Optimum Bluffing Frequency
 
What is the right bluffing frequency? It is a frequency that makes it impossible for your opponents to know whether to call or fold. Mathematically, optimal bluffing strategy is to bluff in such a way that the chances against your bluffing are identical to the pot odds your opponent is getting. Thus, if, as in the example just given, an opponent is getting 6-to-1 from the pot, the chances against your bluffing should be 6-to-1. Then that opponent would break even on the last bet by calling every time and also by folding every time. If he called, he would lose $20 six times and win $120 once; if he folded, he would win nothing and lose nothing. Regardless of what your opponent does, you average winning an extra $100 every seven hands. However, mathematically optimal bluffing strategy isn't necessarily the best strategy. It is much better if you are able to judge when to try a bluff and when not to in order to show a bigger overall profit.

To make sure we agree on what is meant by a bluff, we will define it as a bet or a raise with a hand which you do not think is the best hand. Bluffing can be separated into a couple of different categories. There is bluffing when there are more cards to come and when there are no more cards to come. Secondly, within each of these categories, there is intuitive bluffing, which is the subject of this page, and mathematical bluffing, which will be discussed in the next page.
 
Gutshot and Overcard

 
My bet on the river was probably a mistake. He wasn't likely to fold a pair or to call without one. But I thought I might get a call from him with a worse Ace high than mine. Not likely, but maybe. Also, I didn't want to have to showdown my hand and show the table that I'd been betting without a pair. This latter reason was the main reason I bet. Even so, in retrospect I think the bet was a mistake. It's often better to check on the river to entice a bluff than to make a thin value bet.

But a debate about whether I should have bet the river or not isn't really the point here. The point is to consider how differently this hand would have played out if I'd been in early position rather than on the button.

If I'd limped from early position and gotten a caller, I don't know that I would have bet the flop. I probably would have still won the pot, but it would have been a very small pot. And if I checked on the flop and he took the lead and kept betting, I probably wouldn't even have won it.

If I had opened with a raise and had a player cold call, would I like betting that flop as first to act? I might have bet the flop but checked the turn after he called. I don't think he had a pair, so I probably would have won a showdown on the river. But the pot would have been one big bet of his money smaller if I'd checked the turn. Those extra bets you can get from late position add up.
 
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