you can take in double-dummy play. If partner has the HQ, it doesn't matter too much which heart you lead - partner will play the Q and you will eventually force out the ace. If partner has no heart honor, it also doesn't matter which heart you lead - if declarer haS the Q you've already blown a trick, and if dummy has the Q it was always scoring. The situation where it does matter is when partner has the A but not the Q. Here, if you lead one of your middle cards (J, T, or 9), and dummy has the Q, you are running a finesse. Partner will duck if a small card is called from dummy so that you can repeat the finesse, or win the A if the Q is called. If declarer has the Q instead, partner wins the A and returns a heart so that you can finesse against the Q. In this way you are likely to take five heart tricks off the top, sending you well on your way to defeating the contract. Suppose you had started with KJT32 - now leading the 3 is ineffective when dummy holds the Q and partner the A because partner will have to play the A regardless of dummy's play.

Fourth highest is from a suit with no sequence - four small, or one honor and three small, that sort of thing. It’s a good lead, it gives you some chance to promote one or more of the small to a trick.
However, when you have a se quence it’s important to lead from that sequence for two reasons. First, you may give up a trick if you don’t - in the absurd example you have AKQx, you can see that - but KJTx would also possibly give up a trick if you lead x.
Second, though, is that you communicate the sequence to partner. KJTx is very powerful - partner will definitely lead it back.  xxxx, maybe partner doesn’t lead it back - maybe they have a better choice.  Since the agreement is that you lead away from the sequence in a particular way, leading low denies the sequence.

I would strongly suggest, if you are interested in this, or the arguments on the site you're getting the other questions from, that you find a second-hand copy of Watson's The play of the hand at bridge, and read until your mind explodes (it will.  Even if you're an experienced bridge player, it ramps from "an Ace is higher than a King" to compound squeezes Very Quickly.  In fact, when I recommend Watson to bridge players I tell them to start from page 1 and read until it stops making sense, then put it aside for 6 months.  Then do it again - from page 1! They'll find that there were things they didn't notice last time that are "oh yeah, that" now, things they weren't sure of that make sense on second reading, and they'll get farther.  Probably not to the end, though.  Repeat every 6 months - always from page 1.)
Bridge leading and carding theory has advanced since it was written in the late 1950s, but the introductory chapters on defence will answer your question better, and more completely, than we ever could.
The other answers have given the basics - a sequence lead from three connected (AKQ, KQJ, QJT) or one gap (AKJ, AQJ, KQT, KJT) is a higher chance to set up the suit than low, so it's "standard". (what card to lead from those sequences is arguable, but "one of the sequence" isn't.)
Apart from "what's most likely to win the most tricks", the benefit of fourth-best leads, when that's "standard", is that partner can work out the count of the suit and the location of the missing cards.  Look up "rule of 11" if you want to see that in action.  With that information, partner can decide what card to play, and whether your side should continue the suit or not.  But "I have a long suit to one of two or three sequences" is much more useful to work out what card to play and whether to continue the suit than just count - and when you do lead fourth best (or top of nothing, which you use at notrump when fourth best is also wrong), partner can use the fact that you don't have one of those sequences in using the rule of 11 to determine what cards declarer has (or work out that you can't be leading fourth best, therefore top of nothing).
A final reminder that first, you decide what suit to lead, then you lead the "standard" lead from that suit.  But KQJT9 or KJT86 in an unbid suit is a really good argument that that's the suit to lead.

I would suggest Card Play Technique ; Or, The Art of Being Lucky by Nico Gardener and Victor Mollo instead of or in addition  to Watson, I think it is better written and more useful. But aside from that I fully agree with this answer.

I don't know that one, but anything on play by Mollo is going to be good.  I like Watson because of his rigour and deep explanations, especially at the "beginner" end (which he then uses at the "next-to-beginner" chapters to good effect).  But yes, Watson is a textbook, as bland and dry as any other textbook.  Fair warning.

Card Play Technique Unlike most of Mollo's works is a textbook, but one written with all the style and wit Mollo is known for, as well as the bridge skill both he and Gardener  were known for. I still find it enlightening after 40 years of playing and trying to learn. Still in print and deservedly so. recent edition has an Intro by Mollo & Gardner's joint daughter/stepdaughter. (The authors were married, in succession, to the same woman, and remained partners)

Louis Watson's book is very good but also very old -- published January 1, 1959. My advice is that you get a regular partner, if you haven't already, and try and agree what specific leads the partnership will use.

If you don't know why "standard", then your partnership agreement will be inferior, even if the agreement itself is not inferior.  And Part 1 of Watson explains "why standard" (along with the basics of play) better than anything else I've ever read.  2) I would agree with you in general, but this question thread is written by someone who doesn't play bridge, but wants to understand the basics of the 2015 scandal.  They don't need to be up to date on Rusinow/intra-finesses/Lavinthal/3rd-and-low... just understand the basics, which really have not changed since the 1950s.

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Can bridge-style duplicate play work for Magic and other CCGs?
As I understand bridge, you form teams with four players even though only two play at a table. The idea is that there are two identical hands. Two players in your team play North-South with one of the hands, and the other two players play East-West. This removes luck as a factor because if you are very lucky with one hand, opponents will be equally lucky on that hand. Both you and the opponents are going to win the hand, but if your team are the better players, then you should on average win the hand by a larger margin than opponents.
Will this work for Magic: the Gathering and other CCGs? Here's a sketch of how it might work:

You register for a tournament with two players and two copies of the same deck. For Magic, this would be 150 cards (60 cards + 15 sideboard per deck).
The cards are numbered and shuffled by a computer, resulting in a random sequence of 75 numbers. Then an arbiter manually stacks the decks, removing cards that are in the sideboard.
One of your team exchanges decks with the opponents. Now you have the exact same match playing out for both players on the team.
To deal with cards that shuffle the deck, each time the deck is shuffled, have the computer generate another random sequence, and remove the first card that is searched for. For example if I have four copies of Steam Vents and I search for one of them, the first copy is removed in the random sequence generated by the computer, and the rest of the deck is stacked following the sequence. The sequences are shared in both matches to make sure both decks are still stacked in the same way.
In the same way, we remove all numbers corresponding to cards not in the deck from the random sequence. This handles sideboarding even if both players don't sideboard the same way.
Absolutely no communication with teammate once the match starts, since it can reveal which cards are in opponent's hand.
This can provide some way to tiebreak draws. For example if our team's deck has a strong matchup against opponent's deck, and I win 2-0 while my teammate loses 1-2. We win the match because the net score is 3-2. Alternatively, if I win 2-0 and my teammate loses 0-2, but I win in 10 turns (summed across both games) while my teammate loses in 7 turns, then we lose the match since opponents arguably played better (not ideal since one can reasonably decline to win to play around certain cards, but it is a way to break ties).

