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

104 wins

With a 55% win rate, you would need to play 1040 games, you would win 572 of them and lose 468.

With a 60% win rate, you would need to play 520 games, you would win 312 of them and lose 208.

With a 65% win rate, you would need to play 347 games, you would win 226 of them and lose 121.

With a 70% win rate, you would need to play 260 games, you would win 182 of them and lose 78.

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.