You've had this sequence:
1♣ (various)
1♦-2♦ (hearts / a hand that would open 2♣ in a normal system)
2♥-2NT (5+ without a 5-card suit / 23+ balanced)
3♥-4♠ (4 spades / support, but a bad hand in context)
With a normal minimum and support, partner would bid 3♠; with a better hand he could cue-bid.
You also know:
- The field ranges from BBO "expert" to real-life expert.
- Almost everyone else will have started with the equivalent of 2♣-2♦-2NT, showing 23-24.
- Most of them will then bid a slam.
- Your partner's cardplay is better than that of most of the field.
So:
- How good do you think slam will be?
- What do you do?

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