Some obvious consequences for this could be:

Deckbuilding is less important since the effect of a good deck is washed out. One could show up with a deck of 60 Plains for example and still play an equal match against the opponent. However in this scenario you will need to pilot the opponent's deck as well as they can, and presumably they are going to be more practiced with their deck, putting you at a disadvantage.
You need to learn more than one deck, since you'll need to play with more than one deck in a tournament. However this doesn't seem fatal: it's arguable the most skillful player is the one that can play most decks at high level.
This might not work in limited, unless teams draft together and then acquires a second copy of the same deck from somewhere.

Presumably if this works it'd work best for digital tournaments since it removes a lot of manual work. On the other hand, perhaps it won't work at all because there's some fatal flaw in the setup. Can anyone see anything that might go wrong?

Isn't #1 already a dealbreaker?  A team of goldfish could show up with a deck of plains and be guaranteed to win exactly half their matches, no matter how good their opponents are.  That sounds like a broken game to me.

@ArcanistLupus how can you be sure they will win half their matches? The setup forces the matches to be on equal footing, but it doesn't guarantee a win for either team. If one plays badly, one is still going to lose (c.f. last bullet point).

how, pray tell, will a deck with 60 plains and nothing else beat an opponent with a regular deck playing badly?

@ArcanistLupus so you won't win - but if opponent wins the reverse quicker, they'd still win the match (c.f. last bullet point).

That's still a degenerate game where one player is trying to win against a goldfish quickly instead of playing a real game, and the other player is playing nothing at all. And it still favors the player that knows their opponent is a goldfish in game 1.

Most decks, when given the same hand, are going to goldfish (win against an opponent who does nothing) at the same speed regardless of who plays them.

@ArcanistLupus you sure? Would you have been able to win this game?

The most complex deck you can find is not a real counterexample to the claim that most decks are not that complex.

@murgatroid99 thinking about it, games would likely have to be played with open decklists because it's not practical to pilot a deck without knowing what's in the deck. In fact teams would likely look at opponent's deck and discuss who should play with the opponent's deck. So there is no knowledge advantage in game 1 - if one team submits 60 Plains, all players know they are in a goldfish situation.

@Allure Moreover, without open deck lists, deliberately designing decks around tricking a player who doesn't know its content into piloting it poorly would become a major strategy.

@murgatroid99 I think this hypothetical format would have to have rules for the mana base. No more than 24 lands and at least 8 color sources for each color in the deck. Then each player builds the worst deck for another player to pilot. You probably just end up with a collection of terrible limited decks but who knows that could be fun.

In fact the amount of lands should be forced into relation of the average cmc of non land cards in the deck. So a cmc average of 1 - 3 would get 22 lands. If you make a 5 color version the 22 lands would have to have 40 color sources 8 of each color. So that could give you two of each guildgate and two wastes.

I could easily build a deck with those constraints that cannot win the game and can only damage itself. The deckbuilding challenge itself is interesting but the resulting gameplay isn't.

Deckbuilding is part of playing a CCG.  Playing a game of Magic with a deck you had no control over is like playing a round of Bridge where someone else did the bidding for you.
Any proposal for playing a duplicate CCG involves at some point playing a deck assigned to you by the format, created either by your opponent or by the competition's hosts.  And that's fundamentally anathema to the concept of a CCG.

While I agree with this in general, there are a lot of Magic events where you play decks you have "no" control over, especially on Arena.  The whole idea behind Jumpstart was "take two precon halves at random from 30 or so, mash shuffle them, and play."  Events like the Arena Worlds event played along side the WC, where people got to play with one of 7 former worlds-winning decks are not ubiquitous, but not unheard of either.  And as a casual player (years ago), I've always enjoyed "hey, can I borrow a deck?" - I personally hate deckbuilding.  So, not anathema.   Just not "normal".

@Mycroft Ah, but in every case but a few explicitly random (and highly noncompetitive) events, you always get to choose your preconstructed deck.  Even when you say "hey, can I borrow a deck", you're making a choice to play whatever you're given.  Jumpstart (at least on Arena) explicitly has you draft your deck halves.  You still have agency over what you play.

Even choosing to play blind is still a choice

Some of the Magic Invitational tournaments included “duplicate sealed” events — players are given identical pools, but deckbuild separately.

Not sure this is an answer, but it certainly isn't a comment. Sentences in [brackets] are ignorable side-notes.
In team-of-four bridge events, including the world championships, the two tables in the match are set up so that each team puts one pair N-S at their "home" table and E-W at the other team's home table. Then the same hands (6 is a "short" match, 24-30 is a "long" one, 50-60 is a "day-long"; the finals of the world championships are 192) are played at both tables, and the scores for each pair on the team are added together.  If the sum is positive, you "won" that board; if negative, you "lost" it.  [Most of the time, the scale of the win on each board is important; but that's not relevant here].  Like Magic tournaments, there are hundreds of other tables playing (frequently) the same hands, but only the two tables for your team and your opponent matter to you; the results of all the other matches do not affect your result, just the standings.
[In pair events, the same hand is played multiple times and your results are compared to every other pair who played that hand the same direction (N-S or E-W). The more you beat, the better your score on that board.  The reason team-of-four is usually considered more prestigious is that "the field" can be really random.  Not quite an accurate comparison, but consider "swiss pairing" with "you will face 3 of the top players in your 9 rounds, and 6 others at random.  Matches are set at the beginning of the event and will not change based on results." (also, usually, you won't know the results of anyone else until the end of the event, for what that's worth)]
The difference is that in Bridge (and duplicate Scrabble, and Poker, etc.) the only variables outside of playing skill are the cards, owned by nobody and the same at each table (and the same 52 cards on each deal).  It's a matter of skill and judgement (and bidding system, which is kind of but almost totally unlike deckbuilding) as to who does better with each deal presented to them at random.
I guess in Magic, you could get two players to bring in two copies of a deck, and have them shuffled and duplicated and one given to the "away" player of the other team (let's just not do this in Legacy, at least without proxies, eh?), and play two matches, "our decks" and "opponent's decks".  You'd end up with either two wins, two losses, or a win and a loss (okay, draws, 1-0 vs 2-0 vs 2-1 wins, ... ignore them) scoring I assume 3-0-1 points as normal.
You'd bring one player that is really good at piloting the deck their team brought, and one player that is really good at piloting "anything they decided to bring", against the deck you brought.  I assume decklists are provided to the away player before the match so they at least know what cards are in their deck?
(now, if your "home" deck was a Shared Fate build...?)
Anyone who brought "60 plains" would lose their home match, and likely win their away match, drawing every round and placing well down the rankings.  And wasting everybody's time as well.
Of course, the "pattern" of the deal is static in bridge (players have access to their entire unplayed hand at all times) in a way that fails at Magic as soon as the first shuffle takes place - so that the "computer shuffle to ensure the decks start in the same order" will remain relevant on average, what - two turns?  So that doesn't lend itself to duplicate play much either (duplicate Scrabble has a fixed (for each match) tile drawing order; duplicate poker plays the same cards in the same order, but with no shuffling until the next hand).
A gauntlet, where everybody is paired against the same AI-controlled opponent, playing the same deck (but a different "same deck" each round) might have some of the duplicate style.  But "competent Magic AI" is right up there with "spherical object of constant mass and uniform density": good for theory, in practise doesn't exist.

