Please notice that the payoffs in this program are set up such that you will, in fact, feel cheated. The basis for this is that you will likely spend maybe 30-

Please notice that the payoffs in this program are set up such that you will, in fact, feel cheated. The basis for this is that you will likely spend maybe 30-60s playing this game so you will register something between 100-200 keypresses or so. If you just click the "Randomize" button you can see the problem: a truly random input source will fluctuate over 100-200 keypresses much more than it will be biased upwards, so that after 100-200 you will probably see some run of "bad luck" by which the truly-random algorithm crashes from $1005 to $995 or so. Now if this were you, you would have stopped there with the last 5-10% being predicted perfectly, and said "okay, okay, the algorithm has learned how I behave." But it hasn't.\ Part of this is the fallacy that people generally assume that over a large number of trials the standard deviation of a sum of random variables drops to zero -- that is true of an average but not a sum. So you have a discrete random variable which takes on the values +1.05 with probability 0.5 or -1 with probability 0.5, so its variance is basically 1.0 (off by 625 ppm but whatever) and so its standard deviation is basically 1.0 and if you sum N of these you have a standard deviation that is 1.0 √N while the mean is 0.05 N, these only equal when √N = 1.0/0.05 = 20 and thus N=400. So at 100-200 trials, you cannot generally expect the systematic bias from winning extra money when you are random to visibly outweigh the random noise from just randomly being wrong, you have to go to 500+ trials to really prove your mettle. But most people just won't play this thing for that long.