TECHNICAL DETAILS
The computer used in this experiment was a Dell 486DX2/66. The physical target was an electronic random number generator (RNG) connected to the CPU via a serial port. According to the RNG user manual, the RNG consists of "two independent analogue Zener diode based noise sources. Both signals are converted into random bit streams, combined and subsequently transmitted in the form of bytes tot he RS-232 port of your computer." The controlling program was written by the second author in Microsoft QuickBasic.
The simulated feather had to move down 400 steps to drift from the top of the screen to the bottom. To drift in the X axis direction, left or right, the RNG generated a random bit; if the bit was a 0 the feather would drift left, and if it was a 1, the feather would drift right. Then, another random number within the range of 0 to 2, inclusive, was generated, and if it was a 0 or 1, the feather would drift down one step, otherwise it would drift up one step. This asymmetry in the Y axis ensured that the feather would eventually drift all the way down.
When the feather finally landed at the bottom of the screen, the X deviation from the center line was divided by 20, and this determined the prize category. Thus, a deviation in the X axis of less than (+or-)20 would result in a score of 0, or no prize; a deviation of >(+or-)20 but <(+or-)40 would result in a score of 1, and a small prize, and so on.
Determining the theoretically expected probability distribution of the feather from the center line (i.e., deviation from X=0), was not as simple as applying the binomial distribution for 400 random binary samples. This was because the simulated feather was allowed to randomly drift back upwards, thus the number of samples in the run ranged from a minimum of 400 to an undetermined maximum (although in practice the maximum was about 800 samples). Thus, an empirical distribution was determined via a Monte Carlo run of 7,000 unobserved trials.