Recently Someone asked me...
What board/tabletop game best teaches you strategy and tactics?
My answer to their question was two fold. All of them and none of them. The reason I answered it that was is because the person was asking me two questions. What game teaches strategy well, and what game teaches tactics well. In common language the word strategy and tactics are used interchangeably, and that is completely okay in day to day speak; however when studying military science it is actually referring to two different things. Tactics are what a leader would use to win a battle, or more specifically and engagement. Tactics involve things like flanking, approach marches, employment of fires etc. Essentially one unit fighting one unit, (a duel as Clausewitz would say). Strategy is what you use to win a war. Strategy is using multiple units to engage in multiple dual to reach a desired outcome, the Checkmate. Which segue's nicely into my first answer.
Strategy isn't something that is learned, so much as its a way of thinking that is develop. It is a number of cerebral skills that work together. Like being able to identify objectives, not only the endstate but being able to break it down into other objectives which must be accomplished in order to complete the mission. It is developing courses of action and then anticipating the enemies response. Therefore my first game that I suggest for someone who wishes to develop strategic thinking is chess.
Chess, at least when I started playing, was more or less moving pieces around the board without any real direction, and after loosing a few (okaying I'll be honest, more than a few) games, I realized that In order to win at chess I had two missions I had to accomplish. First of all, force my opponent into a checkmate, and interrupt his process of the same. To be successful at this I began to weigh each move and ask myself a few questions. First question, what do I stand to loose from making this move? Do I open up and avenue of approach to the enemy? Am I leaving a piece unsupported? will that prompt my opponent to counter attack in a way that strengthens his position? If the move can be made without destabilizing my own position. I asked the important question. What do I have to gain from this move. Am I putting pressure on the objective or important enemy resources? Can I draw attention away from my main effort (feint)? This helps, but it doesn't end there, in chess you must Thinking in a cause/effect manner in reference to the future is the fundamental of strategic thinking.
The next game I would suggest everyone play if they would like to be a student of strategy is Stratego. (fun fact, it's Greek for general) The first reason I recommend this game is because its really fun and that is the most important thing about wargaming. For those who are looking for a little self improvement though, Stratego has a lot to offer. The game requires the same analytical process as chess, (and is less stressful) but it adds the element of the unknown. In Stratego you have to use reasoning and resources to identify the strength of the enemy. It also adds in a few elements that can be found in real war, like obstacles (bombs) engineers (minors, or the number 8 piece) and recon (scouts). ( though I have to say my father is awful at this game, he is a competent chess player, however when he encounters the element of the unknown it screws up his process. So this could be a good challenge to some of you out there)
Most games can offer you a chance to develop the skills required to become a strategist. It comes down to applying the analytic process to win the game. Some other games that are effective at this are, checkers and Flames of War.
Now I will explain why boardgames and tabletop games cannon teach tactics. (atleast not real tactics) It is because each game has its own set of tactics that you use in order to facilitate your overall plan. Chess.com has a series of exercise that are one or two move chess tactics that are specific to certain situations, Warhammer 40k has tactics, like placing a squad more than six inches behind the enemy so they cannot consolidate into you if they win the assault. Real life tactics are found in doctrine, and address things that are more or less constant realities of a particular type of warfare. So to learn tactics, break out field manuals and read, and if you really want to learn them go out and do them. (aka join the army/marines) (there are also some pretty high speed air soft guys that are pretty bent on tactics)