Cloaking device increases ship defence +5 against beams and missiles when cloaked. If without this attackers attack level matches your defence level adding the cloaking device will reduce chance of hit from 50% to 5%. Note that ships decloak to fire and take 1 turn without shooting to re-cloack but will always shoot first. So you use to gain initiative for first heavy strike but suffer full damage in return or stay cloaked while you close on target such as bombers attacking planet.
No need to use cloaking, it comes to late to matter anyway. If you ever see stacks of cloaked AI ships, you see the effects of the defense bonus. They are much harder to kill.
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