Had a discussion in the FEUI mailing list with an old friend about game theory. One of the discussion points was whether there is such thing as a 'mixed strategy' in the real world. He argued that no, there is no rationales for any agent in the real world to randomize between strategy. I argued that such thing is possible (remember my piece on Argentina-IMF in 2001), quoting this interesting paper.
In a personal conversation, he insisted that basically the penalty takers are not really randomizing. "They won't kick the ball backward," he replied. I replied back, saying that kicking backwards is NOT a strategy -- it's not in the payoff matrix -- therefore we don't have to bother considering such option.
Anyway, talking about penalty kick, last month Arsenal's Robert Pires found another strategy: instead of kicking directly into the goal, he instead PASSED the ball (yes, from the penalty spot) to Thierry Henry. That new strategy was not successful anyway -- so better to use orthodox ones next time. Yes, just try to kick it directly to the goal, either it to the left, right or center. As Bill Shankly once said, "If you don't know what to do with the ball, just put it inside the net. We can discuss the other options later...."
Speaking about penalty, again, still remember the sweet win in Istambul last spring... Priceless..!! (wave to Ujang).
Note: the paper I referred is A. Chiappori; S. Levitt; T. Groseclose, "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," The American Economic Review, Vol. 92, No. 4. (Sep., 2002), pp. 1138-1151.