How Robots Play

One of the methods used to program bridge-playing robots is a double dummy simulation technique, in which the unknown hands are constructed, many times over, consistent with the bidding and play, and each construction is analyzed double dummy.  In this double dummy analysis, it is assumed that if a contract can be made, it will.  The card that has the best chance of achieving success (making the contract as declarer or defeating the contract as defender), as determined from this analysis, is played.

A further step in robotic 'thinking' is to use single dummy techniques, which allow for your opponent to going wrong, i.e., not playing double dummy.  To that end, a robot places itself in an opponent's seat and uses a variety of schemes to analyze the best play.  Generally, these schemes are either rule based, as opposed to simulation based, or a combination of double dummy simulation with rule based corrections.  An even further step is to use these techniques to make inferences on your opponents hands, based their play.

First, a hand to demonstrate the double dummy simulation technique.

Watch the play unfold on the following deal from the round robin, hands rotated.

Dealer South. Vulnerable N-S.
	♠ A 7 4 ♥ A 9 5 ♦ A K Q 3 ♣ Q 9 6
♠ Q 5 ♥ 6 ♦ J 9 8 6 5 ♣ J 8 7 5 2		♠ J 9 6 3 2 ♥ Q J 8 ♦ 10 2 ♣ K 4 3
	♠ K 10 8 ♥ K 10 7 4 3 2 ♦ 7 4 ♣ A 10

Against 6♥ by Wbridge5, Shark Bridge led the ♠Q. If trumps are 2-2, the slam is cold and if there is a trump loser, then there are squeeze possibilities with threats in the other three suits. The play requires that declarer 'best’ guess which distributions to play for.

Wbridge5 won the ♠K in hand. A double dummy simulation⁽¹⁾ determined that the contract could be made more often by winning the king in hand than by winning the ace in dummy.  A heart was played to the ace and a heart returned to the jack and 3 — Wbridge5 ducked the heart!  A simulation⁽²⁾, at this point, determined that the contract could always be made if hearts are 2-2, and could be made more often by ducking than by winning the king when trumps are 3-1.

⁽¹⁾ The contract can always be defeated if West started with hand (a) QJ9x x xxx Kxxxx.  For any other holding, winning with the king makes the contract double-dummy, while winning the ace loses if West started with hand (b) ♠QJxx x xxx ♣Kxxxx.

⁽²⁾  If West started with hand (a) the contract can be defeated whichever card South plays, but there are many more West holdings that ducking the heart is necessary to make the contract, e.g., if West started with hand (c) Qx x J98xx Kxxxx or hands (d) QJ9x x x(x) K(J)xxxx(x)(x), than winning the king is necessary to make the contract, e.g., if West started with hand (e) QJ9x x xxx Jxxxxx.

East returned the ♦10.  Wbrideg5 won the ♦A in dummy, led a heart to the king and ran hearts coming down to the following position.

Now it was up to Wbridge5 to determine the end position.  On the ♥4, West discards the ♠5 and Wbridge5 got it right by discarding the ♠7 from dummy.  Now a spade to dummy's ace squeezed West.  West blanked the ♣J, by force. Then the ♦K and ♦Q squeezed East into keeping the ♠J and the lone ♣K and declarer pitched the ♠10. Wbridge5 now won the last two club tricks for 1430.

Now a deal to demonstrate the use of single dummy techniques to allow an opponent a chance to go wrong.  A deal from the round robin, hands rotated.

Round Robin.  Round 1, Board 8.  Dealer South. Vulnerable None.
	♠ A Q 9 8 6 ♥ 8 4 ♦ Q J 9 5 2 ♣ 2
♠ 5 4 ♥ Q 10 9 7 5 3 ♦ 6 3 ♣ Q 7 6		♠ J 10 3 ♥ A 6 2 ♦ K 10 8 ♣ A 10 8 5
	♠ K 7 2 ♥ K J ♦ A 7 4 ♣ K J 9 4 3

Shark Bridge-West led a trump to the ♠10 and ♠K.  Bridge Baron returned a spade to dummy's ace, and led a club.  Shark Bridge went up with the ace and led a low heart!  Bridge Baron finessed the jack and ended up losing two hearts, ♣A and a diamond for down one.

At the other table, Bridge Baron-West led a club.  East won with the ace and cashed the ♥A, 420 to Wbridge5.

In the other two matches, 4♠ was played by South three times and once by North (by Mirco Bridge playing weak NT).  In the Jack vs. Q-Plus Bridge, at both tables the defense led a club to the ace, and East cashed the heart ace.  In the RoboBridge vs. Micro Bridge, at both tables a diamond was led, and declarer won the first trick with the ace.  When RoboBridge-South was declarer, declarer put in the nine from dummy, East played the ten South won the ace; when Micro Bridge-North was declarer, East led the ♦8 and declarer went up with the ace.  At both tables, three rounds of trumps were then played and the singleton club led.  At one table, the RoboBridge won the ♣A and cashed the ♥A.  At the other table, the only table that 4♠ played from the North seat, Micro Bridge ducked the club, declarer playing the ♣J, losing to the ♣Q.  After three rounds of diamonds, declarer led a heart to dummy's ♥K ♥J and East rose with the ♥A.

Why did Shark Bridge get it right?  A double dummy analysis assumes that the opponents play double dummy, and therefore always make the play that works.  With this thinking only there is no need for South to duck or underlead the ♥A, as, at double dummy, it can never win.  Many robots use a single dummy rule-based technique to "jump" into declarer's seat to see the problem from its point of view.  Using this technique  Shark Bridge determined there were distributions, such as the actual one, that declarer might go wrong if missing the ♥Q, so it underled the ♥A.  Some of the other robots use similar techniques, but still didn't get this defense right.  It is noted that jumping into an opponent's seat and using a single dummy simulation technique is currently too inefficient, i.e., too time consuming.

Now a deal to demonstrate the need to make inferences from the opponents' play.  Board 34 from the finals between Wbridge5 and Jack follows, hands rotated.

Board 34.  Dealer North. Vulnerable E-W.
	♠ K Q J ♥ 10 5 3 ♦ Q 9 7 3 ♣ J 9 2
♠ 9 8 7 5 4 3 2 ♥ Q 7 ♦ J 2 ♣ 10 6		♠ 10 ♥ A 9 ♦ A 10 8 5 4 ♣ Q 8 7 5 3
	♠ A 6 ♥ K J 8 6 4 2 ♦ K 6 ♣ A K 4

The ♦J was led to East's ace, and Wbridge5 correctly unblocked the ♦K.  Jack-East did well to return its singleton spade. It did so because it found some holdings that South could have where the spade return would beat 4♥, even assuming that declarer plays double dummy.  Wbridge5 erred in winning the spade in hand, and playing a second spade to the king.  East ruffed and returned a diamond, later East got in with the ♥A and returned a third diamond, promoting West's ♥Q for down one.

How should Declarer have played the hand?  East's opening bid places it with the ♥A and the spade return implied shortness, so declarer should win the ♠K in dummy at trick two and lead a heart to the king, and then either lead a trump (making 5) or unblock the ♠K (making four).  Why did Wbridge5 play as it did?   Wbridge5 didn't draw any inference from East's play, placing the odds of a singleton spade at the a priori odds of approximately 1.3%.  Yves writes... jumping into an opponent's seat and using a single dummy simulation is currently too inefficient, i.e., too time consuming.