One of the things that makes duplicate bridge work is that, once the cards are dealt, the random factors are mostly fixed.  The decisions people make in the middle of the game don't tend to change which unknown random factors are important and which are largely irrelevant.  No matter what decisions people make throughout the bidding and play of a hand, if one on sequence of player decisions it is important which player is dealt the Queen of Hearts, on a different sequence of player decisions it will likely still be important who is dealt the Queen of Hearts.
This is in contrast to Magic or any other games where random factors enter the game not all at once and possibly at different times depending on player decisions.  It could turn out in Magic that the order of 2 cards halfway down the deck is crucial in some games and completely irrelevant in others, because some decision made on the first turn meant that those two cards were drawn simultaneously (or tutored) in one game and in different turns in another.

In a spade contract that can be won by cross-trumping, the QH may be quite irrelevant, while in a heart contract it may be vital, and in a NT contract significant but not vital. Or one pair might use it as an entry making it vital, while a pair taking a different line, or played from the other direction, the entry potential may be irrelevant. All that said, I think the overall point is largely valid.

any tutor changes the context of the deck too much for any stabilization between games,   especially in the first few turns if you don't know the match up since it might change the color of lands you want to grab.  If I know it will be mostly about controlling the stack over going fast could be the difference between getting blue source or a red/black source depending on my cards.

Duplicate bridge exists because bridge is a highly random game - if you don’t, then the deal determines who wins far more than the play.  The deal is zero sum - opponents rarely have evenly matched hands.
TCGs are totally different: each player makes their own deck, and they’re positive sum - both decks can have the best cards (equally). That’s most of the skill!  A good deck maker who successfully predicts the meta and knows how to play the deck reasonably well will do better than someone who gets the meta wrong or has an inconsistent deck.  Duplicate style takes this away.
TCGs are also much more tolerant of ‘gambling’ randomness. Bridge grew up in a time where it was a problem to be linked to gambling.  It made a huge effort to differentiate itself from any gambling ties - making it as much a game of skill as possible. TCGs on the other hand are all about gambling - they’re fine with the randomness. Making a deck that reduces randomness of course is also a good thing!  You’d actually massively change the balance of the meta this way. Consistency would go out the window!
Further, it’s not possible to take TCG play and remove all of the randomness. You have to shuffle during the game sometimes - Pokémon in particular but all of them have some shuffling typically. So even if you had both players play pre set decks, they’d add randomness the first time they tutored a card. Taking out shuffling the way you describe fundamentally changes the game - particularly Pokémon where there are plenty of elements that involve setting the top card and other elements where you shuffle the hand into the deck.
Finally, the folks who put on the tournaments - either the TCG publishers or folks they sponsor - wouldn’t want this, because the point of the game is to sell cards - having ‘fair’ matches means you don’t have the incentive to build more decks and spend more on cards.

I do address that ("Taking out shuffling...").

First, duplicate bridge is played in teams of two because bridge itself is played in teams of 2. It is a feature of the game, not the duplicate tournament style, so there is not necessarily a reason to have teams of two here.
In addition, the tournament setup described here does not really reflect duplicate bridge: in duplicate bridge, in different rounds pairs play different hands against different opponents, instead of playing the other side of the same hand against the same opponents. This would be more directly reflected by pairing up decks at the beginning, and having counter-rotating pairs of player play matches with the corresponding pairs of decks. Then each player's performance per round would be compared with other players playing the same deck.

Second, this proposal does not accomplish the same degree of sameness in game options that duplicate bridge does. Even with shuffling being fixed in the way described, the game is practically random from the point of view of each individual player because they have to make choices based on hidden information, and those choices can influence their future options, which can cascade into wildly different games.
For example, say the opening hand contains a Scalding Tarn. Player A plays and activates it on turn 1, and shuffles. Player 2 plays a different land on turn 1, draws a second Scalding Tarn on turn 2, and plays and activates both fetch lands in the next couple of turns. Now the two players will likely see a wildly different sequence of draws for the rest of the game. Those different draws can easily result in the players interacting with their opponents differently in ways that result in their opponents having different options and needing to make different choices.
In short, the outcome of the game can still depend more on luck than skill. In this case, the luck is simply with whichever player happened make choices that would be advantaged by the shared random sequence, instead of whichever player got the better random sequence.
This doesn't even account for other sources of randomness in Magic, such as coin flips, dice rolls, and random choices. How would you even try to align player outcomes for cards like Capricious Efreet or Dementia Sliver?

Third, your proposal of breaking ties based on number of turns in game is fairly arbitrary, and has no connection to any existing way that Magic games are scored. That could easily have a bad effect on deckbuilding or game play as players try to optimize for that scoring condition.

About 1: I'm pretty sure duplicate bridge is played in teams of four, not two. Half your team plays one half of the hand and the other half of your team plays the other half of the hand. Dice rolls can presumably be handled by creating another random sequence. Finally I don't think Magic has any ways to break ties in otherwise-drawn matches right now. Are you aware of any such ways?

I can't find anything about duplicate bridge being played in teams of 4. Wikipedia says "In duplicate bridge, a player normally plays with the same partner throughout an event. The two are known as a 'pair'." There's nothing about multiple pairs in a team playing different halves of the same hand. Fixing the sequence of die rolls doesn't account for the different values of the same die roll depending on the different choices made. That's why I brought up those specific cards.

Example: https://www.hamiltonbridge.com/Articles/TeamGames.html "In a team game, you play on a team of four players. Your team plays against another team of four players for the duration of the match. You and your partner take either N/S or E/W at one table, and your teammates take the other direction at a second table. The opposing team does the same."

I see, there is a variant of duplicate bridge in which players play on teams like that. From other things I've heard and read, I don't believe it is the common tournament style. I don't actually play bridge, though, so I don't know for sure.

Regarding draws, it is usually valid for a Magic match to simply end in a draw. Single elimination rounds have a tiebreaker based on which player has the most life when time is called, if the match would otherwise be a draw. On a broader scale, Magic tournaments have tiebreakers for the whole collection of matches, based on a variety of factors described in Appendix C of the tournament rules.

Yes, but draws are not desirable for either player. I strongly suspect the reason Magic matches ends in draws is because nobody has been able to come up with a good way to adjudicate a match for any player. I believe at one point matches were adjudicated by life totals, which is obviously bad for many matchups, but that's making the best of a bad situation. The tiebreak method in the OP would be similar; if people prefer to have draws then by all means, draw.

Duplicate bridge is commonly played as both pairs and teams ("Teams" means four or more, typically 4 active at a single time with sometimes some "bench" pairs who swap out).   The highest level of play is primarily teams (of 4), i.e. the Bermuda Bowl, but probably most tournament play is pairs.

