I'm glad you brought this up and it's an excellent analogy. And one that I can speak to since I work on a chess engine for a living.
In fact, a chess engine's strategic understanding of the game is folded into its evaluation of moves. It's impossible to say that one move is better, worse, or the same as another move without taking strategy into account. (Otherwise, what do you even mean when you say one move is better than another, if you don't mean strategically?)
So if a chess engine evaluates two moves to have the same score, then it really is a coin toss. There is no "making a strategic decision" to decide between the two, as you describe it. The engine has evaluated that even though each move might result in different strategies, they both have equal probability of winning, so it doesn't really matter which move is made.
This happens fairly often, too. It's not unusual at all for two (or more) moves to have the same score, or scores so close to each other that the difference is basically noise.
(Sorry if this bursts any illusions you might have had about chess engines always making moves very deliberately according to some particular strategic plan.)
Pool can be thought of in exactly the same way. A pool table corresponds to a chess board and shots correspond to moves. And people instinctively evaluate the probability of each player winning for any given situation and choose shots accordingly, just like a chess engine chooses moves based on its evaluation of subsequent positions.
This is the most BS you have yet to post, and as I'm typing this I'm really wondering why I'm taking the time to reply at all, but o well. I don't know who you're trying to fool, but I'm a chess player, and a computer science graduate who has created a rudimentary chess engine as part of a class project. I know how they work, and it is absolutely laughable that you are claiming you work on them for a living.
Chess engines rank chess moves based on raw calculation (with the help of table bases for openings and end games). Engines use brute force by analyzing the tree of possible moves and responses. They are not capable of strategic planning and analyzing the position of a board the way humans do.
For instance, a player may be developing a king side attack by mobilizing all of his pieces toward the king side. An engine has no idea of this type of planning. It simply evaluates every single possible move, and uses brute force through all the possibilities to come up with a relative evaluation of the strength of each move. Therefore, even though it's possible for the engine to evaluate two moves as being the same, one of the moves will be better strategically when considering the player's goal of a king side attack.
Chess engines still haven't solved chess, so their evaluations are not perfect. They can only see to a certain depth, so their evaluations are still just estimations. Humans can't calculate like computers, but they still have certain advantages in their ability to see the board as a whole and evaluate positions. Humans can't see all the way to the end of the game either, so they use strategic planning through each phase of the game to figure out how to coordinate the pieces.
You completely dodged my question, and the whole point of the analogy. Chess players don't ever evaluate two moves as equally strong and then choose one randomly. They have a strategic purpose for every move, and it's deliberate.
Now what I'm saying is that I get into a lot of situations where I'm trying to make a ball (and get a particular leave), but if I make the ball it doesn't result in a higher probability of me winning the game (in my estimation) than if I don't make the ball.
What you are describing now is simply a two-way shot, and since you are trying to make the ball, it's clearly not defensive. What you were describing before, which is what makes absolutely no sense, is not making a decision to make the ball or not, and lazily hit it toward the pocket, not trying for either outcome.
You, and everyone else, is not capable of calculating the odds of winning the game, just as chess players aren't capable of seeing all of the possible chess moves to determine their probability of winning.
If making the ball doesn't help your opponent and doesn't hurt your position, it's the right choice. Not making a ball, and playing safe, is only for certain situations where you would either be making it easier for your opponent to run out later, or if you are attempting a very hard shot you might play safe so that you don't risk missing and giving your opponent a really good opportunity.
The point is that missing the ball and making the ball accomplish two very different things, and this is why you can't evaluate both shots as being completely equal. The only reason you are evaluating them as equal is because you can't see the advantages and disadvantages of each shot, not because they don't exist. As with any other game, you should always make deliberate moves/choices, and not leave the result of the shot up to chance.
I don't know why you think it's impossible for such situations to occur, when in fact they're fairly common in pool. How often have you seen someone miss a shot and walk back to the table and just shrug his shoulders because he didn't see an out after that shot and he left his opponent with a tough shot? Because where I play, that happens kind of a lot, to almost everybody.
Ya that does happen often, and the reason the person is shrugging is because he didn't plan for it to be a two way shot. He went for the shot, missed it, and then saw after the fact that it didn't hurt him. Maybe he should have chosen to miss the ball on purpose, or maybe he should have played a deliberate safe without shooting a ball towards the pocket, or maybe he should have made a different ball or played shape better. No matter what the situation, it's never correct to just not make a decision and let chance dictate the outcome.