Semi-bluffing is a sort of bluff where you have a poor hand or a drawing hand that can possibly improve. Against players with nothing it functions a lot like a bluff. Against players with something it functions as a form of aggression. It is a powerful tool, as it can lead to a deceptively powerful hand if the cards come to you. It can also be a source of great loss if overused or misused.
Semi-bluffing in Texas holdem is used best in typical bluffing situations. It's usefulness comes from the fact that players who recognize a bluff won't necessarily recognize when you make your draw. It is more useful (and preferable) against a lot of players, as opposed to outright bluffing, since the odds tend to be better. Other than that, you'll want to use semi-bluffing in late position, usually on the flop or turn, against mediocre flops, and against poor players.
Let's look at two examples of semi-bluffing from a perspective of odds and from a perspective of bluffing:
1. You have a Jack of Hearts, and a Ten of Hearts. The preflop betting round concludes with six players investing two bets each. The flop is Ace of Hearts, Queen of Spades, Seven of Hearts.
You are in a middle position, and decide to semi-bluff. Why? You've got draws, that's why! Any Heart or King will give you a hand. Whenever you have multiple draws like that, start thinking of what would be ideal. If a Heart pops up you have to worry about a higher flush draw, so you probably want the King of Hearts, as he is the most likely to be in someone's hand. A Queen of Hearts would be dangerous for you, since you'd be looking at a royal flush draw vs. a potentially made full house. Ideally you want a non-Heart King and the straight. That would be the nuts.
For simplicity's sake though, let's say that in your evaluation, either a flush or straight will give you a winning hand. You have twelve outs (don't count the King of Hearts twice). That's a little better than a 25% chance of hitting a winning card on the turn. Even re-raising or check-raising would be a good idea in this position based purely on odds. Even if you miss on the turn, it would be in your interests (based on players reactions) to continue to bet it right out.
2. You have a pair of sixes in the pocket.
Preflop action eliminates all but you and one other player who was in early position before you. You get a rainbow flop of Four, Five, Ten.
In this case you have to think of it more as a bluff. If this only player played a hand in early position, they probably have some overcards in this case. You want the pot right then and there. Most players will bluff back at you in this case with just an Ace in the pocket. Stick to your resolve. Bluff.
Your chances of getting that six are pretty slim, and not worth the odds. You only have to worry about your opponent having overpairs and matching the Ten. So you really have to evaluate the player, as opposed to the math in this case. I'd always try to be on the aggressive. You need information about his hand. Betting is a real good way to get information. Also, a casual semi-bluffing check-raise can be all you need to scare another player if you think they'll bluff at the pot.
Hope that gives a little insight into semi-bluffing. Remember with any bluff, you need to know your players, and not to use any bluffing tactic habitually.
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