The statement "I win" is typically used to declare that the subject has just won the game.
Before the statement, it may well not be known that a "win" has occurred.
Indeed, because the action is so extremely recent in the past, it is effectively considered the present.
While you technically may be right in that the win occurred in the past, language does not make this distinction.
Call it an idiomatic usage case, if you will.
I wouldn't over-analyse the reason.
english.stackexchange.com/users/184/Noldorin
I disagree with the accepted answer in its explanation.
If you've just had lunch, you'd say "I ate" (past-tense) and not "I eat" (present tense) - even if you're saying it "just a few seconds after" having lunch.
It is absurd to argue that "I win" is used because the winning has only happened in the recent past, it is being carried over to the present (although a runner might say "I win" as he is overtaking another runner).This is sledging , whereas the usage above is clearly about semantics/phraseology.
When you say "I win," you're being helpful - by effectively speaking for/on behalf of an umpire/adjudicator (or a referee), who is the proper authority to declare the winner.
Conventionally, an umpire would say "Player X wins ", and not "Player X won ".
If there was a third person (acting as an adjudicator) physically present, and he declares one of the two players the winner, you'd certainly say " I won! "
even if it was immediately/seconds after.
In linguistics, there are three honorifics assigned to any discourse : the speaker, the hearer and the bystander.
Here, the speaker is speaking for the invisible bystander.
You're also likely to say " I won! "
with a particularly tough-to-beat opponent, implying incredulity/emphasis.
english.stackexchange.com/users/None/
I think you can use both.
I win means I've won when the game has just finished.
I've won means for example that you've won 30 minutes ago.
You can call something that happened 2 minutes ago by present, not past.
english.stackexchange.com/users/None/
There are elements of RaghuramMK's and Noldorin's answers at play here.
I do think an exclamation of "I win!"
at least in part serves as an answer to "OK, so who wins?"
(even if that question wasn't explicitly asked).
I believe this is its grammatic function, if you will.
It's a declaration, like a shorter form of "I am victorious!".
I also think there is some period of time beyond which the winner stops saying "I win" and switches to saying "I won", and it's not very long.
But how long depends a lot on the venue and the emotional magnitude of the victory.
Someone who has just won a world championship might be screaming "I win!
I win!
I win!"
for what seems like quite a long time, as they run around in celebration.
Whereas if my brother beats me in a casual game of cards, he might say "I win" as he plays the last card, with the "winning moment" lasting less than one second.
english.stackexchange.com/users/2923/John Y
Usage varies, of course, but I would only use
I win in situations where it's pseudo-future.
Chess commentaries commonly say '...and
Black wins in 3 moves', meaning that the game, though technically still in progress, is effectively over.
There, wins could be replaced by will have won , since the game reported on has finished (presumably by White's resignation); if I were Black in that situation I could say I will win in three moves or I win in three (or, of course, Mate in three ).
The gloating phrase would be "I've won!"
english.stackexchange.com/users/8019/Tim Lymington
I'm winning
I'm winning this time (while the game continues).
I've won
I've won this time.
(after it is over).
english.stackexchange.com/users/482/JFW
For a long time I was wondering why there is  I win  instead of  I won . I met such usage in a lot of games and movies.   For me, it's logical to say  I won , because this  winning  action is done already.  I win  for me seems like  I'm winning right now .  Can anyone clarify this for me?
Why do we say "I win" instead of "I won"?
english.stackexchange.com
<phrases><tenses>
english.stackexchange.com/questions/3798
english.stackexchange.com/users/1609/arteg
Both "I win" and "I won are considered acceptable. However, "I win" is mainly acceptable because it is used to declare that the subject has just won the game. There are divergent opinions as to whether this is expressing a present tense or a past tense or both. For some, it means the "winning" has just occurred and because this occurred so recently in the past, it is considered a present event. In fact, before the declaration of winning, it may not be known if a "win" has occurred. Others contest, that you are effectively speaking for the absent "referee" or "umpire" or the invisible bystander. Finally, others believe that "I win" simply means you are saying you won the game that has just finished; you can use the present for something that happened in a very near past i.e something that occurred 2 minutes ago.
Both "I win" and "I won are considered acceptable. However, "I win" is mainly acceptable because it is used to declare that the subject has just won the game. The statement "I win" is typically used to declare that the subject has just won the game.  I've won  means for example that you won 30 minutes ago. When you say "I win," you're being helpful - by effectively speaking  for/on behalf of an umpire/adjudicator  (or a referee), who is the proper authority to declare the winner. But you can use both.  
The statement "I win" is typically used to declare that the subject has just won the game. It's an idiomatic declaration, like a shorter form of "I am victorious!". Because the action is so extremely recent, it is effectively considered the present. However, both "I win" and "I won" can be used. Both "I win" and "I won are considered acceptable. However, "I win" is mainly acceptable because it is used to declare the winner in the present.
It means the "winning" has just occurred. It may not be clear that this had occurred before the declaration of the win. It is expressing the present tense occurence of the event and not the past. The speaker is speaking for the invisible bystander. Both are an option.  There's a period of time after which the winner would start saying I won. They might scream, I win!
The statement "I win" is typically used to declare that the subject has just won the game.  I've won  means for example that you won 30 minutes ago. When you say "I win," you're being helpful - by effectively speaking  for/on behalf of an umpire/adjudicator  (or a referee), who is the proper authority to declare the winner. But you can use both.  
The phrase "I win" is generally used to declare the winner in the present. Because the action occurred so recently in the past, it could be considered the present. Both "I win" and "I won" are considered acceptable.