Robots in Theory and Practice, III by Alvin Levy (The Bridge World, August 2017, p.26)

To make decisions in the play (and at certain points in the bidding), bridge robots largely depend on double-dummy simulations (the software generates the missing hands that are consistent with the bidding and previous play), and determines, on a double dummy basis, which played card would work most often.  Limited single dummy algorithms (modeled on how a human player might approach a problem) are also used.  Because of time constraints, a single dummy algorithm uses a far lower number of sample hands than does a doubled dummy algorithm.

The deals shown here are from the 2016 robot championship held alongside the recent World Bridge Games in Wroclaw, Poland, and demonstrate the strength of double dummy analysis as declarer.  On deals where the defenders’ plays are irrelevant, the narrower declarer can determine the opponents’ hands, the easier it to play perfectly using double dummy techniques.  Single dummy techniques are especially useful to correctly play certain suit combinations, e.g., A9x opposite KQTxxx or Qxx opposite AKTxx, and also useful (along with the future use of Game Theory) when the opponents’ plays are relevant.  The deals here show the need for both techniques.  Two of the four deals shown were also played in the World Team Championships.

This deal, from the last round robin segment helped Shark Bridge secure the final semifinal spot.

Xinrui reasonably misguessed the location of the ♦Q, playing South for short diamonds, down 1 -100.

¹   one keycard

The lead of the ♠A, ruffed in dummy, was followed by the ♥K. The ♠K was returned, ruffed, and the ♥Q was cashed revealing the (bad) trump break.  A trump coup is needed to make the contract, and requires North to hold at least three clubs and at least two diamonds.  An expert could see this, and so can a robot.  South hand is well defined, with 7 or 8 spades, stiff ♥A, and likely the diamond queen.  Using double dummy techniques it is easy to get this right.  Shark Bridge now played three rounds of clubs, and, playing South to have the diamond queen, played the diamond ace and a low diamond to the ten!  Now running the clubs produced the trump coup.  Note that two rounds of diamonds must be played before running the clubs as North will discard a diamond on the fourth club.  It is not possible for Shark Bridge to get this wrong.

+1660, and 18 Imps to Shark Bridge.

The outcomes of the following two deals from the semifinals were each more than the margin of victory in both matches.

Opening lead ♣Q

¹    strength with 4+ clubs
²   spade stopper, looking for heart stopper for NT
³    one ace

Again, the opponents’ cards are well defined, with West long in hearts including the king, without the club king, therefore the spade ace and queen or jack.  A heart-spade squeeze without the count is the marked play.  For success diamonds must be 2-2 or 3-1 with a stiff honor with West as declarer needs two entries to hand, one to take an early heart finesse and one to run the diamonds. Overtaking the diamond queen with the ace caters to both possibilities.  An expert human knows all this at a (long) glance, and it is also easy for a robot to (quickly) ‘see’ this.  Given the assumed distribution Wbridge5 determines that overtaking the diamond queen with the king at trick two is the percentage play based on a double dummy analysis, as every likely distribution of opponents’ cards, except where there is a trump loser, produces 12 tricks.  With each card played, a new but similar analysis is made.  Play proceeded: club ace; diamond queen overtaken with the ace; heart finesse, diamond finesse (restricted choice); running diamonds and on the last diamond West had no safe discard.

At the table West discarded the ♠Q, declarer led a spade to West’s stiff ace and West had to return a heart, +1370 and 15 Imps as Shark Bridge was in 3♦ for +150.

In the Micro Bridge versus Bridge Baron match, at one table Bridge Baron was in 4♦ +130.  At the other table.

¹ Three spades

Opening lead 3♥

The opening lead of a low heart, finessed, and on the run of diamonds West was similarly squeezed, +620.  Interestingly, with the same ending and West discarding the spade queen, Micro Bridge took the heart finesse and ducked a spade return.

Note that the play must be the same to make both 5♦ and 6♦.  This deal is from the quarter-finals of the team championships (Open, Women, Senior, Mixed).  Of the 32 times the deal was played by ‘humans’ the contracts were: 3NT by South (17); 3NT by North, down (2); 3♦ (7); 3♠ by East (2); 5♦, down (2), making with an overtrick (1); and 6♦ making (1). The players making 12 tricks received the spade ace lead, so did not have a chance to get it right on their own.

Opening lead ♠5

West played ♠Q, ♠A, ♠7 for East to ruff, and East returned a club, West playing the king. With West a passed hand, East was marked for the heart king and was likely 1-2-5-5, so Wbridge5 got it right dropping the stiff ♥K.  Interestingly, after the round we checked with Wbridge5 to see what it would have done had a diamond been returned? Wbridge5 would have still dropped the stiff king. This points to the disadvantage at times of giving declarer too much information.

