If a person can make every move with the intention of winning and still lose, or if someone can make every move with the intention of losing and still win, or if someone can make every move randomly and still win, the decision to play to win does not translate into a decision to win.
Because the decision to play to win can result in winning, then it does translate. That the decision to play to win can result in losing, conveys a mistake in belief. Either way, it would be a choice the player makes.
Beliefs are positions which are held to be true.
We arrive at beliefs as a result of our understanding and perspective of the world. We do not "choose" them in the sense that when presented with a number of viable options we can voluntarily "decide" which one we find to be true - just as you cannot, as a voluntary act of will, decide which foods you enjoy, what shape the sun is, or the outcome of a game of chess.
Some beliefs are preferences. I can choose to like certain foods, and may currently believe I know my preferences. Again, this may be a mistaken belief. I may update the beliefs, based on experience and choices to believe that other foods would be to my liking. IMO, the experience matters only slightly. I am free to believe whatever I wish about the shape of the sun, or the outcome of a game. I can hold these beliefs as true. And I can change my mind, choose otherwise, or even choose to believe both. I believe the world is both flat and round. It is possible to choose both.
We can influence the outcome of these mental processes to a degree, but this does not mean we influence the outcome in the same way.
The outcome may have nothing to do with our beliefs. Or it may have everything to do with our beliefs. Either way, we are free to choose along the way, and after the outcome, what we hold as true.
You cannot voluntarily recalibrate the extent to which you find a given proposition truthful, but instead this is done with adjusting of perspective and new information or experiences.
I can recalibrate the extent to which I find a given proposition truthful. I do this a lot. Everyday I've been alive, I think I've done this. Probably have done it dozens of times today. New information (some of which are other beliefs) and experience will influence this, but belief / ideas / thoughts trump them all.
As such, beliefs are not simply "chosen" as a voluntary process, but are the result of largely subconscious mental processes.
In some cases, yes. Disagree it is largely subconscious. I guess it would depend on the set of propositions. The ones that come up daily to my awareness and that I act on, are chosen beliefs. The others are perhaps not, but even that I find debatable.
That is false. You're welcome to prove me wrong by choosing to believe that sandwiches are hats.
Fine. I choose to believe sandwiches are hats. Not too difficult. I can simultaneously belief sandwiches are food, and sandwiches are a thing that is necessary to be around for my favorite sports team to win, and accept as true that sandwiches are pure evil. Or, tomorrow, I may believe none of these are true propositions. Others may say, "but it is still a food." And I may say, "I no longer believe that, and because of that belief, I have stopped ingesting them." It is a choice in belief I am free to make.