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How many wins do I need to get from Iron 4 to Master?

120 wins

With a 55% win rate, you would need to play 1200 games, you would win 660 of them and lose 540.

With a 60% win rate, you would need to play 600 games, you would win 360 of them and lose 240.

With a 65% win rate, you would need to play 400 games, you would win 260 of them and lose 140.

With a 70% win rate, you would need to play 300 games, you would win 210 of them and lose 90.

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.