The past tense is correct. "I won't know who will win the game" is talking about a future event, looked at from the present time. Your hypothetical looks at the future event from the vantage point of the future.
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Both are possible; , the first one is the only likely one.
If I die today, I won't know who will win the game. probably because the game is tomorrow or some later time
If I die today, I won't know who won the game.
AnonymousDoes adding 'today' change anything? Do you mean adding another 'today'?If so, why do you want to further complicate the sentences by adding to them? And if you understand the original sentences, you should be able to answer your own question.
AnonymousDoes adding 'today' change anything?Yes, it does. As your sentence stands, there are several assumptions which make the time factors clear. "Today" is part of this. It's not necessary to say that the game is tomorrow or later. Our common sense assumes it.
AvangiIt's not necessary to say that the game is tomorrow or later. Our common sense assumes it. I don't agree with that, especially as far as students are concerned.. But more basically, we don't agree on which is the 'correct' or at least most likely sentence.
canadian45Both are possible; , the first one is the only likely one.More likely, the game is tomorrow; and if I die today, I'll miss the chance to learn who won it.
AvangiMore likely, the game is tomorrow; and if I die today, I'll miss the chance to learn who won it.'who wins it' is possible too. But since the game is in the future and the OP asked about choosing between 'won" and "will win", the latter seems more appropriate to me.