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1S is probably fine on a min GF, but with extra values a lot of experts have started to believe that 2c is better. The problem is that after 1h-1s, without a ton of special agreements, there are a lot of auctions where it's hard to both set hearts as trumps at the 3 level and have it be GF, when most people are playing jump preferences as inv, and 1h-1s-2h-3h is also inv. You can go through 4th suit/3rd suit but often partner will bid something inconvenient (3nt, 3S) and again you are deprived of being able to bid 3H. After 1h-2c, it's not really a distortion of your shape if you are playing 2c includes a bunch of balanced hands with 3 or 4 clubs, or even 2 only clubs. Very few people are doing things that make it possible to play 2c as a real serious 5+ suit these days, they aren't playing 2nt bal gf nat or 1nt as absolutely forcing, so 2c is already suspect. Over an often balanced 2c probably you are supposed to do something like have the balanced hands just use relay-style bidding and use mostly artificial rebids by opener, with the option to break the relay with real natural clubs. Most non-expert partnerships or casual partnerships just kind of muddle through, it can make finding 6c a bit dicey and disturbs hand evaluation by opener as you don't know if partner's 2c is AQJxx or Jxx. But most of the time you survive. Non-real clubs just has to steer quickly back to NT or the major if opener shows interest in club contracts.

How sure are you that 3H is splinter though? That requires agreement. Why can't it be 5-5 majors, GF? or 5-5 majors, inv? Those hands are kind of important to show also, in olden SA bidding typically 1d-1s-2d-2h-?-3H was inv, 1d-1s-2d-3H was 55 GF. The question is if you play 2H as completely artificial GF, or quasi-natural F1, or quasi-natural FG, and how you handle lesser both major hands, which can be influenced if you play reverse flannery by responder. Personally, with no discussion, I'm much more comfortable bidding a quasi-natural 3c followed by 4d, which should show heart shortness by inference, than bidding hearts followed by 4d, which would seem more accident prone to me, partner either assuming hearts are agreed (if hearts was raised to 3h), or that we have club shortness.

I am a bit late to this thread and am not in the same league as others who have commented, but I was thinking of first responding 1♠, then when partner rebids diamonds, splinter with 3♥. I'm thinking a diamond slam is in the picture if partner doesn't have heart wastage.

1. 2♣* gf clubs or balanced 2. 1♠ is 100% forcing There is a lot written about 2♣ in a 2/1 auction, here and other forums, I will try to find it

I'm still reading the old thread, so perhaps the rest of this comment will prove to be dated. I think my previous comments in this thread already have. Oh well. Trying to reduce the entropy of best final contract by log(2) each step sounded nice to me when I wrote it, but should be impossible. Not counting sacrifices there are only 21 possible optimal contracts (lowest partscore, game, small and grand slam in each denomination, and passout). If we could really reduce entropy by log(2) each step we should be able to be reasonably certain about the final contract after 5 steps or so, i.e. get our small versus grand slam decisions right at the 1NT level. Even if we allow some 'free' bidding space by claiming that the lowest playable partscores are 1NT, 2♥, 2♠, 3♣ and 3♦ the same logic holds. The old thread's comments on multi-meaning bids are important and relevant. In my mind a final working product would be something along the lines of "on the auction thus far, we have shown one of the following hand types <list>, while partner has shown one of the following hand types <other list>. Based on simulations of my actual hand facing partner's possible hands, our next bids should clarify trick-taking potential in a certain strain". A reasonable example would be asking partner for extra shape (i.e. show increased trick-taking potential in their longest suit), clarify a multi-meaning bid or show min/max range information (i.e. show increased trick-taking potential across the board). One huge brute force option I was thinking of is setting a (global?) maximum of possible meanings per bid, i.e. 4 or so, and requiring that each subsequent bid is a subset of the previous ones. This would give each bid on each auction around 40 weights (min and max length of each suit and in HCP means 10 values per possible meaning, times the maximum allowed number of meanings). I'd also require that these are all mutually exclusive with the other options at each round - i.e. each hand only has one system bid, and each of the categories in each bid are cleanly split (note that standard bidding systems usually don't do this, but we have to start somewhere). Then a cost function of reaching good/bad contracts could help optimise these values. Hopefully the system would gravitate to something like "it is important to clarify suit length/offer extra length when you have it". The main issue is the explosion of the system size, so maybe a good start would be to start this approach with a mini-bridge equivalent. Some restrictions that I think are interesting (and mentioned in that other thread) include: No interference, to simplify. Only score for getting to the right denomination, not caring about level (but include the fact that majors pay better somehow?). Only allow two full rounds of bidding, to reduce complexity. Force a certain start to the bidding, e.g. North opens a strong (15-17) notrump, as a proof of concept. Simplify even further, and use the above approach (force 15-17 NT and give responder something in the 10-14 range) but only allow 3NT, 4♥ or 4♠ as final contracts and see how well that can be optimised with this approach.