ON COMMON NOTIONS OF PROBABILITY. 125 



gives 1716 games, and yet a sturdy whist player, who 

 plays on an average a dozen deals an evening for 200 

 evenings in the year, or 2400 deals per annum, will look 

 grave when he relates that he had bad cards for six 

 deals together, and will assure you that there is some* 

 thing in luck. 



But at the same time, the number of trials which 

 makes a run of the unlikely event extremely probable, 

 will give the same probability to a much larger run in 

 favour of the more probable event. To find to what 

 extent this goes, use the following 



RULE. If it be a to & for A against B, in any single 

 trial, then subtract the logarithms of a and b separately 

 from that of a -{- 6; take any two whole numbers 

 which are very nearly in proportion to these differences, 

 and to each add 1 ; the sums show the runs of the 

 two events, which have the same probability (be it small 

 or great) of happening in a very large number of 

 throws. Thus, suppose it is 10 to 3 for A against B. 



Log, 13 1-11394 log. 13 1-11394 

 Log. 10 1 -00000 log. 3 -47712 



0-11394 0-63682 : : 11 ; 64 nearly. 



Consequently, whatever chance there is for a run of 12 

 B's, there is as much for a run of 65 A's. 



In the last mentioned lottery, when a = 19, 6=1, 

 we have log 20 log 19 = -02228, and log 20 log 1 

 = 1*30103, which differences are 1 to 65 nearly, and 

 as 6 to 390. Consequently there is as much reason to 

 expect a run of 391 white balls as of 7 black balls. 



No person can take a rational view of probabilities 

 until he ceases to recoil from the supposition that an 

 event is never to happen because the odds are very much 

 against his choosing, out of a large number of trials, 

 the one in which it is to happen. The best way to force 

 the mind upon the consideration is to return to the first 



