
Wrong John Silver |

So, an elementalist wizard under the Four Element system must choose the opposition element as its opposition school. Under the Five Element system, she must choose the element that overcomes their element.
In the case of air, metal, and wood wizards, there are no special rules because they only exist in one system or the other. In the case of fire wizards, it doesn't matter if they're four-element or five-element, because their opposition school is water in either case.
But what about earth and water wizards? Under the four-element system, earth's opposition school is air and water's opposition school is fire. But under the five-element system, earth's opposition school would be wood and water's opposition school would be earth.
Can an earth or water wizard choose a five-element opposition school instead of a four-element opposition school?

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The two systems are made to represent two different philosophies of magic. The wizard should have whichever opposition school is appropriate to their philosophy of magic.
Assuming that both philosophies are available to the PC, then they should indeed have a choice in which one they ascribe to, and thus which element is their opposition. This may or may not have thematic consequences for the character depending on your game world.

Azothath |
the two systems while not the same are both legal and mutually exclusive. Your caster chooses which system and element, denotes that on his character sheet, and then follows the rules for that school. It's not a combination of both nor can you switch back and forth from one system to the other. Retraining may allow changing the choice with an appropriate cost.