Hmmm…I’m not sure why you would want to put “determinism” in the pluaral–I see no problem with that. The sentence sounds off to my ears, but I can’t figure out why. I would want to put the “to you” in, but I can’t see why the sentence as written would be technically wrong. This is a stumper for me, because it’s really coming across as incorrect to my ears.
The passive voice is probably a little confusing, so consider the active version: “The hand that the dealer deals to you represents determinism.” In this case you is the indirect object of the verb deals. There are cases where English drops the preposition to from a direct object (e.g., “Give me the ball” vs. “Give the ball to me”), and that’s what’s going on here. So the original quote is grammatically reasonable, if maybe not the sort of thing the textbooks would encourage.
On the other hand, “The hand that is dealt you represent challenges.” is definitely wrong. Drop the descriptive clause “that is dealt you” and you’re left with “The hand represent challenges.”. That has a pretty big subject-verb agreement issue.
Yes, it is the passive that is throwing me off and making things sound odd to my ears.
“Give him the ball” sounds okay.
“I want the ball that was given him” sound wrong. I really think the “to” needs to me in there (and is analogous to the sentence in the OP). However, I’m not sure why it would be wrong. Or perhaps “I want the ball given him” is grammatically correct. shrug. It just sure as hell doesn’t seem like it should be.
Indirect objects are among the few places you can actually see some inflections in English. You* would never expect to have a preposition in the phrase “Give yourself a pat on the back,” because the pronoun you gets inflected to yourself, obviating the need (IIRC it’s the reflexive case, but it’s been a while and I don’t feel like cracking open my old grammar textbook). The structure is exactly the same, it’s just that in “The hand that is dealt you …” the indirect object pronoun doesn’t show any inflection in English. I leave it to Mssrs. Quirk and Greenbaum to debate whether that is because it doesn’t change case or because we don’t inflect whatever case it declines to.
“You” should be read to mean “A native speaker of English.” I try not to assume what people who speak English as a second language will expect.