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After 1 (P) 1 (P) 1NT (P), under what conditions should you bid 2 with a five-card heart suit?

You are responder with five hearts and 7-10 HCPs.

The auction goes:  1 (P) 1 (P) 1NT (P) to you. 

You play Walsh-style with two-way checkback. Under your system, partner's 1NT bid promises 12-14 HCPs, 2-3 hearts, and a hand that is not distributional (no singleton, or more than one doubleton).  Partner does not deny a four-card spade suit.

Because you play 2-way checkback where bids of the minor suits by responder show mild or strong game interest, a bid of 2 by you must be passed by partner.

Using that system, when do you bid 2 and when do you pass 1NT?

This is another poll where I have done substantial DD simulation to back my opinion.  However, I wanted to see the intuition of others.

Matchpoint scoring.

Never bid 2
Bid 2 only if I have the HA or HKQ.
Bid 2 only if I am distributional (have a singleton or more than one doubleton).
Bid 2 only if I have the HA or HKQ, and I am distributional.
Always bid 2.
Other -- because there's always an other.

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