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In the second game, the multiplayer functionality has been improved to a satisfactory level, unlike Heroes 1, so it's almost as enjoyable as playing the third game.
In Heroes 1, you can also play online, but it's quite challenging due to numerous network-related bugs. You'll practically have to restart the game after every turn or action. For example, the game often freezes when morale drops during a battle, so you'll have to reconnect almost every time.