OK, few answers :
Is it only the single closest prediction that gets to win the equivalent of half a life, which can be purchased in the cash shop?
Yes, the winner of the round will receive 50
BTC as a reward. From time to time, the winner will receive other things. I'm being vague about this, but you will soon understand after a few rounds.
Or will there be some kind of range where every prediction that falls within it gets the same reward or a specific number of predictions will be chosen from the range, while the range or numbers is decided after each round?
Apart from the winner, from time to time, some player(s) will receive something, but it will not be 50
BTC. How will this (these) other player(s) be selected ? I have to remain vague, The Game Master is watching me

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If none of that applies, then what happens to all the other predictions apart from the furthest one?
They will have the tremendous joy of surviving one more round, and that's priceless

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