Jonathan Mestel, 19 Apr 1995

A few years ago I gave some thought to whether retro-problems occur in Bridge. Here is a simple example:

You are walking past a bridge table, when someone is called away to an urgent phone call. Five cards are thrust into your hand, and you are told. "You need all the remaining tricks. There are no trumps." Your cards and dummy's are:

You Dummy spades A 2 hearts A 2 diamonds A 2 clubs 2,3 A,Q

Opponents refuse to tell you what has happened previously. You cash the three aces, and both opponents follow suit. you then lead the 2 of clubs, and the next hand plays small. Do you play the ace or the queen? What is the probability of winning the last two tricks?

Cute. Play the queen, because the other opponent has no clubs left. To see this, assume the contrary. Then nobody was ever void, so no discards have occurred, and the number of cards remaining in each suit is 13,9,5, or 1. But that would give the opponents at least four more cards than your or dummy have. Therefore your right-hand opponent is void, and the play of the queen is sure to win.

I haven't seen any retro-bridge problems, but I wonder whether there are any published "double-dummy endgames" (problems with all hands visible after some tricks have already been played) which are not legally reachable for lack of discards.

Thanks to everyone who responded to my original posting. It is my belief that several text-book endings are flawed because of retro-problems, i.e., they could not have arisen from legal play. Here is an amusing example from The Complete Book of Bridge (Reese & Dormer). Although the position is legal, something strange has occurred previously....

KQ2 - 6 - 1087 J94 - Q K - - - 3 10 J K

South is on play, and CK catches EW in a double squeeze. But think about the history of the hand. No-one is void of spades, yet only 3spades are missing, including the ace. Perhaps the defence would have stood a better chance of winning a trick if they'd refrained from discarding the ace of spades earlier!

>Perhaps the defence would have stood a better chance of winning >a trick if they'd refrained from discarding the ace of spades earlier!

Maybe one of them accidentally exposed the ace and was forced to sluff it as a penalty card, or something of that nature... But can we really demand that the diagram be sensibly, not just legally, reachable? We don't even do that for endgame studies (though introductory play can at times serve to illustrate the reasonability of the key position); when it comes to problems it is rare to find a natural diagram in a direct-mate, even more so in a self-mate.

But often we can look at a master game after 10, 15 or 20 moves and reconstruct the entire game up to harmless transposition, even some time after they've left "Book". We are thus solving what might be called a Reasonable Proof Game problem. (It seems that the 10x10 retro-checkers problem was intended as a challenge to reconstruct reasonable, not merely legal, play, else the solution wouldn't continue past the diagram until one side "gagnent".) Some years ago I read of a contest to construct such a game culminating in the Saavedra position, a deceptively difficult task because it's hard to imagine why in actual play the black King would have reached a1 while White's King is deep into the Black Queenside. Did anybody even come up with an RPG?

>Perhaps the defence would have stood a better chance of winning >a trick if they'd refrained from discarding the ace of spades earlier!

Maybe it was jetisoned from dummy for some reason (shortening and keeping a low card for some obscure reason) or maybe it was actual prcatice and Reese just pitched it from dummy for the hell of it!

By the way it would seem that retro type analysis is the norm for good bridge players, although, as Elkes points out, there is a requirement for "reasonableness" based on the bidding, the state of the game and the level of skill of all 4 players. There is a certain Bayesian quality lacking in chess retro work, but after all (except for betting or fun) there is not the purpose for retro analysis in chess that there is in bridge.

P.S. Bob Hamman, bridge champion and former chess master once told me that the difference between the two games was that in chess you had to solve the problem, in bridge you had to figure out what the problem is...

> But can we really demand that the diagram be sensibly, not just > legally, reachable? We don't even do that for endgame studies [...]; > when it comes to problems > it is rare to find a natural diagram in a direct-mate,

In short direct-mate problems this is often because Black is so clearly doomed that, had any proof game *really* been played, he would have resigned earlier.

If White starts with no big advantage, but in a few moves gets so big an advantage as to force mate, this would not be set as a problem, because the solution would presumably be obvious. Checking and capturing keys are rare, exactly because the solver would try such a key first. (I've only seen one short direct-mate with a checking key; it's a "white correction" problem where many discovered checks are legal and the problem is to find the right place for the discovering piece.)

I have heard one objection to tablebases of endgames such as QvBB: it is unlikely that, in a real game, exchanges would have taken place which would bring about the material of the positions in the tablebase. I don't know whether that's true, but if it is, then the same can be said of the positions of many chess problems.

> even more so in a self-mate.

Yes, but now we're in the realm of fairy chess, and all pretence of reasonableness disappears. Yes, selfmate positions are usually not "natural". The reflexmate was invented as a compromise between natural positions and the "suicidal" nature of selfmate play.

> Some years ago > I read of a contest to construct such a game culminating in the Saavedra > position, a deceptively difficult task because it's hard to imagine > why in actual play the black King would have reached a1 while > White's King is deep into the Black Queenside. Did anybody even > come up with an RPG?

In "Chess Curiosities", Tim Krabbé says that the Saavedra position is a position in the main solution line of a problem by Barbier based on a game Potter-Fenton. So something like it happened in a real game, even though the Saavedra position didn't occur.