Consider that humblest of automata: the room thermostat. It has a sensor (temperature) and an actuator (boiler on/off control) and some artificial intelligence, to decide whether to switch the boiler on - if the room is getting cold, or off - if the room is getting too warm. (If the thermostat has hysteresis the 'on' temperature will be different to the 'off' temperature - but that's not important here.)
I said that the theromstat's AI 'decides' whether to switch the boiler on or off, which implies that it has free will. Of course it doesn't, because its artificial intelligence is no more than a simple rule, 'if temperature <> 60 then switch boiler off', for example. So, depending on the temperature, what the thermostat decides is completely determined. With this simple deterministic rule the thermostat can't simply decide to switch the boiler off regardless of the temperature just for the hell of it.
Well all of that is true for 99.99..% of the time. But consider the situation when the temperature is poised on almost exactly the value at which the thermostat switches. The temperature is neither going up nor down but is balanced precariously at a value just a tiny fraction of a degree away from the switching value. Now what determines whether the thermostat will switch? The answer is noise. All electrical systems (actually all physical systems above absolute zero) are noisy. So, at any instant in time the noise will have the effect of adding or subtracting a tiny amount to the temperature value, either pushing it over the switching threshold, or not.
For 99.99..% of the time the thermostat is deterministic, but for the remaining 0.00..1% of the time it is stochastic: it 'decides' whether to switch the boiler on or off at random, i.e. 'just for the hell of it'.
But, I hear you say, that's not free will. It's just like tossing a coin. Well, maybe it is. But maybe that's what free will is.
Consider now that oldest of choices. Fight or flee. Most of the time, for most animals, there is no choice. The decision is easy: the other animal is bigger, so run away; or smaller, so let's fight; or it's bigger but we're trapped in a corner, so fight anyway. Just like the thermostat, most of the time the outcome is determined by the rules and the situation, or the environment.
But occasionally (and probably somewhat more often than in the thermostat case) the choices that present themselves are perfectly evenly balanced. But the animal still has to make a choice and quickly, for the consequences of dithering are clear: dither and most likely be killed. So, how does an animal make a snap decision whether to fight or flee, with perfectly balanced choices? The answer, surely, is that the animal needs to, metaphorically speaking, toss a coin. On these rare occasions its fate is decided stochastically and brains, like thermostats, are noisy. Thus it is, I contend, neural noise that will tip the brain into making a snap decision when all else is equal - the neural equivalent of tossing a coin.
This is why I think brains evolved to be noisy.
The long extinct ditherers probably had less noisy brains.