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So, if water is good for your game, does that mean coffee is bad for your game because coffee dehydrates you?

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The following has no scientific backing:

Drinking lots of water keeps your brain and body more alert than not drinking water. Eating lots of fruits and vegetables has a similar effect. Consuming caffeinated beverages will not make you more or less alert; it will just keep you awake. If you are having trouble concentrating because you are tired, coffee will just keep you at the table longer, without actually improving your game. Eating large amounts of meat before a session is likely to make you tired, as your body's resources will be required to digest your food.

I used to avoid drinking lots of water during a session, for fear of missing hands. Remember that taking a 3-minute break every hour or so is probably more +EV than playing a couple hands in early position, especially if you are drinking enough water to keep you focussed.