Why does a brush with 50% opacity and 100% flow take 8 individual strokes to reach 100% opacity?

I have a simple round brush with 100% hardness, 50% opacity and 100% flow. All other brush settings are disabled (brush dynamics, transfer, etc). Since it has 50% opacity, I would expect 2 brush strokes to equal 100% (50 + 50) opacity. However, it takes me about 8 brush strokes to reach the same level of opacity that a single brush stroke on a 100% opacity brush makes. What kind of rules does Photoshop use when adding the opacity of overlapping brush strokes? I’m using Photoshop CC.

Answer

Basically it blocks 50% of what is left behind, as opposed to being a pure 50% opacity in a additive way. Therefore working in an inverse exponential way towards 99.999…% opacity.

So laid on top of each other:

• 1st stroke: 50%
• 2nd stroke: 75% (50% + 50% of 50%)
• 3rd stroke: 87.5% (75% + 50% of 25%)
• 4th stroke: 93.75% (87.5 + 50% of 12.5%)
• 5th stroke: 96.875% (93.75% + 50% of 6.25%)
• 6th stroke: 98.4375% (96.875% + 50% of 3.125%)
• 7th stroke: 99.21875% (98.4375% + 50% of 1.5625%)
• 8th stroke: 99.609375% (99.21875% + 50% of 0.78125%)

etc…

Attribution
Source : Link , Question Author : Jorge Luque , Answer Author : Digital Lightcraft