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I am not saying that raising the turn is always wrong, I just don't really understand it.

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Not sure what to say other than to read the ToP section on the free showdown/free card.

If we raise the turn and "lose" him, so what? We win the pot, that's good. Given the board, if he was behind, he had outs to win. Between the odds of him not betting the river and the odds of him hitting a hand on the river, having him fold the turn isn't a big deal.

Most won't fold though. They'll call your turn raise and check the river. This means you see showdown for 2BB anyway, but if you hit your hand in a big way on the river, you can suck another 1BB out of them when you're ahead.

Free showdown is the same principle as a free card, just at different street. Same caveats apply though regardling likelihood of success. You can't always buy a free card, nor can you or should you always buy a free showdown.