Concrete slab for my kids games room/gym.......

Foundation.... 150mm hardcore, levelled then compacted is pretty standard procedure. It All depends on the ground if it's soft and wet, you'll want more if it's firm you'll need less. You're aiming to create a stable level surface for the concrete. 150mm (6inches) of concrete is plenty, we run 13 tonne machines with steel tracks over that depth slab without remotely damaging it. You don't need to reinforce the concrete, if however you felt the need to go the extra mile. Structural fibres are said the be the equivalent as steel mesh and are low cost, finer structural fibres also prevent cracking. They're a nice touch, we use them for 300+ cubic metre heavy traffic slabs. You're on the right lines, don't overthink the foundation and take it to extremes. 150mm hardcore compacted with a wacker plate, 150mm concrete sat on polythene is absolutely plenty. Soft sand on top of your hardcore and (under your polythene) will allow your slab to move more as concrete expands and contracts, but this is all going abit too far for a gym/games room. Keep it simple. Best of luck, any more questions feel free to ask. Sincerely, Joseph.

Any concrete that is to used as a placement for a structure will need steel reinforcing orotund edges at very least especially if it's less than 300mm of concrete. Just check with planning first to make sure they don't come along and say you have to put in a deep foundation.