"Alright Rarity, here we have the grid. There is a mathematical limit to combinations that will result in a win in games like this one, since the grid here is a small one we could almost go through all of them, but that won't lead us anywhere. Instead, we'll ignore rotations and inversions, so in the end there are 3 ways to make a line: 2 horizontal or vertical, and one diagonal-"
"But Twilight", interrupted the unicorn, "surely there must be more ways to win than three?"
"That's what I meant by rotations and inversions. For example...", Twilight began to draw up a couple of states; it came almost disgustingly easy to her, "there's no topological difference between these states, whether the row is horizontal or vertical, if it is along one edge, you can say it's the same constellation. So if you know how to build one like these, you can apply that to any similar state."
"But Twilight", began Rarity, "I don't even know how to start a game!"
"I'm getting there, Rarity. It'll all be clear in a moment, I promise. Now, the complete number of states the game can adopt is 3^9, that is each of the nine spaces can have one of three states - claimed by X, claimed by O, or not claimed. You can adapt this formula to any similar game with any number of players, if we played with Spike and Fluttershy, on a twelve by eight grid, there'd be 5^120 states! Isn't that amazing?"
"But Twilight", said a puzzled Rarity, "How in Equestria is that going to help me? I really just need to know how to begin the game first!"
"Trust me, this may not seem relevant, but you will need this. So as I was saying, we have for the base the number of players plus one, since a space can be empty in addition to claimed by either player, and for the exponent we have the total number of spaces. So exponentiation is pretty much multiplying a number by itself several times. But this isn't where this all stops; since for the game it doesn't matter if we start in one corner or another - because we can clearly just rotate the paper, see? - this means that any moves our opponent makes are in relation to the others. Because we can rotate - and by extension, reflect - a state, this cuts down on the numbers of total combinations, as we already mentioned over the course of this seminar, so that in total..." Twilight didn't notice Rarity's mind had already begun to wander off. In the end, it didn't much matter, did it? It's not like she had to be ashamed of herself for not having grasped this simple game at an age where she already was a successful businessmare.
Having borrowed a raincloud for personal use from Rainbow Dash, who tactfully didn't ask for its purpose, Rarity trudged across Ponyville, drenched by the constant downpour upon her now thoroughly wet mane, tail and coat, a deep scowl on her face. She had to find a way, and merely succumbing to the despair did not yield any results aside from venting, but venting could only take you so far. Since Twilight, though well-intentioned and certainly educated enough, managed to turn a little explanation of a game into a lecture on maths, Rarity may need somepony more blunt to keep the explanation strict to the point. She already had a certain farm pony in mind, and thus headed towards Sweet Apple Acres, hoping that Applejack was able to clear the fog for her.