How close are top Bridge players to perfect play?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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

1. Two top human players play regular bridge.
2. 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.
3. Two top human players play bridge with all cards open on the table.
4. '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.

Answer 4

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.