Help
Got interested in this hand and ran a full blown simulation on it. Ended up with 75 cases conforming to the bidding as given. Even after this investigation, the best bid still is not clear to me. About 10% of the hands offer a good play for game, which is lost by passing. On the other hand, the deal is a misfit (85% of the hands will have fewer than 16 total tricks playing in 2♥), so passing has a lot going for it. The only way to compare passing with double would be to play out 75 hands in both cases - too much effort for me. It does look like PASS is the easy winner at matchpoints, but at IMPs it is unclear because of missed games and no doubled contracts.
One thing did become clear. Double is MUCH superior to bidding 2 NT. The bad side of the double is missing some of the eight games in the simulation set when partner has passed over 2♥ with one of the following:
7
753
K1087653
A3
K4
10
Q1096
QJ9864
43
65
1085
AKQ875
94
62
Q53
AJ9864
10
863
KQ10985
Q87
K10
72
10876
KJ976
9
865
986
AKQ984
or
10
Q76
764
KQJ973
How many of these games would be reached after a reopening double. I dunno.
In favor of the double is that 2♠ is the optimum spot (given that you declined to play 2♥) in 60% of all possible hands. When partner passed with three or four spades, but not enough high cards to bid or has a doubleton spade, 2♠ is almost always the best spot. If you reopen with 2NT, you stand to lose a partscore swing on most of these hands. You make 7 or 8 tricks in spades on lots of hands, but nine tricks are hard to come by.