[nekthen]

Partner opens 1♦ opp bids 3♣ you bid 4♣
Pick up partnership playing SAYC allegedly
What should your partner expect to see in your hand?

[apollo1201]

I guess some kind of strong D raise that does not fear going past 3NT. Not sure it guarantees a C control though.

[nekthen]

My thoughts went like this

If p had not bid, 4♣ over 3♣ opening generally shows a desire to play in one of the majors.

So what is the difference on the actual sequence? Partner actually had a 4441 hand and 4 of either major would roll home. However, he chose to believe that I was showing ♦ support and we wound up in 4♦

I was 5512. I thought my shape and power wrong for a double and did not want to bid 3♠ and find myself passed out'

I suppose that all the viewers who have not commented agree with Apollo1201, so I stand corrected

[Zelandakh]

SAYC explicitly states that such cue bids of RHO's suit show the values for game without clear direction, often a GF raise. However, your question was stated as what one should expect - I rarely expect SAYC players to have the faintest notion of what the bids mean according to the booklet. We get good evidence of that regularly on BBF when a poster proudly proclaims themself an SAYC expert but clearly has no idea.

[WesleyC]

Diamonds support and slam interest.

[apollo1201]

Nekthen, partner won't pass you out in 3S as it is a forcing bid. But with less than 11HCP, X is the only option you have if you want to compete, true not what you wish for when you are 55 but sure not to get overboard. And if partner passes, your 2 trumps with the singleton in his suit could set the contract on the lead.