[Pokey]

On page 166 of The Theory Of Poker, Sklansky discusses how frequently a person should bluff:
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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...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 <a $20 bet into a $100 pot>, 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.


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I have a few problems with this idea, especially with regards to SSNL:

1. To say that mathematically optimal bluffing shows a $100 profit in this situation is true only in comparison to checking through. If opponents will call a value bet, even occasionally, then the "extra $100" from optimal bluffing is much smaller.
2. Given our opponents' tendencies to call too frequently, a strategy that works equally well whether our opponent always folds or always calls is not going to be profit maximizing. We should set up a strategy that pays decently well if our opponent always folds, but extremely well if he always calls. Recognize the weakness of the enemy and exploit it.
3. This theory of mathematically optimal bluffing applies best in closed-river games (where every player's last card is dealt face-down). Texas Hold'em is an open-river game, and that changes the dynamic profoundly, because bluffs and value bets will not be equally likely to be called.

While points 1 and 2 are details that suggest minor alterations in our strategy, point 3 is a potentially fatal flaw in Hold'em bluffing. Example:

You hold A [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/heart.gif[/img] and on the turn the board is K [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/club.gif[/img]. You decide you want to make a pot-sized value bet if any of the (nine remaining) hearts hits the board, and a pot-sized bluff on three other preselected cards. (This strategy randomizes your play in completely unpredictable ways; the deck is telling you when to bluff). This gives your opponent 3-to-1 odds on a 2-to-1 payout, so if he always folds you come out ahead, and if he always calls you come out ahead even more.

But what bluff cards can you pick that will be just as likely to be called (or folded) as any rivered heart? The obvious choices would be some non-heart straight cards.

If we bluff when a non-heart 6 hits, will our opponent give us credit for the straight as often as he'd give us credit for a flush when the heart hits? How about if we bluff the non-heart Js? Ts? 7s? When our opponent can see our river card, the odds of our bluff succeeding are NOT the same as the odds that our river value-bet gets called.

Never bluffing at SSNL can't be optimal unless our opponents NEVER fold. But given the open-river nature of Hold'em, how should we approach bluffing?