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Ok I know people are going to tell me to look at the PHB but I am having a debate with the DM on how the multiclass table works specifically with fighter/rogue

If a person is fighter5/wizard1 would they be a lvl 2 spell caster because its Floor(5/3) = 1 + 1(wizard) = 2

or is it...

round up as you do most times 5/3 = 2 + 1(wizard) = 3

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The correct level is 2 if your character is an Eldritch Knight, 1 otherwise.

Each level of wizard counts as a full spellcaster level when multiclassing. Each fighter level counts as a third of a level but only if you have the Eldritch Knight class feature. Fractional levels are rounded down as is the general rule (Player's Handbook, page 7) and as is also explicitly stated in the multiclassing rules (Player's Handbook, page 164). To be absolutely clear, one always rounds down in DnD 5e, unless a feature specifically tells you to round up.

Five levels divided by three, rounded down, is one level. Add your wizard level, and you get a caster level of 2. If your character is not an Eldritch Knight, then only the wizard level is counted.

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