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We are using all of the standard PFRPG multiclassing rules, with the exception of how you calculate your character Base Attack Bonus (BAB).

For a multi-classed character, please use the following formula:

Calculate a partial BAB for each of your character class levels, add them together, and round down. That is your BAB.

Full-BAB classes: +1 per class level
Three-quarter BAB classes: +0.75 per class level
Half-BAB classes: +0.5 per class level

For example, a 7th level character that’s a Rogue 3 / Wizard 3 / Arcane Trickster 1:

Rogue: 0.75 * 3 = 2.25
Wizard: 0.5 * 3 = 1.5
Arcane Trickster: 0.5 * 1 = .5

Total partial BAB = 2.25 + 1.5 + .5 = 4.25, for a +4 BAB.

Compare standard rules:
Rogue 3 BAB = +2
Wizard 3 BAB = +1
Arcane Trickster 1 BAB = +0
… for a total BAB of +3.