GROUNDS OF DISBELIEF. 173 



words, that there is some general tendency of things, some 

 law, which prevents regular combinations from occurring, or at 

 least from occurring so often as others. Among these thinkers 

 maybe numbered D Alembert; who, in an Essay on Proba 

 bilities to be found in the fifth volume of his Melanges, con 

 tends that regular combinations, though equally probable 

 according to the mathematical theory with any others, are 

 physically less probable. He appeals to common sense, or in 

 other words, to common impressions ; saying, if dice thrown 

 repeatedly in our presence gave sixes every time, should we 

 not, before the number of throws had reached ten, (not to 

 speak of thousands of millions,) be ready to affirm, with the 

 most positive conviction, that the dice were false ? 



The common and natural impression is in favour of 

 D Alembert : the regular series would be thought much more 

 unlikely than an irregular. But this common impression is, 

 I apprehend, merely grounded on the fact, that scarcely any 

 body remembers to have ever seen one of these peculiar coin 

 cidences : the reason of which is simply that no one s experience 

 extends to anything like the number of trials, within which that 

 or any other given combination of events can be expected to 

 happen. The chance of sixes on a single throw of two dice 

 being ^, the chance of sixes ten times in succession is 1 

 divided by the tenth power of 30 ; in other words, such a con 

 currence is only likely to happen once in 3, 650,1 58,440,002,976 

 trials, a number which no dice-player s experience comes up 

 to a millionth part of. But if, instead of sixes ten times, any 

 other given succession of ten throws had been fixed upon, it 

 would have been exactly as unlikely that in any individual s 

 experience that particular succession had ever occurred ; 

 although this does not seem equally improbable, because no 

 one could possibly have remembered whether it had occurred 

 or not, and because the comparison is tacitly made, not be 

 tween sixes ten times and any one particular series of throws, 

 but between all regular and all irregular successions taken 

 together. 



That (as D Alembert says) if the succession of sixes was 

 actually thrown before our eyes, we should ascribe it not to 



