Bluffing

Bluffing is the intentional misrepresentation of the strength of one's hand. You may over-represent the strength of your hand (what is commonly thought of as bluffing), in order to chase opponents with stronger hands out of the round. You may equally well under-represent the strength of your hand (``sand-bagging''), in order to retain players with weaker hands and relieve them of spare cash. These are tactical purposes behind almost all (human) instances of bluffing. On the other hand, there is an important strategic purpose to bluffing, as von Neumann and Morgen stern vonNeumann53 pointed out, namely ``to create uncertainty in [the] opponent's mind'' (pp. 188-9). In BPP this purpose is already partially fulfilled by the randomisation introduced with the betting curves. However, that randomisation occurs primarily at the margins of decision making, when one is maximally uncertain whether, say, calling or raising is optimal over the long run of similar situations. Bluffing is not restricted to situations where the optimal normal action is uncertain; the need is to disguise from the opponent what the situation is, whether or not the optimal response is known to the player. Hence, bluffing was desirable for BPP as an action in addition to the use of randomising playing curves. Since BPP's randomised play already resulted in some apparent bluffing, the probability with which BPP bluffed outright was somewhat lower than would have been otherwise. The original BPP bluffed (by over-representation) in the last round of betting with a low probability (5%).