@murgatroid99
Most bridge tournaments include both pair events (two players playing as partners) and team events (4 or more players on a team, exactly 4 playing at any given moment). Many players consider team games the better test of skill, and for that reason most championship matches use the team form. Club games typically use the pair form. Rubber (non-duplicate) bridge normally is played by pairs.

Could also mention the insane logistics of having a computer decide every single deck shuffle and having a judge order the library according to the result. That alone makes this  proposal digital-only, if anything.

The question does acknowledge that it would work better in a digital game so I didn't feel like going into it myself.

You are also not grasping the reasons why people prefer tcg over poker/bridge. There is an inherent unfairness to tcg that you don't have in casino card games. If you where a legacy elves player queuing into a miracle deck then no matter what you did you will not win more than a third of your matches. Proper assessment of the meta is crucial we call this favourable matchups.
This why I enjoy MTG over poker. Although I have played a fair bit of both. Tcg gets new cards added all the time. These games are in a constant state of flux. Although metas these days gets solved awfully quick. Your success at tournament tables are determined to great extent before the first hand is dealt.
Trying to change this fundamental aspects of magic the gathering is simply not going to work.


text:
Is there an AI that can build decks?
Examples of the games I have in mind are Magic: the Gathering and Pokemon Netbattle (the latter is not a traditional card game, but it does involve teambuilding so should be similar).
AI can beat the best humans at a variety of games now (most recently Go and Starcraft 2), so they are undoubtedly good players, but can they build decks? For example, can one feed an AI all the Magic: the Gathering cards currently available in Standard as well as the deckbuilding rules (in Magic: the Gathering, that would be "not more than 4 copies of a card per deck unless it's a basic land", "not less than 60 cards", etc) and have it tell you what the best decks are?
It sounds like a formidably hard endeavour, especially since once your list is known your opponent can "counterbuild" by adding counters vs. your specific deck, so I'm guessing there is no such AI. If that's indeed the case, I would be interested in any attempts at creating such an AI.

I would look at Kyle hills video on if it is possible to play a perfect game of magic to see why AI hasn't gone in this directions.  Especially with a game like magic you can build a deck to deal with one type of deck but would lose to another type so it is not that there is always one best decks.

This seems a challenge AI would be suited for, likely much simpler than Starcraft 2 for example.

@Styxsksu sometimes there is a "best deck", though.

@NPSF3000 Magic is Turing-complete. I doubt very much that it's simpler than Starcraft (in the general case).

@wizzwizz4 start craft is real-time, has fog of war, each unit has real world positions and can take time to move, there is geography, etc. Not familiar with magic, but comparatively it seems like a much simpler optimisation problem.

@NPSF3000 Magic games can (with certain decks) take multiple years to play.

@Allure if it is a health Meta then there shouldn't be one best deck and there is normally a little bit a flexibility with a few of the cards and that is a big problem when trying to program a computer to build the perfect deck.  The counter building is what makes magic such a great game.  You normally can build a deck to counter a strategy that might not win agonist most other decks but would beat the top deck.

@Styxsksu not every meta is healthy though (c.f. Eldrazi Winter, Aetherworks Marvel). When there is a clear best deck, the AI should ideally be able to identify what that deck is, even if it can't identify all 75 of its cards.

There are certainly ways an AI could assist. You can create a tool that assigns cards a relative potency (within reason) and use that to help with card selection and/or pruning. And, you can run some basic stats level and even perform a Monte Carlo analysis to maximize your gameplay consistency. (MTG Deck Analyzer does a little of each of these). But, there's somewhat of a rock-paper-scissors mechanism in MTG. I suspect an AI would find many local maxima and almost never find a clear global maximum.

@wizzwizz4 and?  If humans can play a game for years, an AI can do it in a fraction of the time.

The Go example is more relevant than the Starcraft one. Starcraft AI's have the advantage of very precise and consistent mouse-movements that are humanly infeasible. Deckbuilding is less like that, and more like Go, in the sense that self-play seems to be the most reasonable approach. It is probably best to start with a simplified, though interesting "format". For example, one could consider the set of cards including all sliver creatures and all basic lands. It seems non-trivial to design an effective deck for this format, yet not too difficult for an AI to find something decent.

There is now, if you play MTG Commander: https://edhgen.ai

First, just so you know where I’m coming from, I’m a professional programmer, and I’ve studied AI, but I don’t work with AI professionally, so there are limits to my expertise. I defer to anyone who is an expert in AI, but I think currently my expertise is most applicable to this question. That said,
There is a major constraint on the way we currently build AI, that makes its application to deck-building games intractable, at least on our current hardware.
Our general approach to AI—“machine learning”—involves the AI trying some random approach, evaluating it for effectiveness, and then doing so over, and over, and over, refining that randomness towards something better and better.
It is absolutely crucial, in this scheme, to be able to tell how good a given random try was. To learn, the AI needs to know that attempt 1354235 was better, or worse, than attempt 1354236. In a large sense, this is all machine learning requires, which certainly makes it very powerful, but it is a hard requirement. We need to be able to assign a number to how good a try something was, because what the AI is really doing is maximizing that number (or minimizing, whatever).
To my knowledge, no deck-building game out there enables any easy calculation of the general quality of a given deck. What do human “optimizers” of the game (e.g. pros) do? They create a deck and play it a lot, leveraging their considerable experience. Not just to see how it does in a variety of situations—but also to learn how to play it, that is, figure out the optimal strategy for playing the cards the deck makes available.
So here, for each deck, the AI wouldn’t just be able to obtain a number for how good the deck is—they’d have to have some sub-AI that’s training with that deck, learning how to optimize play with that deck. Since machine learning requires thousands or millions of iterations, having each deck iteration itself require thousands of strategy iterations just to learn how good the deck is, is going to be a huge problem. Our computers simply aren’t fast enough to get through all of that in a reasonable amount of time.
And there isn’t really any way around this. If you just program some game-playing ability into the AI, so it doesn’t iterate its strategy, it just tries to play, you aren’t really learning about the potential of each deck the AI comes up with. You’re just learning how well that deck happens to match the strategy you pre-programmed, which is probably not going to be terribly interesting or useful.
The way humans get around this is through heuristics—which roughly means something like “rule of thumb.” We have ideas about what is or isn’t a good idea, we can evaluate at least some options on paper as just not worth considering. Our brains are very heavily optimized for this task, and we do it constantly, considering only a tiny subset of the possibilities before us, based on our experience and understanding, to keep everything manageable. But the power of AI is to avoid these human heuristics, try out things that we never would have considered. We don’t want to influence or narrow the potential solution space—the whole point of this exercise is to explore it more thoroughly than a human can do.
We’re not there yet. When we have working deck-playing AIs for one of these games, where the AI can take a random deck and optimize playing that deck, then we can think about optimizing the deck-building part of things. But ultimately, the only way to know if you’ve built a good deck is to play it, so start there.

