Tread water essentially means you're making no progress possibly while waiting for something else to happen. Staying put shows determination; you're persevering - you're not giving up - you're quite determined to achieve what you set out of achieve. You're going to stay put until you get what you want.
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Blue JayTreading water is a term that comes from swimming, where it means to float upright in the water while kicking with the legs in order to keep the head out of the water, but without moving in any direction. The person isn't drowning, but they are not going anywhere either. Metaphorically it means that one's efforts are keeping one going in the present situation, but
soheil1So, What does 'tread water' mean in:White treads water to lull the opponent into a sense of security. (from Play Winning Chess)I would take it to mean that White makes some moves that seem to be minor re-positioning of some pieces and that do not appear to be part of an attack, so that Black doesn't realize what is about to happen.