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When one has an asset that grants +2 skill and one that grants +1, the effective bonus is not additive. Rather, we apply the highest bonus. My questions is: do the bonuses from improvement tokens count as similar "+" bonuses or are they separately added as "additional die rolls" are. Namely, if I have a +1 improvement token on my strength and I hold an asset that grants me +1 to strength, is my effective bonus +2 or merely the best "+" bonus (ie +1 in this case)?

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Improvement tokens are neither a "skill bonus", nor "additional dice", they provide dice in a separate step.

When an investigator resolves a test, he performs the following steps:

  1. Determine Dice Pool: The investigator determines the number of dice he will roll. This number is his DICE POOL.

•  He starts with a number equal to the skill being tested.
•  He adds or subtracts the test modifier (the number that follows the skill icon on the effect).
•  If he has an Improvement token for the skill being tested, he adds the Improvement token’s modifier.
•  He may use one effect that provides a bonus (for example “Gain +3 Will”). If multiple effects provide a bonus, he uses only the highest bonus.
•  He adds any “additional dice” he gains from effects that apply. Additional dice are cumulative and are in addition to other effects

Source: Reference Guide, "Tests" (page 11)

Everything, except "skill bonuses" stacks.
Only the effects worded as "gain +X [some skill]" are skill bonuses.
All other effects are not skill bonuses, and stack.

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