Do the decisions you make over the course of the game have any kind of significant influence on the story?

i.e.: who you select at the raffle, whether you kill Slate or not, etc.

They have little effects like if you don't throw the ball at the couple, they give you gear later, but it doesn't affect the actual story.

The first combat scenario with Elizabeth if you choose demand tickets over pull out gun, the ticket guy will stab you and you will have a blue bandana tied over your hand. Nothing big, but I have been playing through a second time and have been choosing everything different from the first time.

It's a bummer that the decisions don't lead anywhere interesting.

In term of Slate, you just see him later on if you let him live, right? I assume there's nothing more beyond that?

it actually makes a sort of meta sense once you see the ending.

GODDAMM that ending is GENIUS

No. They change some little shit: you get gear from the couple if you don't throw the ball at them, Elizabeth has a different choker for the rest of the game, you can meet Slate in a vegetable state if you leave him alive and you won't have a bandage on your hand for the rest of the game if you decide to pull on the clerk. It all serves to reinforce the ending - there are variations even on the same stories in the multiverse, but they are outweighed by the constants.

Except that the coin flip, which isn't a decision is EVERYTHING. Consider that the decisions you are making (like the bird or cage) isn't for your benefit, but a check on reality that the Lutuces set up.

I played through the beginning twice in a row, and even though the coin always comes up heads, it seems to alternate whether Booker will guess "heads" or "tails". I am not sure if this is random or not.

This pretty much sums up the significance of the "choices."

That's fascinating :o It seems to be a perfect representation of constants and variables. What you pick my vary, but it doesn't matter, since the coin will always end up heads.

What he said. The significance of the choices is their insignificance.

But at the same time that's the entire premise of the game, so...