They started equal. Sam won 15 and Darren lost 24, so Sam is now 15 + 24 = 39 ahead. Sam now = 4 units, Darren now = 1 unit, so the 3-unit gap is 39.

Plain numbers are given; italic underlined numbers are worked out.

1. Sam ahead now → 15 + 24 = 39
2. Sam − Darren = 3 units → 39
3. 1 unit (Darren now) → 39 ÷ 3 = 13
4. Each at first → Darren now + 24 = 13 + 24 = 37

Each of them had 37 cards at first.

Check: Sam 37+15=52, Darren 37−24=13, and 52 = 4 × 13. ✓