The game is played on a 55 point grid, like alquerque. Pieces are positioned at the intersection of the lines and not inside the areas delimited by them. Directions of valid movement between these points are connected by lines. The game play takes place in two phases. In the first phase the goats are placed on the board while the tigers are moved. In the second phase both the goats and the tigers are moved. For the tigers, the objective is to "capture" five goats to win. Capturing is performed as in alquerque and draughts, by jumping over the goats, although capturing is not obligatory. The goats win by blocking all the tigers' legal moves. Bagh-chal has many similarities to the Indian game aadu puli attam (lambs and tigers game), though the board is different.
The player controlling the goats moves first, by placing a goat onto a free intersection on the board. Tigers may move along the lines from one intersection to another. Once all of the goats have been placed on the board, goats must move in the same fashion as the tigers, one intersection to another. Moves alternate between players.
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Sometimes the game can fall into a repetitive cycle of positions. Goats especially may use this resort to defend themselves against being captured. To avoid this situation, an additional rule has been established: when all the goats have been placed, no move may return the board to a situation that has already occurred during the game. For instance in the following position the goat-player can not move forever in the upper right edge while tiger-player may continuously play the middle bottom edge tiger waiting for a goat to sacrifice itself.
Bagh Chal is an ancient hunt board game from Nepal. Its name means "moving tigers", and is played by two players, one controlling four tigers, the other controlling twenty goats. The four tigers must eat five of the goats, but the goats must trap the tigers. Some have called bagh chal the national game of Nepal.
It is said that the game is a thousand years old. Some sources say the game originated in the Himalayas, and others that it came from further south in India, where similar games have been played for centuries. Whatever its antiquity, the game is still popular today, with traditional brass sets with cast pieces still being made and sold across the world by Nepali craftsmen.
Rules for Bagh Chal Bagh Chal is played on the alquerque board by two players. One has four tigers, while the other has twenty goats. Henceforth they will be called the tiger player and the goat player.
9. To eat a goat, the tiger player must jump with one of his tigers along a marked line, over an adjacent goat, to an empty point beyond. The goat is then removed from the board and takes no further part in play.
Bagh-Chal, which means "Change of Tigers" or "Tigers' Moves", originated in Nepal. As the country's national game, Bagh-Chal was created by Himalayan herders, whose job the game resembles. The game, which has been played for more than a thousand years, is played by some shepherds on a grid scrapped into dirt with stones used as bagh (tigers) and pebbles symbolizing bakhri (goats).
The first (GOATS) player plays with twenty goats and the second (TIGERS) player plays with four tigers. At the start of the game, the tigers are placed at the corners of the board and no goats are placed yet, as shown below.
The set of moves available to the GOATS player depends on whether there are still goats to place. If not all twenty goats have been placed, then the GOATS player shall place one of their goats on an empty point. If all goats have been placed, then the GOATS player shall move one of the goats on the board to an adjacent unoccupied point.
On their turn, the TIGERS player either (1) moves one tiger to an adjacent unoccupied point OR (2) performs a goat capture by having one tiger jump over an adjacent goat to an unoccupied point adjacent to and on the other side of the goat, after which the goat is removed from the board and cannot be placed again. Only one goat may be captured at a time. A tiger may not jump over another tiger. In the above example, the rightmost tiger may jump over the goat below it in order to capture it.
Instead of diving straight into the project, I want to introduce Artificial Intelligence and some of the relevant concepts first. If you would like to skip these upcoming sections, directly refer to the Bagh Chal AI Project section.
When programmable computers were first created, they rapidly overtook humans in solving problems that could be described by a list of formal mathematical rules, such as mathematical computations. The main obstacle to computers and artificial intelligence proved to be the tasks that are easy for human beings but difficult to formalize as a set of mathematical rules. The tasks such as recognizing spoken words or differentiating objects in images require intuition and do not translate to simple mathematical rules.
We generally do not give our brain enough credit and are unaware of the extent to which our intuition plays a role in our everyday thinking process. To that, I want to start the blog with a perfect example that Andrej Karpathy gave in his blog back in 2012 that holds to this day.
This list could go on and on. The mind-boggling fact is that we make all these inferences just by a simple glance at this 2D array of RGB values. Meanwhile, even the strongest supercomputers would not even come close to achieving this feat using today's state-of-the-art techniques in Computer Vision.
For the sake of this blog, let's start with something more straightforward. Imagine that we are given a task to identify handwritten digits in a 28x28 image. How would we go about solving this problem? It might sound ridiculously easy at the start considering that even a small child introduced to numbers can get this correct almost every time. Even though this example is used as the typical "Hello, World!" program equivalent for people learning Artificial Intelligence, the solution to this problem is not as trivial as it first seems.
One obvious classical approach would be to use handcrafted rules and heuristics on the shape of strokes to distinguish the digits. However, due to the variability of handwriting, it leads to a proliferation of rules and exceptions giving poor results. Some sample variants of the handwritten digits are shown in the following image.
Before we start talking about how to solve this problem, let's first understand how machine learning differs from the traditional programming or algorithmic methods. Machine learning refers to the concept that allows computers to learn from examples and experiences rather than being explicitly programmed.
Basically, we trade-off the hard-coded rules in the program for massive amounts of data. Mathematical tools in linear algebra, calculus, and statistics are cleverly used to find patterns in the data and construct a model that is then used for prediction. The model is trained through an iterative process where its predictive accuracy is evaluated and improved. This is done by using an optimizer to minimize a loss function that tells us how bad the model is doing. As a result of this training process, the model becomes proficient in accurately predicting outcomes for data it has not encountered before.
For instance, instead of using handcrafted rules to identify handwritten digits, we can show the computer lots of examples of how each digit looks like. It can then use information from the example data and try to fit them to a model. Over time, it learns to generalize over the shape of each digit.
Supervised learning is a type of machine learning in which the learning is done from the data having input and output pairs. The goal is to create a model that learns to map from the input values to the output.
It is called supervised learning because we know beforehand what the correct answers are. The goal of the machine learning algorithm is to learn the relationship between each input value to the output value by training on a given dataset. In doing so, the model should neither prioritize specific training data nor generalize too much. To avoid this, a larger training dataset is preferred and the model is tested using input values that the model has never seen before (test dataset).
We can see that the last model correctly predicts all the training data (all points pass through the purple line). However, this model is said to be an overfit model (too specific to the training set) and it performs badly on the test set. Similarly, the first two models are said to be underfit models (too much generalization).
Regression problems are related to predicting real value output in continuous output space. The above problem of finding the best-fit polynomial to predict output to its other input values falls under this category.
Unsupervised learning is a type of machine learning in which the learning algorithm does not have any labels. Instead, the goal of unsupervised learning is to find the hidden structure in the input data itself and learn its features.
Dimensionality reduction is used to convert a set of data in higher dimensions to lower dimensions. They can remove redundant data and only preserve the most important features. This pre-processing technique can reduce a lot of computational expenses and make the model run a lot faster.
The new unsupervised deep learning field has given rise to autoencoders. Autoencoders use deep neural networks to map input data back to themselves. The twist is that the model has a bottleneck as a hidden layer. So, it learns to represent the input in a smaller amount of data (compressed form).
The agent interacts with the environment by performing certain actions and receiving feedback in the form of rewards or penalties. The objective of reinforcement learning is to develop a policy that enables the agent to take actions that result in the maximum possible long-term cumulative reward.
A reward is a scalar feedback signal which indicates how well an agent is doing. The agent's goal is to maximize the reward signal. For instance, in the example of flying stunt maneuvers in a helicopter, 152ee80cbc
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