I noticed when initially googling "Monte Carlo Algorithm", google artificial intelligence was first to come up, providing no specifics on its workings. Is this proclaimed algorithm the same as used in Iota or is any correspondance incidental?
I am pretty sure that the name is a coincidence.
In general statistics, "Monte Carlo algorithm" refers to an algorithm that does not calculate an exact result, but performs several random simulations and then uses the simulation results to estimate the exact result.
IOTA's algorithm is called "Markov Chain Monte Carlo" (Wikipedia link), and I think the "Markov Chain" part is more important in the name than the "Monte Carlo" part.
MCMC ("Markov Chain Monte Carlo") is used for tip selection in IOTA. It is not mandatory, but the default iri algorithm (see Does the Tangle enforce a tip-selection algorithm?)
White paper says: "The MCMC algorithm of this section, which is adopted by a considerable proportion of nodes, defines a probability distribution on the set of tips"
So the part of finding a good probability distribution for selecting new tips is paramount. E.g. not to allow someone to forge the mechanism to only select specific (his preferred tips).
The "markov chain" means that you walk through a tree of possible states and describes the fact that within the tangle you have such a real-time stochastic space when selecting tips and building up a tangle (analogue to a stochastic tree).
In fact the "monte carlo" part guarantees that you kind of like throw a dice and get a good random stochastic distribution of your selected tips. Which in turn makes sure, that an attack is much more difficult, since you do not know which tips will be selected by a node.
Btw, since you mention google AI.
Monte Carlo Tree Search (https://en.wikipedia.org/wiki/Monte_Carlo_tree_search) is a heuristic search algorithm for some kinds of decision processes, currently used in DeepMind's evolving AI programs such as AlphaGo, AlphaZero, AlphaStar to build a general purpose AI.