Bidding a skinny game pays off

Playing online last night, Kate and I bid to a skinny game:

                  ♠ A 8 6
                  ♥ A J 9 8 3 2
                  ♦ K 2
                  ♣ A 6
♠ Q 10 2                        ♠ K J
♥ K 7                           ♥ Q 10 6 4
♦ J 10 7 3                      ♦ 9 6 4
♣ K 9 8 5                       ♣ J 10 7 2
                 ♠ 9 7 5 4 3
                 ♥ 5
                 ♦ A Q 8 5
                 ♣ Q 4 3

       North        South
       1♣ (1)      1♦ (2)
       1♥ (3)      1♠ (4)    
       2♥ (5)      2♠
       3♠          4♠
       Pass

(1) Artificial, 16+.
(2) 0--8 high-card points.
(3) Relay to 1♠. Shows hearts or big balanced hand.
(4) 99% forced.
(5) Confirms hearts.

After a mostly artificial auction we reached 4♠. West led the ♦J. Kate won with the king and cashed the ♣A. Then she led a diamond to the ace and played the queen, discarding the club loser.

She followed by ruffing a club, cashing the ♥A and ruffing a heart to return to her hand. Then, she led her ♣Q and ruffed it with the ♠8. At the end of the deal, she had taken 10 tricks via one club, three diamonds, one heart, two ruffs in dummy, the ♠A and two more spade tricks in her hand.

Out of 64 pairs who played this deal, only four bid and made 4♠. Doing so was worth 9.33 IMPs.

Many pairs played part-scores in hearts. Some bid game in hearts or notrump. Should it be hard to find game in spades? You can see what all the pairs did, if you click here.