Solid Hardwood, Engineered and Laminate Flooring - Sub-flooring for bamboo hardwood

Having ripped up the carpet throughout our house it has become apparent that the whole floor is covered with 3/4" particle board on top of the floor boards. We hope to lay bamboo hardwood throughout but are not looking forward to pulling up all that nailed down particle board. What would be the feasibility of screwing down 1/2" plywood to the particle board and laying the floor onto that? We wouldn't want to increase the floor height by any more than another 1/2" so if it is not reccommended to use less than 3/4" ply then we would go ahead and pull up the particle board, lay 3/4" ply and floor over that. Any help here would be much appreciated.

p.s. We are using plank flooring, not engineered.

Having spent two days last week pulling up a lousy 400' I can understand your angst, but it must be done. If it ever gets wet, it will undermine your whole floor.
Sometimes it comes up very easily depending on what they used to nail/staple and how carried away the idiot with the stapler got.

Thanks MARCO1, invaluable advice. Guess I'd better get on with it.