" Since machine learning requires thousands or millions of iterations, having each deck iteration itself require thousands of strategy iterations just to learn how good the deck is, is going to be a huge problem"
Why is this a problem different than say Chess or Starcraft?  There are more possible permutations than any computer could ever calculate.  AI is just a method of exploring the problem space and coming up with a reasonable answer using, essentially, statistics.

@NPSF3000 The difference is very simple: chess and Starcraft require that number of iterations to play. But we’re talking about building the deck first—and in order to test how well we built the deck, we need to then do that many iterations for each deck. So if we can manage n iterations (which are enough for chess and have been making progress with Starcraft), we now need n ² iterations. Since n was “what we can manage,” we can’t manage n ².

It's also that twice - not only is your deck not a constant, but neither is your opponent's deck. Playing chess is like saying "given these two fixed decks, optimise your playstyle with one against the other". It's not analogous to "make a good deck".

@RobGrant I’m assuming that the competition is decks from previous iterations, whose play has already been optimized. But true, the variety of decks that must be considered adds another factor that expands the steps necessary to optimize play.

These seem to be issues of scale, rather than fundamental barriers. I think that starting with a very limited card-pool should be tractable on even consumer level hardware. Something like standard might be feasible using a high-end server cluster. It is hard to tell this in advance, many people thought Go would be out of reach from AI for years. Besides, why would so many play iterations nessecary? The goal of most decks is consistency, to get the same hand most of the times. With a bit of clever sampling, 10 self-play iterations might already be sufficient.

Also, there are already Mtg games with computer controlled players that play a deck decently. I don't think learning to play the deck would be that complicated.

@Discretelizard You are, quite simply, wrong about the scale of the task involved. I don’t really know how I would go about proving it to you, but the number of variables here is much, much larger than anything we’ve successfully tackled with AI to date.

Sounds like Pokemon Netbattle is much easier to attack than Magic: the Gathering. There are only 9 choices per turn, and maybe 40 turns in total, but it should be relatively easy to identify who is winning at some of the leaf nodes.

"Since n was “what we can manage,” we can’t manage n ²."
We can't manage N.  The problem space of starcraft is enormous. AI in these cases is just statistics figuring out how to find a reasonable solution within those constraints.
Keep in mind Starcraft has a full map where units can go anywhere at any time. Starcraft has build orders.  These things are dynamic and can change. A starcraft AI has to be able to work against different players doing different stratergies.
In comparison, Magic does not seem any more challenging.

@NPSF3000 True; I’d had chess and go in mind with that comment. StarCraft is definitely intense for this approach.

@KRyan Perhaps. But they are merely issues of scale. These are issues where AI has kind of a track record in surpassing expectations, in particular if an organization like Google throws clever people and money at it.

@Discretelizard Yes, surpassing expectations is very much a trend in technology—but this is already me hedging my bets in deference to that. We are not remotely close here; even if we manage to maintain exponential growth, we are a long way away from the necessary scale. I suspect that “simply” scaling up won’t do it—we’ll sooner see some revolution in hardware (quantum? I am not knowledgeable in that realm but my impression is that it’s best for handling large combinations like this) or software (singularity?) that would enable something like this.

"where the AI can take a random deck and optimize playing that deck": It is possible to construct a Turing machine in Magic the Gathering, at least in Legacy, see https://arxiv.org/abs/1904.09828. Therefore deciding optimal play in Magic is equivalent to the halting problem and no such AI can exist.

@CainGoldhardt Magic is Turing complete, but that won’t be a problem here. We do not need to solve, in the rigorous, mathematical sense, the optimization problem, which is honestly something that almost never can be solved, often even if the system isn’t Turing complete. That’s why we turn to machine learning in the first place. The distinction here is that we are not attempting to determine the optimum, only to optimize, that is, through successive iterations improve our play in some meaningful sense. And that can be done. (A timeout to turn undecidable cases into ties may help.)

@Discretelizard "Perhaps. But they are merely issues of scale" - issues of scale indeed, but most of AI (and non-AI) can be handwaved away to being a way to deal with "issues of scale".

All I'm saying is that I remain unconvinced by qualitative arguments if the problem is in the quantity.

The issue pointed out in this answer is probably the main issue that's blocked the development of an AI to automatically build MtG decks. One workaround I can think of is to develop a language that can encode a strategy; and instead of developing an AI that builds a deck, develop an AI that builds a pair (deck, strategy).

Don Goodman-Wilson made a program to build decks given a pool of cards. (I guess you could make the pool 60 copies of each card legal for the format).
From his post on Hackernoon:

So I started building just such a tool. Read along to find out how it works, how you can start using it, and better yet, how you can help make it awesome.

In this article, I want to outline at a high level how I approached this challenge, how my approach works, what went well, and what didn’t. If you just want to jump directly to the code, or a deep-dive into the technical nitty-gritty for yourself, you can dig deeper on GitHub.

In particular, I want to talk about an approach to deck building using a technique called genetic algorithms or GAs. GAs allow us to literally evolve good decks using artificial selection. Ooooooooh! Yes, it is as exciting as it sounds!

The article goes on to talk about the approach he used. And it links to a GitHub with the source.
As the comments note, this may not be a high quality attempt nor one that handles any card set set you throw at it, but it is an attempt, as per the original post's request:

I would be interested in any attempts at creating such an AI.

His program requires you to manually annotate how many creatures, artifacts, enchantments, instants, sorceries, and lands you wand in your deck, and most importantly requires you to manually annotate how synergistic each card is with certain archetypes. This is functionally most of the work that goes into constructing a deck in the first place. His program has no mechanism to actually read the text on each card other than mana cost and power/toughness, so would not work at all to make a deck from a new set, for example.

@BradyGilg Extracting the text from cards is an easy problem (Arena has it in a nice JSON format). The rest of your criticisms are very valid though.

@PhilipKendall Reading card text is easy, interpreting it for the purposes of deck building is not.

You will need a good playing-algorithm.
The most straightforward way is by running a tournament of sampled decks:

Sample decks (randomly / heuristically / using some data)
Play many games using identical playing-algorithm. This way the only difference are the decks.
Keep the winner(s).

bypass: sample strong decks from a DB (for example: hearthstone top decks).

This sounds like a "here's how it could be done" rather than an answer to the question (examples or examples of attempts).

@L.ScottJohnson, you have a point but my answer is not just a theoretical hypothesis. I think that If I will look hard enough I will find algorithms that work exactly that.

... decks don't play each other. People play decks.

@ArcanistLupus The "many times" constraint somewhat implies that the decks will be played by a computer rather than a human. I doubt that will be too much of a problem, given how strong MCTS algorithms have become at card games like Magic.

@Stef - just because the work has already been done, doesn't make it trivial work.

@Stef is there Magic-playing AI that can match the best players in the world? If so, can you point me to results?

