When playing a repeated game with a mixed strategy equilibrium, it is important not only to play each strategy an equilibrium proportion of the time, but to have each play of the game be an independent draw from the distribution. Consider a soccer player deciding whether to kick a penalty kick to the left or right corner of the goal. Often, the optimal strategy is to randomize, kicking left half of the time, and right the other half. However, if the player simply alternates, kicking right the first time, then left the second time, then right the third time, then left, etc., it would not take long for goalies to catch on and adjust, to the penalty kicker's detriment.

The key is that, in each period, there has to be a 50-50 chance that a player will kick right or left. The random sequence applet lets you try to come up with a random sequence of 0s and 1s over twenty periods. Three statistical tests tell you if there is a pattern to your selections. Remember, any pattern that can be discerned can also be used against you. This is why statisticians for football teams, soccer teams, baseball teams, etc., are so well-paid.

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