The very last board in a knockout match is about begin. Your round started well, but you also scored some bad results. It is hard to guess what the actual standing is.
Your opponents play quite standard at medium to decent level.
The bidding starts:
Partner usually does not have 4♠ and also not 22(54) unless his hand looks very notrumpish.
Other than placing the contract, your bids have the following meaning:
2♣: Transfer to 2♦, any follow-up bid below 3♠ will be a natural invite.
2♦: Any GF, typically looking for the best game. Partner will bid a 3-card ♥-suit. If he doesn't have 3♥, he will choose the most natural response.
3♥: 6+♥, slam-interest.
Surely you want to be in game with this hand. Simply bidding 4♥ may seem obvious at first glance, but there is no need for a rush. A good technique is to imagine a few partner hands and see how each possible contract fares.
When one bid seems obvious, a sensible method is to try to construct reasonable partner hands where the bid does badly. But quick, the others are only waiting for you.
Did you catch one?
Two examples could be:
a) With the hearts running, we can easily visualize 9 quick tricks. For instance, partner may have xxx KQx AJxx xxx.
b) Another possibility would be to place partner with typical notrumpish holdings, e.g. Qxx Kx KQxxx Qxx.
The question is whether we can sensibly find out that 3NT is the right contract. The best approach would be to bid 2♦ and see what partner does.
If he bids 2♥, we could bid 3♥ which would be ambiguous, showing either a slam-interest hand or a hand looking for the best game. Partner would respond 3NT with a hand suitable for playing in NT and else most likely 3♠, showing a hand that is slightly better than a minimum. After 3♠ we could close the bidding with 4♥.
This sequence caters for hand a). But there are risks. Partner does not know that we hold a singleton ♦ and certainly will bid 3NT with a hand such as KJx Qxx Qxx KQxx. Therefore this approach seems doubtful. When it's unclear whether the imaginative or the obvious action will succeed, it's usually advisable to go with the obvious one. We might be able to outplay our opponent in 4♥ when that happens to be an inferior contract, but when 3NT is the worse contract there is likely no recovery.
What about the other responses ?
2NT. Partner's shape is 3=2=4=4. Similar, we could follow with 3♥ and pass if partner chooses 3NT. But will that be the better contract on average ?
3♣. Partner's shape is 3=2=3=5. It is unlikely that ♥ are running and after partner's ♦- stopper is knocked out the opponents will have too many tricks. Thus 4♥ seems clear.
3♦. Partner's shape is 3=2=5=3. That shape offers best prospects for 3NT, since the opponents don't have a 8-card fit and the ♦'s are under control. This caters for example hand b). If partner bids 3NT on our 3♥, it most likely will be the best contract.
Are there disadvantages of taking the low route?
A double on 2♦ does not accomplish much for the opponents.
The only drawback might be that the opening leader has more information about partner'shand, but my guess is that this disadvantage is small.
To get a better feeling for the critical cases I ran a couple of simulations. The results are on the next page.
For 1,000 deals each (superior := game only makes in this denomination):
Partner has any 3=2=4=4: NT superior 88 times, ♥ superior 186 times.
Partner has 3♥ and any balanced shape: NT superior 53 times, ♥ superior 240 times.
Partner has any 3=2=5=3 : NT superior 132 times, ♥ superior 104 times.
This indicates that the best strategy seems to be to bid 2♦ and follow with 3♥ if partner bids 3♦ intending to pass 3NT, and bid 4♥ else. The 3=2=5=3 shape occurs in about 9.4% of the cases.
If we had a way to tell partner about our singleton ♦, it might be possible to reach the other good 3NT contracts as well.
Back to to our hand.
At table I didn't go through any of this analysis and bid a quick 4♥.
The ♠K is lead.
Prospects are good after this lead and there does't appear a reason to not draw trumps.
So you grab the ace, RHO following with the 8. You lead the ♥5 to the jack, king and 4. You continue with a low ♥ to the 8.
Plus... it's free!