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While answers will vary depending on the case, I'd love to hear about what people have seen in their past experiences. The question mainly relates to DirectX though if you have some numbers for any other API (OpenGL, consoles etc) I'd be glad to hear them too.
Thanks in advance.
It depends what states you're changing; different things cost different amounts. Simple state like blend equations and most other SetRenderState stuff is cheap, and gets batched up till the next draw call so doesn't incur a large penalty for hitting the driver. Shaders and render targets are more expensive and will generally cause issues if you swap them excessively.
Usually though render states are not something you have to worry about overly - draw call overhead will almost always dwarf render state costs.
In terms of numbers I'd suggest aiming for no more than a couple of hundred shader swaps per frame, as few render targets as you can get away with and not worry about the rest. Typical numbers for simple state might be 5-10 state changes per draw call, but it's very variable.
It doesn't matter how much renderstate changes really is, you should always minimize that number, using sorting, etc, as renderstate changes are expensive on most APIs.
Two. Enabling and disabling depth-testing for the UI.
Everything else is handled by shaders.
