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How many wins do I need to get from Emerald 2 to Master?

30 wins

With a 55% win rate, you would need to play 300 games, you would win 165 of them and lose 135.

With a 60% win rate, you would need to play 150 games, you would win 90 of them and lose 60.

With a 65% win rate, you would need to play 100 games, you would win 65 of them and lose 35.

With a 70% win rate, you would need to play 75 games, you would win 53 of them and lose 22.

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.