Don't touch the actors and they won't touch you

The 'normal' way of making a conditional in English is with an 'if'-clause:

If you hurry up, we'll be in time for the train.
We'll be in time for the train if you hurry up. 

There are plenty of others too, of course (As long as you keep walking, we'll be in time for the train) and of course -- isn't it always -- it's much more complicated than this, but there's also a cool way of doing conditionals with and and or.

Consider this warning, which I saw at Dreamland in Margate at their Screamland Hallowe'en thing a couple of years ago:

Don't touch the actors and they won't touch you.

Poster for 'Screamland' in Margate

You could interpret that as an instruction combined with a simple statement of fact: the instruction is not to touch the actors, and the statement is a reassurance that they won't touch you, independent of the instruction. That might in fact be what is intended here, because even if you do touch the actors, they're probably still not supposed to touch the visitors.

But we're funny things, humans, always looking for connections, patterns, reasons, and causes. Those two things being joined makes us want to think that there is some meaningful link between them. It's like if someone says The car is making a funny noise and Jen borrowed it yesterday. You can be pretty sure they're blaming Jen for the funny noise the car is making, and not just telling you two unrelated facts about the car.

Generally, in an and sentence, both bits are the same type: both statements, for instance, in which case they must both be true (so for the sentence about the car to be true, it must be true that it's making a funny noise and that Jen borrowed it -- notice that the inferred link that Jen was to blame does not have to be true). Or they might both be instructions, in which case you're expected to obey both (at the same time or in order), as in Sit down and shut up. Our example sentence, about the actors, is a mix of an instruction and a statement. So we might be expected to obey the instruction and for the statement to be true. I don't know about you but I don't really know where I stand right now, as there is no obvious link between my obedience and objective truth.

It would make so much more sense if, say, the truth of the statement was conditional on me obeying the instruction. So if I don't touch the actors (obey the instruction), then it will be true that they don't touch me. And all of a sudden, we have a conditional like the 'if'-clause type I mentioned right at the top, but with and instead.

Can we do it with or, a disjunction? Well, yes we can, but it comes out as a warning or threat rather than a deal or an agreement.

Don't bother the tigers, or they'll attack you. 

Now, we still have to obey the instruction but if we don't, then the second part will be true: a punishment, rather than a reward for our obedience.

We can even do it with neither at all, just so long as it is a proper threat and not just a warning:

Touch my stuff, I'll beat you up. 

Now the instruction is an elliptical conditional. There's probably an understood 'If you' at the beginning, or else the link between the parts is the same as with and: if the first part is 'obeyed' (the person does carry out the action), then the second part is true.