@ArcanistLupus, People can not play many times.  Algorithms do. For example, Alpha Star agents played up to 200 years of StarCraft.   https://deepmind.com/blog/article/alphastar-mastering-real-time-strategy-game-starcraft-ii

@Allure I haven't been following that close; maybe you can find interesting research papers on google scholar: scholar.google.com/?q=magic the gathering ai or on DBLP: dblp.uni-trier.de/search?q=magic+the+gathering

ChatGPT can do this, but not terribly well.
ChatGPT is a text generation AI that's been trained to statistically generate the miat likely text based on a corpus of writing that is basically the entire Internet.
This includes a whole bunch of Magic: the Gathering deck lists.
As a result, if you ask it to build you a MtG deck list, it will happily do so for you. It will promptly give you the statistically most likely text for your prompt, which will most likely be a list of competitively viable MtG cards.
Whether that deck would be good (or even legal) is something that it's not capable of judging, however, since it doesn't understand anything about the actual game, and it's not capable of doing things like counting how many cards it's putting into your deck or understanding that a card that used to be strong has now been banned.
It's just generating text based off of the text that humans who are capable of playing the game have made.

ChatGPT can do this, but terribly bad

Hi. Interesting, but is there any reason to believe that the produced deck would be any better than the human-made decks that it takes inspiration from? In fact, is there any reason to believe that it wouldn't be much worse that the human-made decks that it takes inspiration from? Note that you could also take a database of human-made decks, and try to randomly combine these decks into a new deck using a "very dumb" algorithm; is there any reason to believe that ChatGPT would do any better than this random algorithm?

Note that my question in the previous comment is not a rhetorical question; I'd be happy of an answer to it along the lines of "someone has put some reasonable effort into trying to use ChatGPT for this and here are their results".

ChatGPT is also quite likely to not make a (legal) deck, just a bunch of words that sound like one. What do you do if it uses a name that isn't a real card, or suggests 5 Griselbrands?

@Caleth I've given it a shot a few times, and I haven't gotten any made-up cards or decks with too many copies of a given card yet. I have gotten a deck with 65 cards, though, because ChatGPT can't count.

ChatGPT can't build decks with cards it's never seen before (e.g. new set release) though, can it?

@Allure Nothing post-2021 unless they've upgraded it with more recent data, no. It can do Modern decks, though.

I put together this site that provides recommendations based on an existing set of cards that you have on your deck. Seems to be working well! Any feedback is welcome: https://swampgpt.pythonanywhere.com/
EDIT: I hope that this is a better answer. I used ChatGPT creating my own GPT by adding information from Magic cards and providing instructions to the GPT that describe MTG synergies as well as things to avoid. The rest is built with Python as well as Java and HTML. I hope this helps! I am currently working on improving the functionalities of the website.

Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center.

Hi! Intriguing. Could you describe a bit the algorithms you used?

+1. I gave the algorithm Psychatog & Island + Swamp and it gave me some amusing (and sensible) responses of synergistic cards - although it's still very far from a complete decklist.


text:
How close are top Bridge players to perfect play?
Let's say "God" is playing a hand of bridge. "God" can see all cards, and also controls both hands of the partnership: so "God" plays both North-South or East-West, and makes bids for both of them as well.
How are top Bridge players likely to perform against "God"? They are obviously not winning, but how much will they lose by? Mycroft's answer to one of my previous questions says top players concede a trick on a particular type of hand over 20% of the time, but what about across all hands?
For comparison, in chess, there is no equivalent "God", but the world's best chess players lose 100% of the games against top engines when unassisted, so top chess players are very far from perfect play. There is reason to believe however that top correspondence chess players are quite close to perfect, and most games are drawn as a result. The same goes for checkers - top players are so close to perfect that most games are drawn.

I'm not sure if using "God" is the best way to imply a hypothetical perfect player of bridge

I don't remember who was attributed to this quote, but I think it was Bob Hamman, who at the time could legitimately argue this:

I am not a good bridge player.  I am a bad bridge player.  It's just that everyone else is worse.

Bridge has got a lot better since then, but it's still true to an extent.  It's also argued that a decent A 2021 pair could beat the world champions from 1950 (once.  Then the WCs would study the methods, take what worked for them and ignore the dumb stuff, and come back and destroy them).  The science in the game - much in bidding theory, but also in play and carding agreements/understandings - improved so much between 1950 and 1980, and then again between 1980 and now.  Things that were "the judgement of a master" in the day are now simple enough to explain that they can be taught to low intermediates[#] - imagine what the judgement of a master now is.
The answer is "not even close."  It is also "but that's the point, bridge is a game of imperfect information, and removing that breaks the game."  It would be interesting to determine how much better a "best play" player would be, given just the information they're allowed to have.  Oddly enough, that's one of the really hard things to computerise, though (the other, and linked, one is "how to encode the meaning of the opponents' calls."  There's a reason the "World Computer Championships" has such a limited convention chart.  It's something that humans are far ahead of computers on, and will be for a long time.)
Unfortunately, we can determine to an extent how much better "god mode", or at least "trying to hide it god mode" is, to normal expert standard.  We have records of N- and S-[*] and others who admitted to self-kibitzing; just look at them.  There are also, according to Nicolas Hammond, pairs who are colluding - they don't have full information, but they do know partner's hand, and their rates of "concede a trick to DD on the opening lead" and "guess their fit level in the auction" are magic; they certainly take C+ players and make them A-flight.
Agreeing with Joe that a lot of the game as it is played is "take away room to investigate".  Against God-mode players, this is totally irrelevant (but would be a searchlight-level flag that they were God-modeing!), so until the normals figured it out, that would also be an advantage.  After they figured it out, it would change system completely - and things would move closer.  Not close, but closer.
One final thing here - stamina is a huge factor in bridge.  The mental effort involved in the game is massive, and whether it is a normal 2-club-games-a-week player in the 6th round of the Swiss (the sixth session in three days of the sectional, after a week at work) or the best in the world on the last day of the final of the Bermuda Bowl (after two weeks of 50-60 hands a day against "the world's best" (even the "no-hoper" teams are still the best in their country, and likely to cruise over most normal fields), mistakes will be made due to stamina failure that just wouldn't be on a normal day.  if God-mode doesn't tire as well, that's an even bigger crushing.
[#]A self-quote from elsewhere, parsed for anonymity:

30 years ago without all these shortcut tools, explaining why this is a bad 18 to [a C player] would take pages. Now, you can say "a 6-loser 18 shouldn't be treated as 18, that's below average, and this hand has bad spots and no known fit. I don't think I want to game force with it. Bid 2♥, and if partner raises, reconsider." [I]t would be a hallmark of an expert (as opposed to just Flight A) that they could and did do this consistently, intuitively applying what we can now objectively teach as "90% efficiency" tools to intermediates willing to learn.

[*]I see no reason to add to the permanent stain these players already have.  If they are truly repentant and have served their penance, they should be treated as such.  If you need to know who I'm talking about and don't, it's all over the 'net.
[**]Note that I'm much less interested in the continued reputation of the ones who were actually colluding (closer to God-modeing) or who "acquired the hands beforehand" or whatever.  Especially those who did so not in some random tournament, but in the World Championships.  They can yeet themselves into the sun for all I care.

