During the Middle Ages, Knights in training were required to play Chess in addition to conventional education and arms training.

Chess actually does teach an individual a lot about decision-making.

Chess players enter a purely rational game of strategy. Emotions only have negative impacts. If you get enraged at the loss of a piece, you are more likely to make a rash poorly decided moves that result in defeat. To create an effective strategy, a commander must manage his emotions very carefully.

Wargames also teach young men the general concepts of probability and game theory and how these limits strategic possibilities.

A non-cooperative game between two players is a complex adaptive game. Both players engage in a zero-sum competition where they change and adapt strategies in reaction to their opponents.

This teaches the need to guess your opponent’s intention and strategy and not just focus on yourself. You have to imagine moves and countermoves several turns in advance to formulate a useful strategy, yet you cannot create a ‘perfect’ long-term plan do to uncertainty. None of your plans work in practice, so the best strategies are ones that are flexible and adaptive.

Simple games produce wide variations in results in just a few turns. Take a hypothetical game where each player has 10 alternative moves each turn. Player 1 can make one move in any of 10 places, and then player 2 moves. There are 100 possible outcomes after the first turn. After the second turn, there are 10,000 possible outcomes, then 1,000,000 possible outcomes at the end of the third turn.

For chess – in the first turn, White may make one of 20 possible moves. Black may make one of 20 possible moves. There are 400 possible variations at the end of the first turn. The second turn grows more complex. Bishops are free to move out. Pawns can block other pawns from advancing. White’s moves restrict Black’s possible moves. I don’t know know how many possible results there are 2nd game of chess (Never bothered to count and never will). I’ve read that there is an average of 35 legal moves per player per turn. So 35×35 per turn, cumulative. After 1 turn, 400 possible outcomes, by turn 2, the number is 4,900,000. By turn three, they could be 6,000,250,000 possible outcomes.

Out of these possibilities, clear and complex strategies can emerge. This limits the number of likely moves per turn by each player as they commit to specific strategies and counter-attacks.

Chess is actually a very simple game. Go is much more complex. Hex is another interesting game. Invented by Thomas Nash, if you’re curious.

These are deterministic games, where information is complete (both sides see all moves and rules are constant – there is no fog of war or mechanism changes).

Technically, you can win a game of chess by doing the math. It’s just not very polite to keep your opponent waiting for hours every turn.

Computer AIs play these games the best. Take Deep Blue, the famous computer that can beat chess grandmasters. Basically, Deep Blue is a Dumb AI programmed to obey legal moves and make blind searches for available moves.

Deep Blue tediously calculates the probabilities and utilities of each of its 35 possible moves per turn, the opponent’s probable countermoves, many turns in advance. It continually updates its probability for every move. Mathematically, Chess is a more limited game than we first thought.

There are games that model fog of war – like Battleship. You don’t know where your opponent placed his ships. You infer their locations via hits or misses when you attack and you race to sink his fleet before he sinks yours.

There are pure stochastic games, usually dice games like Monopoly, where random chance creates outcomes, not just player choices.

There are very advanced wargames designed to model real-life combat. HPS produces such games. I played one back in the DOS era, and it was absurdly complicated. Amongst other things, it modeled how dampness affected gunpowder and bullet velocity and penetration. Dampness.

Of course dampness is a major logistical concern. Archers used to put their bowstrings under their helmets to keep them dry during rain storms otherwise they would be useless in battle. Keeping gunpowder dry remains a major concern today. It’s usually considered such a minor point that games don’t model it.

Militaries still use wargames to teach general concepts and train officers and soldiers. They more accurately model environmental conditions (like dampness) and try to model enemy reactions.