Why don't two 50% opacity layers of the same color make the solid color in Photoshop?

I am trying to create a gradient that when flipped and overlayed on itself will show a solid color.

I thought I would make it with a regular solid-to-transparent gradient on Photoshop, and save it as PNG, but when superimposed on one another, it still shows some transparency.

I tried to do it inside Photoshop and the same experiment with regular layers that had 50% opacity does not show the solid color (i.e. it does not "kill" the transparency).

What am I missing?

The opacity is a multiplier. Assume:

• Layer 1 opacity = 50%
• Layer 2 opacity = 50%
• Layer 3 opacity = 50%

Net opacity = Layer1 + (Layer2 * Layer1) + (Layer3 * Layer2 * Layer1)

Or, 50% + 25% + 12.5%. You would mathematically never get to 100%.

The way I look at it, each layer lets 50% of the light through... you don't get 100% with it.

It's like the weatherman saying there's a 50% chance of rain on Saturday and on Sunday, and concluding that it must rain sometime during the weekend. Obviously it doesn't mean that. :-)