Research on "probabilistic thinking" in non-human animals? We all seem to have a "probabilistic sense", which manifests itself in certain types of expectations (e.g. even if one has never used a bow to shoot an arrow, one expects that hitting a small target will be more difficult than hitting a large target, all other things being equal), and also in certain characteristic responses when events do not match those expectations (these responses consist primarily of surprise, but also include suspicion, and in extreme cases maybe even awe or fear).

For me at least, this probabilistic sense feels subjectively very fundamental, in the same way that physical pain, hunger, thirst, etc., "feel fundamental".  In other words, I could not describe them to someone in simpler terms.  (I may be able to explain to someone the mechanics of shooting an arrow with a bow, but I would not know how to explain to someone how to feel the immediate intuition that hitting a small target would be harder than hitting a large one.)

Motivated by the kind of questions that follow, I'm looking for a review of research on "probabilistic thinking" by non-human animals.

How analogous is this "probabilistic sense" to the more traditional
   ("classical") senses like vision and touch?
In particular, how much does it depends on human culture?

I've searched for these keywords online, but I have not come up with anything.  Maybe I'm not using the right keywords.  Also, since probabilistic methods as standard tools in research (and hence, the research literature is awash in terms like "probability", "expectation", "Bayesian", "statistical", etc.), it is very difficult to craft searches that are selective for the research I'm looking for.  Some specific pointers (i.e., to specific papers, or books, or at least specific researchers) would be appreciated.



FWIW, the clearest example I can come up with to illustrate what I mean by "probabilistic thinking" is this thought experiment.  Imagine presenting a human subject the opportunity to participate in a raffle for some prize that the subject finds desirable, and suppose the subject is just told that he/she has the choice of having (A) one, or (B) two tickets for the raffle (at no cost in either case).  We would expect, of course, that every "normal" subject would prefer (B) over (A).  (In fact we would question the sanity (or at least the seriousness and sincerity) of any subject who fully understood the situation, and still preferred (A) over (B).)

What makes the universal preference for (B) an example of "probabilistic thinking" is the simultaneous recognition on the subject's part that choice (B) is unequivocally better, and that still it could fail to lead to the prize, even if the raffle had only three tickets.

I'm not sure how one would go about setting such an experiment with non-human animals, but I've been impressed before by the ingenuity of the experiments that researchers devise to test animal cognition, so I remain hopeful that something like the "probabilistic thinking" I illustrate above has been investigated.

That said, I realize that it would be rather difficulty is to distinguish between pure "probabilistic thinking" (as a distinct, independent faculty) and conditioning.  In fact, it can be (and has been) argued that what I'm calling "probabilistic thinking" is nothing more than a special case of conditioning.  (After all, conditioning may be thought of as the nurturing of certain expectations, and preferring two tickets over one could be simply a manifestation of one such expectation.)  Ironically enough, when it comes to humans, I can't think of any ethical experiment that would be able to establish "probabilistic thinking" as a faculty that would be present even in the absence of any conditioning.  With animal subjects, however, it may be possible to set up experiments that minimize the possible confounding by conditioning.
Try an internet search on animal learning probability.  Although that might not be what you want because it sounds like you specifically want insight as opposed to learning in general.

Your particular example is problematic because you're inferring far too much on the subjects part. They might prefer B because they just want more of anything offered. The experiments need to be much more careful than that in order to attribute effects to probabilistic thinking. What kind of response will occur doesn't just depend on the probability of events but what kind of reward contingencies are associated.  Both people and animals do dumb things with simple probabilities and rewards.  But they do the same thing. Does that justify an argument that they have a probabilistic sense?

Deriving a distinction between insight and conditioning is sometimes problematic (for example food aversion in rats) and insight is usually only accepted when it can pass the interocular impact test.  While I can show you lots of papers on probability learning I'm unaware of any that tap insight about probabilities.

Consider the problem for the researcher. In order to establish insight into probabilities the subject has to experience the events repeatedly in a relevant way so that they become learnable. Given this takes a degree of exposure in the first place it would be very hard to dissociate conditioning from insight based learning.

Also consider that people sometimes can learn probabilities but don't always do intelligent things with them. For example, when there are two possible events and one happens 75% of the time people tend to select the frequent event 75% of the time. This is rather boneheaded because selecting the frequent event all of the time will give you the most accurate performance. Animals actually learn to do the latter. So maybe animals have a stronger probability sense? Regardless, they clearly they learn probabilities.