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

112 wins

With a 55% win rate, you need to play 1120 games, win 616 of them and lose 504.

With a 60% win rate, you need to play 560 games, win 336 of them and lose 224.

With a 65% win rate, you need to play 373 games, win 242 of them and lose 131.

With a 70% win rate, you need to play 280 games, win 196 of them and lose 84.

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.