Some of the most successful organisms by total biomass are social insects like ants: complex 'super-organisms' that work together so closely that they can be considered as a single unit of natural selection. A common problem in Bayesian statistics, and elsewhere, is to sample from unknown probability distributions, with efficient sampling preferring to locate regions of high probability first. I use Markov chain Monte Carlo methods developed to solve such problems as models of animal exploration, and use the idea of Kelly betting from information theory to develop a probability matching model of collective ant foraging. The technique of approximate Bayesian computation is used to understand the ants' quorum sensing decision procedure as approximating the probability that a location is the best option for a new nest. These models allow the efficiency of such tasks to be measured in informational terms. Studying the movement behaviour of individual ants, I find evidence for motor planning, and relate this to information processing effectiveness at the level of the individual and colony. I identify a new method of collective exploration in T. albipennis - avoiding the chemical markers left behind by previously exploring nest mates - and show that this allows both real colonies and a biomimetic MCMC method to sample from an unknown space more efficiently. I report experimental work that finds colonies navigate more efficiently to a new nest site when a sloping landmark is present, compared to a horizontal one. I identify lateralization in foraging Australian meat ants, Iridomyrmex purpureus, and in T. albipennis, as the ants prefer left turns when exploring unknown nest sites, and associate this with slight asymmetries in their eyes. I also find that T. albipennis males have much larger eyes than queens, consistent with a 'female-calling' mating system where the males fly to the queens for matings.