In the other semifinal match, at one table Micro Bridge was in 3NT, making 4, after West opened 2♠, North doubled and then bid 3NT over partners 3♣.  At the other table Bridge Baron reached 4♥ with no opposing bidding.  The ♠5 was led, and after the ♠Q, ♠A and ruff by East, a diamond was returned.  Bridge Baron, not locating the ♣K, and not having any idea of the distribution, ruffed the 3rd diamond and took the heart finesse for down one and the difference in the match.  Less opponent information leads to less success by declarer.

This deal was also played in the team championships round of 16.  Of the 64 times the deal was played, the contracts included 4♥N (52) and 3NT making 9 or 10 tricks (7).  Of the 49 times the singleton spade was led against 4♥, declarer made the contract 20 times.  Assuming West passes in open seat, if declarer can find the ♣K with West, then East would be marked with the ♥K.  Less opponent information leads to less success by declarer.

It seems that West might signal for a club return at trick 3 knowing that a diamond return could be fatal if partner led away from an honor, in which case East could work out that if partner has the club king and it is discovered, declarer will surely drop the stiff heart king, so leads back a diamond.  Declarer might work out that East held the ♥K as it did not return a safe heart back.  Then again, if declarer is to think that way, it might go further and think that East might not return a safe heart when West held king third, as then declarer might go wrong.  Bridge is sometimes a cat and mouse game, which could be accounted for using game theory.

So it was Wbridge5 versus Micro Bridge for the title.  On the last board, with Micro Bridge up by 5 Imps, Wbridge5 needed to make its 3NT contract to take the title.

opening lead ♠4

A diamond opening lead or return when N-S first gets in is needed to defeat 3NT.  The spade lead was won by the king and a club was ducked to South.  This sets up the club suit, assuming a 3-2 break, and retains an entry to cash the spade ace.  South, in with the club ten, had one last chance to return a diamond, but returned a low heart, which would be right if declarer had the diamond queen and misguessed the heart position.  For the robots, as for human, defense is more difficult than declarer play.  Wbridge5 went up with the king and now had 9 tricks and the title.

Checking with Micro Bridge (yes, it is possible to ask the robots what they were ‘thinking.’ North’s 3♠ bid showed a 7-card suit and 5 or more playing tricks.  Micro Bridge interprets the 3NT bid as showing a spade stopper and a minimum of 8 hcp.  North did not play the spade ace at trick one, so South plays East for the ace.  Micro Bridge assumes QJ10xxxx as 5 playing tricks, but QJ9xxxx as 4.5 playing tricks. Simulations give the ace of club to North to fulfill 5 playing tricks more often than QJ10xxxx.  Here is a typical generated hand:

North
♠ QJ97632
♥ J105
♦ 8
♣ A5

A heart return at trick 3 will defeat the contract while a diamond lead will allow a make (I leave it to the reader to work out the end position).

See the full play of the semifinal and final KO stage along with robot information and the 20 year history of this event at www.computerbridge.com

------------------------Additional deals, not in the article----------------------

Interesting deals with the same theme.

An early board in the final match saw the use of a single-dummy approach in defense.

¹ clubs and hearts

Opening lead, ♦3, Micro Bridge won in hand, led the spade queen but went up with the ace; a spade to the king, club to the ace, and heart 5!..Micro Bridge played low, down one, -100.

The underlead of the heart ace is unlikely using only a double dummy techniques, as double dummy, it can never win.  Wbridge5 uses single dummy techniques on defense as well.

At the other table,

Opening lead ♣6.

South cashed the two aces and returned the ♦ 6.  Wbridge5 won in hand, led the spade queen and overtook with the ace.  A spade return and +620. Wbridge5 +12 IMPs.

The sixth round robin session ended with a simple endplay by Q-Plus Bridge against Wbridge5 for a big pick-up.

Opening lead ♥9

Down 1, -50 (best score for Q-Plus Bridge)

Opening lead ♦K (1); followed by ♠2, won in dummy (2); heart to J, Q, A (3); diamond return? (4); heart (5); heart (6); spade (7); spade to ace (8); ♠10 (9); club to queen (10); end-played; +620.  Q-Plus Bridge +11 IMPs.

Wbridge5 had an opportunity, at trick 4, to return a club, but missed the obvious play.  This is surprising as a double dummy algorithm would produce a club return, however, a single-dummy algorithm on defense (starting at trick four) allows for declarer to mis-guess the club situation holding ♣Qxx when there is no endplay.