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It might have small effects either positive or negative. Utilization is scored both on total utilization and individual card utilization.
Scenario A.
Card a 800 used out of 1000
card b 0 used out of 1000.
After the transfer you still have 1 card at 0% one card at 80% and total cards at 40% This would be neither losing or gaining points.
Scenario B.
Card a 800 used out of 1000
Card b 0 used out of 2000
After transfer you would have 1 card at 0%, one card at 40% and total cards at 26% this would give net points
Scenario C
Card a 800 used out of 2000
Card b 0 used out of 1000.
After transfer you would have 1 card at 0%, one card at 80% and total cards at 26%. This could lose some points due to the higher uti on an individual card reported.
Obviously real life situation is much more complicated. As you could have more than 2 cards, and you could have existing balances on both before transfering from 1 to the other. But I hope this helps.
Overall % util wont change, but the % utils on the individual cards will.
Util of revolving credit is scored based on overall % util, the % util of each revolving account, and the % of revolving showing balances.
Thus, there will likely be some score change.
As long as the whole balance is being transferred, your score at worst would remain flat. Aggregate util remains static, and indivdiual util is guaranteed to drop if an entire balance is moved to a card with a higher limit. If that drop crosses a threshold you may gain some points.
There's a chance for a temporary score drop if one of these two things happens:
If either of those things happen, the dust will settle as soon as your reports catch up. After that, if the balance transfer is the only change, your score should either remain flat or increase slightly.