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This is something I've been thinking about lately, and it's an underutilized facet of my game as well. I could be way off base here, so please take the following with a grain of salt:
The main advantage to pushing is fold equity. It gives your hand additional value. For example, if you have a drawing hand on the flop out of position against an aggressive opponent, and you have a 45% chance of winning the hand by the river, your opponent has more equity than you. You could try pricing yourself in on the draw by making a small blocking bet to give yourself correct odds, but this may not be effective against the particular opponent. Check/calling each street will usually be a bad play as well, since many opponents will not give you correct odds.
However, pushing gives your opponent incentive to fold a certain % of the time, depending on stack sizes and other factors. Sometimes he'll fold and you'll win the pot outright, and the rest of the time it'll be a virtual coinflip. This can be very +EV if the pot is big enough and you have significant folding equity.
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