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How many wins do I need to get from Plat 4 to Diamond?

36 wins

With a 55% win rate, you would need to play 360 games, you would win 198 of them and lose 162.

With a 60% win rate, you would need to play 180 games, you would win 108 of them and lose 72.

With a 65% win rate, you would need to play 120 games, you would win 78 of them and lose 42.

With a 70% win rate, you would need to play 90 games, you would win 63 of them and lose 27.

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.