Good question. It brings up the important consideration of practical computibility, what digital processes that exhibit intelligence can run fast enough on available hardware to be of use.
Rules Based Systems
In rules based (expert) systems, the search is based on predicate calculus, a mathematical model of human reasoning. The rules are an attempt to encapsulate the domain knowledge needed to solve expected problems.
In the case of chess, the rules are
a. the rules of the game and
b. the rules of excellence in winning game-play.
The search through the rules for each move presents an astronomical number of combinations 1, placing a burden on computing resources and the stake holders waiting for results. Strategies have emerged to achieve practical computibility, including these.
- Limiting the permutations by dismissing nonsensical permutations
- Following the more probable search paths first based on heuristics
- Distributing the rule set (in a compiled and optimized state) to multiple computing nodes in a cluster
- Finding commonly successful strategies and the conditions of when they are favorable and then executing them when appropriate
Artificial networks are circuits that attain acceptable behavior by progressively encoding knowledge in an N-dimensional array of parameters. The knowledge begins with an initial state, which is a guess, and then successive guesses2 converge on what is sufficiently encoded knowledge to produce acceptable circuit behavior in use.
MLPs, CNNs, RNNs, and other static topology machine learning components have their own characteristics that, taken together, place a heavy burden on computing resources and the stake holders. Each of these characteristics either produce a nested loop or a need for parallelism to replace the loop.
- Iterations required for convergence
- Iteration through each sample used in training
- Iteration through layers for both forward propagation of the signals and the backward propagation and distribution of corrective feedback
- Iteration through the channels specified by the width of each layer
- The heart of approximating complex behavior are the functions that are not first degree equations, which are often called activations even though their action has little in common with the activation of neurons in vertebrates.
If, in your scenario, the game contains pseudo-random moves and is played by a robot that must bluff and detect bluffs, there may be additional dimensions added to both training and game-play.
- Video adds pixel layer, horizontal and vertical positions, frame, and possibly camera angle
- Audio adds FFT Hann windows, frequency with phase, and channel
Convergence and Practical Computibility
What is termed stochastic gradient descent does parameter updates after each example, which can be too slow. Strategies have emerged to achieve practical computibility, including these.
- Shortening convergence time using back-propagation variants such as Momentum and Adaptive Moment Estimation
- Batch gradient descent performs model updates at the end of each training epoch, where each epoch iterates through all training examples
- Mini-batch gradient descent segments the training examples to find a balance between the robustness of stochastic gradient descent and the efficiency of batch gradient descent — This stragegy is in common use and the batches can be distributed to nodes in a super-computing cluster 3
The comment in the question that these methods do not produce the same result as stochastic gradient descent is correct. Mini-batch results (in terms of accuracy of convergence and reliability at finding the global minimum at all) is dependent on order of the batches if done serially with parameter adjustment at the end of each mini-batch. In other words if there are four mini-batches, Q, R, S, and T, the result of the training sequence Q-R-S-T will not be the same as Q-S-R-T or any other ordering of the four 3.
What is often abbreviated dataset is, from the perspective of statistics, a sample from a population. In chess, the population is every possible combination of moves and opponent moves to a game ending, including wins, loses, and stalemates.
When segmenting for mini-batch in a single computer process, the goal in selecting the sub-samples from the sample is to obtain a distribution of distributions of sub-sample characteristics that minimizes the difference between Q-R-S-T results and T-S-R-Q results.
The previous sentence is difficult to parse, but important. In simpler terms, the goal is to make the mini-batch produce results independent of mini-batch order. This equality in feature distribution between mini-batches is also important when the mini-batches are parallelized across a cluster because relative entropy4 impacts convergence rate.
Distributed Computing and Mini-batch
In a distributed computing scenario, once a convergence iteration is complete, the nodes communicate to distribute the results. The nature of the sharing of results between nodes can be as simple as averaging error, weighted by interim convergence accuracy, as the question implies, or as complex as another learning circuit to learn how to distribute results between nodes in parallel mini-batch architectures.
If you wish to understand practical computibility more deeply, study the two incompleteness theorems of Gödel, the limited completeness defined by Turing, the game theory of von Neumann, feedback theory of Wiener, and the application of these in deep learning.
Though seven years old, the concepts of this great primer covers some enduring concepts: Computability, constructivity, and convergence in measure theory, Jeremy Avigad, Department of Mathematical Sciences, Carnegie Mellon University, November, 2011
 The detection of a rule's condition, its antecedents, may lead to the execution of the rule's consequence. If there are several antecedents that apply, which one first is applied first may be a result of the order of the rules in a sequence of them. There may be meta rules to guide selection. If one takes the game of chess and examines the logical permutations of rule execution, even for a single chess move, the possibilities can grow astronomically. That challenge to practical computibility was termed the combinatorial explosion.
 Successive guesses in an optimization scheme are generally not random, although the injection of pseudo random perturbations or tries may increase convergence rates and reduce risk of confounding convergence by landing a local minimum when searching the error surface for the global minimum. This search is often accomplished via gradient descent, a scheme that uses the Jacobian of the feed forward functions (and sometimes their Hessian) to intelligently seek the minimum of disparity between current circuit behavior and some specified ideal. That ideal may be a closed form (formula) or a set of correct answers associated with each example, called labels.
 Except under the extremely rare coincidence that R is identical to S or by the much rarer coincidence that they are functionally equivalent in the given particular training scenario even though they are not identical.
 Kullback–Leibler divergence or relative entropy is a concept built over Claude Shannon's information theory. The term entropy, borrowed from the thermodynamic concept of entropy as a measure of disorder, is an important concept to understand in the quest to achieve practical computibility for a larger set of learn scenarios and the larger networks needed to learn them.