What von Neumann showed in his ground-breaking 1944 book, A Theory of Games and Economic Behavior (written with economist Oskar Morgenstern), was that you should bluff only with your worst hands, rather than with something half-decent.
The reasoning is simple enough. A modest hand may beat another modest hand, so it’s worth limping along to a low-stakes showdown. A bad hand will only win anything if the opponent folds, so bad hands should be played aggressively or not at all; indeed, when the best players are caught running a huge bluff they are often holding the most atrocious cards. Von Neumann’s model also highlights the other benefit of bluffing: it forces the opponent to match your bids frequently, and so wins more money with strong hands.
Von Neumann’s book was hugely celebrated, but academics were soon disillusioned: they found that game theory was too narrow and too difficult to apply to the real world. The book sold poorly, although a few copies, as the Princeton University Press noted sheepishly in 1949, “were bought by professional gamblers”.
What to make of this? Clearly, one should fold one's worst hands as quickly as possible.
The old dictum, when unsure whether to call or fold, RAISE might apply.
Consider this, a jack and a king appear on the board. You hold a jack. If your opponent holds the king, you lose. Betting AS IF you hold the king makes sense in this situation; if he folds, you win. If he holds the king and calls, you gained information about his hand.
To me it makes the most sense to bet large when you probably hold the same or similar cards to your opponent. If you both hold pairs, a medium or large bet tossed out on the river, provided it's consistent with your earlier betting, will often get them to fold.
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