344 JOSEPH PETERSON 



has only one run past cul de sac 10. Hence, if 



In general, in a maze with y blind alleys the number of times 

 that the first would be passed in forward runs in n trials is 

 (4/3) 3 '- 1 times the number that the last would be passed, i.e., 

 (4/3) y - 1 w. 



Now, on the assumption above, it is evident that the number 

 of entrances to the respective blind alleys will be to the number 

 of times that they are passed in the forward direction as (%i — 

 1/4) : Xi, (x, = 1/4) \Xt (#10 — 1/4) : x 10 .* Substitut- 

 ing the values determined above for x u x 2 , x 3 , etc., we get the 

 following ratios of blind alley entrances to forward runs past 

 blind alleys in order from the first to the tenth: 



13.07n : 13.32w, 



M 



Now when n equals any small number, as 1, 2, or 3, it is evi- 

 dent that the number of times of passing successfully a blind 



4 Each is passed 3/4 of the number of times it is encountered, and is entered 

 1/2 of that number. Since each trial has one extra forward run it is evident that 

 the course past the blind alley has an advantage of 3/4 — 1/2, or 1/4, run or prac- 

 tice over the course leading into the blind alley. This advantage is not relative, 

 but absolute; for an equal number of forward and back runs past any cul de sac 

 gives equal frequency, as we have seen, for the two directions. 



