PS5: DualSense works with PS3 and Nintendo Switch, but not with PS4
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How does it work on PS3? Probably because the console from two generations ago was compatible with generic Bluetooth controllers and therefore can recognize the DualSense as such without any particular effort.
On the Nintendo Switch it is a bit more complicated, because it requires the purchase a third party adapter, but it is still possible. On PS4, on the other hand, it is impossible, unless you resort to an intricate trick: you have to connect the DualSense to the PC via USB and stream PS4 games via Remote Play.
Before leaving, we remind you that PS5 will be available in Europe starting November 19, 2020. In other territories it will be launched a little earlier, on November 12, 2020. The console is already a best seller, which has sold out with reservations. We will see in the long run whether it can maintain the same level of sales.