The author doesn't need to have the same tactical genius of those characters, because the writer has a serious advantage.

As an author, you know everything and you can change everything of your story. You almost have omniscience and omnipotence over your fictional world. I say almost since you won't know every detail immediately - especially if you are a discovery writer - but surely you know more than the characters involved.

You don't need insight, since you don't need to make any "prediction" on future events. What you need is to portray your characters as insightful, intelligent, innovative or sly. And that's just a matter of portrayal!
How do you portray a character as brave? You make him face his/hers fear. You make him/her confront danger.

Showing tactical mastery might be slightly less straightforward, but it can be done still. You have to keep in mind that the characters, unlike you, don't know everything about the world and are working with limited resources.

Let's say the heroine Alice, tactical genius in a medieval setting, has to lead her ragtag rebel army against the Evil Dark Tyrantâ„¢ Bob. You already decided that Alice has to win the battle for plot reasons, but of course, she doesn't know that. And her victory has to be believable and portray how much a good strategist she is - she can't just pull fresh troops out of nowhere, erase the enemy army with make-believe magic, or anything like that.

So, how can she win? To her, winning the battle must be like solving a puzzle - maybe crossworld one. Ask yourself: what does Alice know ....

About the enemy's generals?
About the enemy's information network? What do they know? What do they believe? Are there blind spots in their knowledge?
About the enemy's army? Composition, average size, location, morale? Possible weakpoints? Possible points of strenght?
Who will lead the enemy's army? Bob himself or someone else? How did he fare in other battles? Is there any peculiar / recurrent trick or strategy he uses? Does he rely much on something?
About the battleground? Can she pick a battleground of her choice? Is she forced to lay siege?
About her own generals, her own armies and strenght? Her own supply line?

Alice must try to answer those questions in order to plan. Some of those will be difficult, if not impossible, to answer. As the leading general, she must have a network of spies/messangers/scouts tasked with providing her with useful informations. Some will be reliable, some will be misleading. She has to listen and make assumptions in order to formulate her plan.
If you show this, you will show how versed she is in dealing with strategy. Quoting Sun Tzu's Art of War:

Every battle is won before it's ever fought.

and so, a great deal of tactics happen way before the actual battle (or war).
When she's finished gathering information, Alice's goal should be maximizing her gains while minimizing her losses. That usually means winning with the fewer cost in terms of lives/resources lost, (of course it all depends on what Alice wants. Maybe she's not so protective of her men).

In order to do so, she might...

..leverage one of her strenghts against the enemy,
..make use of the enemy weaknesses or blindspots,
..trick the enemy into doing something - falling into a trap or in a predicted behaviour

We could make countless examples of what are good tactical moves. For example, if the enemy is known for relying on a strong cavalry, the number one priority could be negate his cavalry. Alice could choose to fight upon a hill, in a marsh, build trenches, deploy pikemen, and so on.

Like a chess game. You both need powerful and less powerful pieces, but what you need most is the ability to outthink and outmaneuver your adversary. This means that you can see "farther" that he does - meaning you can predict a greater number of moves into the future. A simple example of that, often show is movies, is the Feigned Retreat: you make your army run away from the front line, in order to make the enemy think you are fleeing. If the enemy falls into the trap and pursues, there is a good chance that its soldiers will break formation, becoming more vulnerable to your retaliation.

There's surely a lot to consider, and it might be a lot to take in. I do recommend some books on military tactics - I have already mentioned Sun Tzu, but others may be found.

Now, if you want to have multiple strategists in your novel (as, for example, in game of thrones) things will get a little more complicated. Now it's not only Alice and Bob playing chess, but it's 10 playes on a very odd, 10-sided, four dimensional chessboard. Yet the basic rules are the same - tacticians will try to get information, predict what their enemies will do, and try to outsmart them.

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