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Well, I watched this video about "Game Theory" some time ago, but the concept got stuck with me to this day.

In one moment of the video (or other similar videos of this channel), it is said that they use this equation (of the prisoner's dilemma) to help calculate the balance of characters in games.

In a resumed way, the video is about the test of two strategies of survival: if type A of blob faces another blob when eating, they share the food equally. If type B of blob faces another blob when eating, type B will take most of the food to itself. And so, the rest of the video is statistically analysing the survival rate of each type.

I tried to find a way of finding a solid equation/formula to calculate the victory rate of certain strategies in a game with little to no success.

The idea would be to use for multiplayer RTS games like Starcraft 2 or Total War.

So, game balancing is something that it can only be done by manually testing and exploring the game, or there is a way of easing things up, like with a mathematical formula?

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    \$\begingroup\$ You can use mathematical formulas, but there's no "one true formula" to use. The process starts with identifying your goals for the feature in detail. Then you can transform those goals into mathematical forms that, while they might not give you a single unique solution, can at least help bound the parameter space and help you understand the dynamics, guiding the fine tuning you do for game feel. The trouble is, usually folks go looking for a formula because they don't have a clear idea what their goals are, and hope the math has a "right answer" for them. For most game questions, it doesn't \$\endgroup\$ Commented May 26, 2022 at 18:36
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    \$\begingroup\$ So: my advice to you would be to get concrete. Not just a genre and example games, develop a clear design for your unique game in that space. Then zoom in on one particular aspect of the balancing, like the counter relationship of 2-3 specific units. Try editing your question to describe that one specific balancing problem in detail: what stats and resources are in play, what game outcomes should we see when it's balanced "right", what outcomes do you want to avoid? That should narrow the question enough to start throwing math at it. \$\endgroup\$ Commented May 26, 2022 at 18:40
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    \$\begingroup\$ This is the confrontation between the strategy and the environment. The environment is dynamic, so it is difficult to describe it with a fixed mathematical formula. Its unpredictability brings entertainment : king-of-the-hill. You can get a rough idea of the strength of a strategy in the current environment based on the results of extensive testing and adjust it. But you can't get the original numerical model through it. \$\endgroup\$ Commented May 27, 2022 at 9:28

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