[paulmh]

How much extra strength (if any) is needed for a free bid? Specifically, 1H-P-1S-2C-2H? Is extra high card strength needed to bid 2H rather than P? Is having 6 sufficient reason for bidding with a minimum?

[Flameous]

Shape is enough. At least usually as I can't immediately come up with a situation where I wouldn't bid with just extra shape.

I might not bid here with lousy 6 carder but typically yes.

[aguahombre]

Opener's rebid is usually not what we are discussing under the subject of freebids, but here is a thought about how to look at the situation you posted:

You had a rebid in mind as opener, and the interference has not prevented that rebid; so, unless the interference as created a tool to use, it is generally best to not let it disrupt your auction.

In some cases, the interference clears up opener's hand better (even without resorting to a tool). Take the following auction:

1H (p) 1N* (2C)
?..... 1NT was forcing, and you might have been forced to rebid a minor with fewer than 4 of that minor. But here, 2D would show a second suit because the interference took away the need to bid at all.

[daveharty]

What agua said. Also, when the auction threatens to become competitive, it's important to tell partner as much about your shape as possible so he will be able to make better competitive decisions later. Extra trump length is an important message.

By "free bid" what you are usually referring to is an auction like 1S - (2C) - 2H, and there are different schools of thought about how strong a hand that should show. But if you are using the term more generally to mean "a bid which I don't have to make in order to keep the auction open for partner", I think there are just too many possible scenarios to make any kind of blanket statement.

[FrancesHinden]

On the specific auction you give, opener doesn't need extra high card strength to bid 2H, but does want a sixth heart.
It's often said that if you can make the rebid you were going to in an uncontested auction, you should make it anyway. That isn't quite true: I think that you must have a hand that actually wants to bid.

So if I had opened 1H on

Jx
AK109xx
Kxx
xx

I woud not be at all worried about rebidding 2H, even though it is both balanced and minimum HCP - I have a good suit, and nothing wasted in clubs.

However, if I'd chosen to open 1H on

Jx
KJ6xxx
Axx
Qx

I wouldn't bother bidding 2H here - the CQ is a bad card, the heart pips are very bad: in summary, there's no reason to bid again. (You might say that was a reason not to open, but take whatever you think is a minimum opener and put some horrible club holding into it)

[neilkaz]

I agree with Francis' nice post above.

[P_Marlowe]

A 6 card suit is sufficent - you opened, partner responded, this means
you have half of the deck, except in rare case, 12+6 is 18.

Go and fight for the part score.

With kind regards
Marlowe