We have records of N- and S- and others who admitted to self-kibitzing; just look at them - what are those records? How much better than expected did they perform?

The records are there - not sure the general public has access to them any more (I think the records are searchable publicly for 6 months).  I know Nicolas Hammond has it.  If the excuses the players gave mean anything, it didn't get them much above their "normal" skill - but without expending their "normal" effort.  It was the oddity of their plays, that their partners noticed, that prompted the confessions; not the sudden skill increase.  Because of who I am in Bridge, I try to avoid getting too deep into situations I don't need to know about.  But I'm sure BW has several discussions.

@Allure: Confession of a self-kibitzer. Also Using the "C" word

@ForgetIwaseverhere thanks, but I don't see any numbers in the article - of the "usually I would win 50 of these 100 hands, but since I can see every card, I win 70 (?) instead" kind.

Unfortunately, in the case he mentions, there are no numbers.  What he said in the confession matches very strongly with my "one final thing" - he found that being at home with new baby and other stresses was sapping his stamina, and he was playing badly (for him) as a result.  He was "just" using the extra information "to counter that and get back to normal".

too late to edit: "in the case [@ForgetIwaseverhere] mentions", all other "he's" are the author of the article.

The comparison to chess and checkers is somewhat irrelevant, because they are games of perfect information: it’s possible to play them perfectly as a result.
Bridge is not; a player does not have perfect information. That means both that the player likely will not end up in the perfect contract somewhat often and also will not win every possible trick. Double dummy solvers like your posited God will always beat even the ideal bridge play, in part because it’s not optimal to reach some contracts as they’re less likely to make - so no human would go for them.
The other problem is that because of imperfect information, some of the strategy is human based: maybe not misdirection, but disguising as best as possible (and legal) your true intentions. Chess has that possibility also, except it’s always possible to see the true intentions - with imperfect information it is not always possible.

I think you are looking at two effects at the same time which makes it more complicated. Consider the following 4 scenarios:

Two top human players play regular bridge.
Two instances of 'god' play regular bridge. They have the perfect bidding convention etc but they don't know each others or the opponents hands.
Two top human players play bridge with all cards open on the table.
'God' plays bridge with all cards open on the table.

You where asking about the difference between 1 and 4 which do me is not a useful question for bridge. First I think the difference between 3 and 4 is probably insignifant. The difference between 1 and 3 on the other hand is huge. For some hands they may coincide but in general they will be quite far apart.
The difference between 1 and 2 is a very interesting but also very hard question. We can try to estimate the answer by replacing 'god' with 'computers' but as far as I know current bridge programs do a good job of playing perfect or near perfect with a given bidding convention but there is no software yet that can improve existing human made bidding conventions.

Experts outperform your definition of God in an objective sense, because they cater for all plausible layouts of the opponents' cards rather than one single layout. This is how the game is played in real life - "single dummy".
God, seeing all four hands, is making inferior anti-percentages plays, which happen to work on the actual layout. This X-RAY vision style of play is called "double-dummy", as if all four hands are visible. Deep Finesse analyses hands double-dummy, so God would reach a draw with Deep Finesse declaring the same hands. Deep Finesse is free bridge-solving software which you can download if interested.
Bridge is a game of incomplete information (unlike Chess, where the pieces are all visible), and at this stage, experts are still ahead of computers on the bidding, which is enough to carry through and win when you include the play.

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text:
Opponent has unbeatable bomb, do I sideboard in narrow hate card or hope they don't draw it?
Let's say I'm playing limited and my opponent has an unbeatable bomb. The bomb is so powerful that it effectively beats my deck on its own if it resolves. Examples of such bombs could be: Dream Trawler, The Immortal Sun, Primeval Bounty, The Scarab God.
After losing game 1 to the bomb, it's now sideboarding time for game 2. I have a narrow hate card in my sideboard that specifically beats the bomb. Examples of such cards for the bombs above could be: Run Afoul, Deconstruct, Cursebreak, and Leyline of the Void. However, I haven't seen any other targets for these hate cards in my opponent's deck, making them very narrow.
Should I bring the narrow hate card in, or should I hope opponent never draws the bomb?

I wouldn't easily put Deconstruct or Cursebreak in my sideboard (instead of Disenchant or Broken Wings), unless the meta is either very artifact heavy or very enchantment heavy (or one is practically non-existent), or my deck is already capable of dealing well with one of the two. If you're sideboarding "hate cards", I'd aim for something more general if it's not too expensive. Instead of "destroy target artifact", go for "destroy target artifact or enchantment". Keep in mind that your opponent may also sideboard in more such cards, or support cards, if you've shown that you can't deal with it

@NotThatGuy it's limited, so one doesn't get to choose the best sideboard cards.

Consider whether your sideboard card is even good enough - how likely are you to lose the game anyway? Without graveyard synergy, The Scarab God is still a 5/5 beater in a deck that has probably been doing a good job of keeping the board clear; and even with graveyard hate that specifically interferes with the removal-dodging, you still need fairly high quality removal (not a lot of red spells do 5 damage).

It depends on your deck and the rest of your opponent's deck. If you have a relatively fast, aggressive deck and your opponent's deck is relatively weak without its bomb, you can hope to get under your opponent's bomb and you can focus on winning without the removal. Otherwise, it's better to include the removal.

The answer is a definite maybe.
It depends on a lot of things that the situation is too general to really answer:

How fast is your deck, how fast is theirs?
How much of a bomb is it?
How narrow is the answer?

For point 1, if you're fast and their deck is slow, you have a lower chance of seeing their bomb and are less likely to need to deal with it.
For point 2, some things are bombs but can be worked around. There's a difference between "If they play and I don't answer this I lose" and "this is annoying but I still have a chance win after it"
For point 3, a lot of the answers may be meant for their bomb, but can still be useful in other situations. From your examples, Run Afoul is a pretty bad choice to deal with an Azorius bomb, they likely have other less important sac options, but unless their only enchantment is their bomb, you can still make some use of Cursebreak and Leyline of the Void can interfere with a lot of other cards in Dimir colors, not just Scarab God.
It really depends on a lot of variables, there's no single perfect answer to "should I sideboard this hate card" and the question is even more difficult in limited than it is in constructed formats. Usually though, if it's enough of a bomb you seriously feel the need to ask yourself the question, the answer will be yes.

