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How many wins do I need to get from Gold 2 to Diamond?

44 wins

With a 55% win rate, you would need to play 440 games, you would win 242 of them and lose 198.

With a 60% win rate, you would need to play 220 games, you would win 132 of them and lose 88.

With a 65% win rate, you would need to play 147 games, you would win 96 of them and lose 51.

With a 70% win rate, you would need to play 110 games, you would win 77 of them and lose 33.

Assuming an average LP gain of +/-25 LP per game below Emerald and +/-20 LP for Emerald+ as per Riot Phroxzon's tweets here and here.