play into someone's hands
US /pleɪ ˈɪntu ˈsʌmwʌnz hændz/
UK /pleɪ ˈɪntu ˈsʌmwʌnz hændz/

1.
思う壺にはまる, 相手の思う通りになる
to do exactly what your opponent wants you to do, so that they gain an advantage over you
:
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By arguing with him, you're just playing into his hands.
彼と議論することで、あなたはただ彼の思う壺にはまっているだけだ。
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The opposition's mistakes played right into the government's hands.
野党のミスは政府の思う壺にはまった。