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

72 wins

With a 55% win rate, you would need to play 720 games, you would win 396 of them and lose 324.

With a 60% win rate, you would need to play 360 games, you would win 216 of them and lose 144.

With a 65% win rate, you would need to play 240 games, you would win 156 of them and lose 84.

With a 70% win rate, you would need to play 180 games, you would win 126 of them and lose 54.

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.