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I have an O&G army and I never run magic. The chaotic nature of orcs combined with the need for Black Orcs to lead units makes justifying magic hard. Plus my luck is always poor and more often than not I end up with a miscast.
Fortunately I can take a bunch of dispell thanks to Morks Spirit totem so I can still put a bunch of greenskin hurt in your face. Sure I get hurt by armies with good magic but orcs are tough and cheap so it all evens out imo.
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I think all of the replies thus far are re-iterating the same point.
So long as your army has an ability to survive the magic phase, you can ditch your wizards. You either need to have surefire ways of dealing with magic casters (Hochland Long Rifles) or you need some form of non-wizard magic defense.
You can't ignore both and expect to win. Our last local tourney saw one player only take combat characters and no magic defense in his WoC list. He couldn't win a game because even my level 2 with 1 bound was able to be game breaking (Tree Singing FTW!).
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as a TK player I'd have to say magic is godly but I can also see no-magic working with other armies
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I have to say that while you may struggle against some enemies you can generally do huge damage in return.
I am a Lizardmen player and for awhile I have been using the Slaan + 2 Priests(In 7th one even got on a EotG) however for fun I tried no Magic. Yes it hurt me but the fact that I was able to field 6 Cold Ones, an Ancient Stegadon with Blowpipes and Chief, 20 Skinks, 12 Saurus and 2 Scar Veterans for the cost of those units was a huge advantage.
The inability to stop raised dead can be annoying however I found that I crushed so much that in a straight VP match I was miles ahead. The only thing that hurts is a few powerful spells and even then I find that the larger/more units present makes up the difference.
That said some armies cannot play no-magic and others look weaker doing so.