If it WILL be one way, it is incorrect to say that it CAN be different.
The problem is that, lacking omniscience, we often DO NOT KNOW what will happen. When we do not know what will happen, we imagine what can happen to prepare for what does happen.
And every case of CHOOSING begins with the same UNCERTAINTY. When we do not know what we will do, we imagine what we can do, evaluate those options, and by that evaluation we DECIDE what we will do.
Whenever faced with such an uncertainty, we STOP speaking of what WILL happen or what we WILL choose, and switch to the context of possibilities. In the context of possibilities we have certainty as to what CAN happen and what we CAN choose, while still being uncertain as to what WILL happen or what we WILL choose.
Now, if we always KNEW what WILL happen, we could dispense with the notion of possibility. But we don't, so we can't.
Thus, despite the logical fact that things WILL only happen one way, we still must be able to say that events CAN be different, and COULD HAVE BEEN OTHERWISE.
Otherwise we BREAK THE LOGIC that we humans have evolved to deal with our uncertainty.
Breaking that logic creates nonsense, like in the example:
Waiter (a hard determinist): "What will you have for dinner, sir?"
Customer (hungry): "I don't know. What are my possibilities?"
Waiter: "Because the universe is deterministic, there is only one thing that you can order."
Customer: "Oh. Well. Okay then, what is the single thing that I can order?"
Waiter: "How should I know? You haven't told me yet!"
In your example, the waiter would actually be able to answer the question. All he has to do is look at the different events, and figure out what they will cause.
And, how would that conversation play out?
Waiter (a hard determinist): "What will you have for dinner, sir?"
Customer (hungry): "I don't know. What are my possibilities?"
Waiter: "Because the universe is deterministic, there is only one thing that you can order."
Customer: "Oh. Well. Okay then, what is the single thing that I can order?"
Waiter: "With my complete knowledge of all events leading up to the instant you place your order, as well as my total understanding of the laws of nature, I have performed the required calculations and figured out that you are going to order the steak."
So, your solution is to simply give the Waiter omniscience? How would we go about doing that?
If everything that happens is determined (caused) by all previous events, then there is nothing in principle that is stopping us from calculating the outcome of the future.
Wow. You actually are suggesting we make the Waiter omniscient!
Can you describe the mechanism by which the universe renders such calculations impossible?
Well, we can start with the limited size of the Waiter's brain. Then there is the problem of capturing the total relevant causal history of the Customer's prior dinner choices. But no restaurant has attempted this beyond offering the option, "Your usual, sir?", which still allows the customer other real possibilities.
And as I've pointed out before, in a deterministic universe, us thinking we are making a choice does not mean we are making a choice.
Why would you insist that in a deterministic universe we would have a different set of NAMES for common events? "Choosing" is the proper name for an operation that inputs multiple options, applies some criteria of comparative evaluation, and outputs a single choice. The only reason that we think we are making a choice is that we just observed ourselves doing exactly that. And we can eliminate subjective feelings by walking into a restaurant and watching other people doing exactly that.
Determinism doesn't actually change anything. We are still doing the same things that we always have done. Determinism simply makes note of the fact that each event was the inevitable result of prior events. The choice to have dinner at the restaurant led us to travel to the restaurant, walk in the door, sit at a table, pick up the menu, consider the MANY things that we CAN order, and decide the SINGLE thing that we WILL order. That is the way that everything would necessarily happen.
If that is the way that things are determined to work, then that is exactly the way things will happen. And, given determinism, they must necessarily work out exactly that way, without deviation. Determinism doesn't actually change anything.
All events are reliably caused by prior events, such that every event is causally necessary and inevitably will happen from any prior point in eternity. Now, the question is this: Why you think this limits your freedom in any way?
Because in order to have freedom, I must be able to make decisions myself.
And determinism guarantees that we inevitably will make the decision ourselves. Within the entire physical universe, the only object that will be choosing for us what we will order for dinner will actually be us.
If the outcome of anything I "decide" has been set in stone since the big bang, then I am not making any decisions at all, and therefore I am not free.
So, the question is why you think that you are not free to make the choice yourself? After all, determinism has guaranteed that it will inevitably be you and no one else that will be making that choice at that time and place.
Universal causal necessity/inevitability is neither a meaningful nor a relevant constraint. What you will inevitably do is exactly identical to you just being you, choosing to do what you choose to do. It is basically, "what you would have done anyway".
If you can show that a different horse winning was a possibility - an actual possibility, not just that we thought it was possible - then the universe is not deterministic.
So, what is an "actual possibility"? An actual possibility exists solely within the imagination. We cannot walk across the possibility of a bridge. We can only walk across an actual bridge. But we cannot build an actual bridge without first imagining the possibility of a bridge. Possibilities are necessary parts of the real function of creating new actualities, like that actual bridge that wasn't there before and now is there for us to walk across.
A possible bridge is a bridge that we are ABLE to actualize IF WE CHOOSE TO DO SO. The fact that we do not choose a specific option does not mean it was ever "impossible" to actualize. It only means that we did not choose to actualize it. It is something that we COULD HAVE DONE, but simply did not do.
Our ability to make that possibility really happen is what makes the mere thought of a possibility an "actual" or "real" or "true" possibility.
And, within a deterministic universe, every thought that we experience is causally necessary from any prior point in eternity and inevitably will happen. So, determinism doesn't actually change anything.
You say the other horse could only have won under different circumstances, but since your universe is deterministic, such different circumstances were always impossible, weren't they?
Different circumstances are always possible. They are just never actualized.