Balance and Overkill
The answer is quite involved, but a balance you'll constantly need to run in limited pools - being careful and mindful about probabilities when you can afford to
View a potential game as if the opponent will always have their bomb and it takes 5-6 turns before they attempt resolve it, in that time you'll see 12-15 cards
If you only put 1 anti-bomb in which is useless otherwise, you still actually always want it, but you may not find it - play exactly 1-2 if you can make space, and 3-4 if their deck is otherwise very weak or they may counter your solution(s)
Assuming 12-15 cards are available to you, the chance of you having at least one anti-bomb when they're resolving it will be1 2

Card QTY
40c deck
60c deck3

1
30-37.5%
20-25%

2
51-61%
36-43.8%

3
65.7-75.6%
48.8-57.8%

4
76-84.7%
59-68.4%

You can of course aggressively mulligan, draw more heavily, etc. to offset this further, but this will likely make your deck play further worse in the matchup than not if the chance to draw is more in your favor.
Therefore, if you must stop them, you must put at least 2 solutions for a limited pool 40 card deck, or 3 for a 60 card deck3 to have any reasonable chance of finding a solution, and consider that more will be early dead draws (which you may actually need, and so be glad of)

Where to Focus

Opposing Strong Deck
Single Threat (stable)
Single Threat (unstable)

Your Weak Deck
<LOSS>
measured counter threat
pack in removal

Your Strong Deck
aggressively attack casting ability
aggressively counter threat
aggressively attack casting ability

If the resolution is so dire, they have nothing else which is quite as dangerous, and especially if they have an otherwise low-output, but stable deck (no color problems, <5% 4+ power creatures), you should consider they will aggressively attempt to find and resolve their bomb and you should attempt to aggressively counter it by following what they do (if they are)

play enough solutions to it
aggressively mulligan, prioritizing getting a solution
lots of draw

If you find you have a stable constructed deck facing their stable one and far more so if they have a very unstable one, work to their weaknesses to debase their ability to cast the bomb at all by destabilizing their deck

aggressive artifact/land-destruction against rarer colors they need to cast it
high-count discards (even if the cards aren't considered particularly good; 2+ cards at 3-4 mana, 3+ at 5-6 mana)

prevents powerful abilities from being immediately active
forces them to choose immediately useful cards or their bomb if it's in their hand

put in every efficient creature you have and attempt to aggro them out while they ramp
stalling them so they suffer from their early and mid card draw to get at their threat

you can often stall out quite strong creatures indefinitely with a hexproof wall or discarding to create a 1/1 token every turn
luring them down and using some big mill; even a humble each draw X=8 is sufficient to take out many strong opponents if they've been drawing heavily

play activated abilities that involve discarding and many more solutions to their bomb, as the dead draws can be discarded and even lure them into playing their bomb at a good time for you when you really have 2+ solutions and discard 1

NOTES

Only intended to show a relative and naive balance of the card counts
The chance of finding exactly one will be lower than at least one
Yes, you can endlessly improve the model beyond this, these are

60c only included to show how the quantity is proportionally worse with more cards


text:
How do Cenn Tactician and Lifelink creatures interact?
I'm playing Magic the Gathering, running a Heliod Deck and have a question regarding interaction with Cenn's Tactician:

Each creature you control with a +1/+1 counter on it can block an additional creature each combat.

Say I'm being attacked by someone with two 1/1s, and I have 3 Heliod-buffed 2/2s with Lifelink, and Cenn is out, allowing the 2/2s to block an additional creature. Could I theoretically use each 2/2 to block separate 1/1's, overlapping and gaining 12 life?

No, each creature can only deal damage equal to its power in a combat phase, no matter how many creatures it is blocking. So each of your three 2/2s will deal 2 damage, gaining you 6 life, not 12.

Combat Damage Step

510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. This turn-based action doesn’t use the stack. A player assigns a creature’s combat damage according to the following rules:

510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power. Creatures that would assign 0 or less damage this way don’t assign combat damage at all.
510.1d A blocking creature assigns combat damage to the creatures it’s blocking. If it isn’t currently blocking any creatures (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If it’s blocking exactly one creature, it assigns all its combat damage to that creature. If it’s blocking two or more creatures, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocking creature to divide its combat damage. However, it can’t assign combat damage to a creature that it’s blocking unless, when combat damage assignments are complete, each creature that precedes that blocked creature is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it.

Even worse, the attacking player will now be able to kill one of your 2/2. Since its blocking both, the attacking player can assign both of his creatures to deal one damage to it.

Creatures deal damage equal to their power divided between blocked atrackers in that situation. Meaning 6 damage is dealt so 6 life is gained.


text:
In Magic: the Gathering, how often on average do the top players make day 2 of a tournament?
Definitions:

Top player: the old platinum-ranked pros, or MPL members. If there isn't enough data for this small group, I'm also interested in the old gold-ranked players.
Tournament: an open tournament with several hundred, if not thousands, of players, such as the GPs of old. Small invitationals don't count, although the former Pro Tours are borderline since they're still pretty big.

Last I saw Magic: the Gathering tournaments followed a format where everyone plays Day 1, at the end of which there is a cutoff for Day 2. At the end of Day 2 there is a cut to top 8, where single elimination matches decides a champion. For many players, making Day 2 is an achievement, and a realistic, achievable target.
I am interested in how often the best players in the game make the cutoff for Day 2. Are there statistics for this anywhere?

I asked professional player Raphael Levy and he said platinum-level pros win about 65% of their matches at this level (it drops to 60% at pro tour level). To reach day 2 one needs 7-2 or better, and platinum-level players get 3 byes, so they need to win 4 out of 6 matches or better.
We can do calculations:

p(6 wins) = 0.65^6 * 6C6 = 7.5% chance
p(5 wins) = 0.65^5 * 0.35 * 6C1 = 24.36% chance
p(4 wins) = 0.65^4 * 0.35^2 * 6C2 = 32.80% chance

Therefore they are about 64.70% to make day 2. If they didn't get three byes, then:

p(9 wins) = 0.65 ^ 9 * 9C9 = 2.07% chance
p(8 wins) = 0.65 ^ 8 * 0.35 * 9C1 = 10.04% chance
p(7 wins) = 0.65 ^ 7 * 0.35^2 * 9C2 = 21.62% chance

For a total of about 33% chance.

This assumes that individual results are independent; while that may be a reasonable assumption at large scale, within an individual tournament I suspect it's going to be not a good assumption. If a player has for one reason or another brought a deck which is good against the field, their chance will be much higher than a third (or much less with a bad deck).

@PhilipKendall yeah, it neglects the fact that the average opponent will be stronger or weaker depending on whether one won the previous round as well. I think it's good enough of an estimate though, and it also looks reasonable, e.g. https://magic.wizards.com/en/content/zvi-mowshowitz-hall-fame-top-players here is a Hall of Famer's profile page. Their win rate at GPs is 59.32%. I also doubt we'll get much better estimates.

You also have the outlier that a superior meta choice or more effective side boarding can on occasion win tournaments. There were occasions where the cawblade was beat by burn decks at certain SCG events only because they where so bent on beating the mirror that they stopped running the kor firewalkers in the sideboard, giving the burn decks a chance.

Correction: Zvi Mowshowitz's (the Hall of Famer in my comment above) GP win rate is 62.78%. The site gives 59.32%, but that apparently includes draws and byes. This makes the 65% win rate given by Raphael Levy more believable: 65% win rate on day 1, 60% on day 2, averaging to 62.78%.