The site needs to recognize that you are genuinely logged off before it will start emailing you. When you leave Chess.com, try hitting "Logout" under the settings gear on the bottom left corner of any page.

Also, make sure that you have added "@chess.com" to your allowed senders list in your email program. This will ensure that our email doesn't get filtered out before it reaches your inbox.
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You can adjust your email settings at any time from your notification settings.

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