When partner opens 1NT and you pass, that should deny having a 5 card major. Therefore, to balance by bidding 2 of a major after LHO has overcalled, as in this deal, you are really showing a takeout double of their suit. That way double can be for penalties. You lose the ability to make a takeout double and have opener convert it to penalty but that doesn't happen much anyway. You could still play X by responder instead of 2♥ as takeout but with more tolerance to have it converted - more like a hand that's almost good enough to invite and not short enough in their suit to give up on penalizing them. Personally, I like it to be penalty, especially at matchpoints. Regardless, north's 2♥ is definitely takeout of hearts, not "to play to 2♥." Here is an example, which turned out to be a fairly interesting hand to play as well, but only for matchpoint freaks.
| Dealer: S Vul: Both | North ♠ JT9x ♥ QT87 ♦ K ♣ KJxx | |
| West ♠ Qxx ♥ K9x ♦ Txxx ♣ xxx |  | East ♠ xx ♥ Axxx ♦ AQxxx ♣ Qx |
| South ♠ AK8x ♥ Jx ♦ Jxx ♣ AT9x |
| West | North | East | South |
| — | — | — | 1NT |
| Pass | Pass | 2♦ | Pass |
| Pass | 2♥ | Pass | 2♠ |
| Pass | Pass | Pass |
1NT was 11-14 and at first glance it looks like a fairly boring hand. You have 4 sure losers and have to pick up clubs for no loser or pitch 2 clubs from hand on dummy's hearts to avoid a 5th loser. Odds are slightly in favor of east having that card just because she bid but why finesse if you don't need to? After a diamond lead and spade switch, I led a low heart toward dummy. West did well to not rise with the ♥K as that would have made it easy for me to get 2 heart tricks. I could have (and probably should have) finessed the ♥8 - 1 heart trick does me no good because it still leaves me having to guess the ♣Q. Anyway, I played the ♥Q, which east won and led another spade. Now I had to go ahead and trump diamonds before dummy's trumps went away, coming back to my hand with the ♣A to ruff my last diamond. Then when I led to west's ♥K, she cashed the ♠Q and led her last diamond.
East pitched a heart on the last spade, which left me in a bit of a bind as to what to discard from dummy from ♥T8 and ♣KJ. In my hand I have left a small ♠x and ♣Txx. East definitely doesn't have it, so now I basically was left with a club guess but only one way to finesse now instead of a two way finesse but by now I put myself in a position where I would be risking the contract by finessing into east who still has a good diamond. I pitched a heart and played a club to the K fully convinced that east had the ♣Qx and west had ♥9x. Either way, I was able to work out that it doesn't matter what I pitch - if the ♥9 is a stiff now, then the ♣Q also has to be stiff, regardless of which hand has it, given that east has the last diamond. Alas, I was wrong on that too and we came out with a very normal score.
So, if I finesse the ♥8 at trick 3 and it loses to the 9, is the contract ever in danger of going down? Only if someone has 5 hearts and makes me use a trump for one of the hearts, which is fairly unlikely. Otherwise I will always be left with a good trump in hand before having to guess clubs. So, my conclusion is finessing the ♥8 at trick 3 is the right play.
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