Red ants or black ants, in terms of nuisance value in the garden, I regard them as equal! True they don’t actually eat your plants but they can prove pretty unpleasant if they start to colonise areas where you like to sit or, worse still, to sit and eat or drink! In addition they do cause grief to plants, their tunnelling activities will loosen the soil around the plant roots sufficiently to cause plants to suffer from drought, even if their neighbours are happy as can be. This damage may only be indirect but it can cause plant fatalities, poor growth and lower flowering and cropping too. On a lawn their ‘hills’ may make mowing tricky and, as you drive the mower over an ant hill you create a perfect seed pan for weed seeds too.
So what is the answer. To be totally honest, whatever you do. You’ll not win in the long term, as an area cleared of ants rapidly attracts in new queens to set up new colonies and you may end up with more than you started with|! BUT that said you can do a lot to improve the situation, particularly if you just concentrate your efforts on controlling the ants in the areas about which you mind most eg the patio or the area where kids play. There are ant treatments available which act as baits and then poison them and these can work well. Alternatively try the nematode treatment, this id 100% my preferred option as it is totally harmless to wildlife (unless you happen to be an ant!), pets or humans . This treatment acts as an irritant and I’ve had a huge number of gardeners (and non-gardeners!) tell me how brilliant it is. The small pack contains about 16 million microscopic worm-like creatures called nematodes and can be mixed up with water in a normal watering can with a coarse rose and then used as a drench onto moist soil. It works really well when applied any time between about April and September and on both red ants and black, for more details see www.pippagreenwood.com/products/protect-your-crops .
If you allow some nests to remain you will find that the cleared areas then tend to remain clear for longer and, as an extra bonus, if there just happens to be a green woodpecker anywhere nearby, you may even find one visiting and helping to keep ant numbers down for you!