This prompts the question "can kutakata go on for ever?"; and if so, what characterizes an initial state which can go on for ever? - or alternatively, can we prove that all kutakata moves come to end, whatever the initial state?
This question is not yet precisely posed since we have not mentioned how many kete may be on one player's two rows. We will leave this issue hanging, noting that it could be that there are self-perpetuating board states which involve more kete than are used in a normal game of Bao; so perhaps the rules of Bao have been chosen such that infinite loops are impossible. Often in theoretical physics, we find that a system changes from one sort of behaviour to another sort of behaviour as we increase the concentration of particles (for example, as we compress a gas, it turns into a liquid then into a solid); so one exciting idea is that perhaps Bao has a similar `phase transition' --- maybe we'll find that infinite loops only happen when the number of kete is bigger than 137, or something like that?
From here on, I lead you through a partial solution to the above question. My aim is to try to illustrate how theoretical research proceeds. There are many strategies that are helpful.
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