PROBABILITY AND ENTROPY 149 



view of thermodynamics, let us consider a fresh 

 pack of cards, all sorted, for example, ace, king, 

 queen, etc., of spades, ace, king, queen, etc., of 

 clubs, and so on. Such a grouping of the cards 

 is easily described and easily discernible. If I 

 spread the pack before you, one-half is obvi- 

 ously black, the other red. If I should put this 

 pack into some sort of shuffling and dealing 

 machine the first deals might give some very 

 singular hands, but as the process continued a 

 point would be reached where we would say that 

 the pack was well shuffled. Now any one of the 

 particular arrangements obtained by shuffling 

 is just as improbable a priori as the first well- 

 sorted arrangement, and by this we mean that if 

 we note the arrangement, card by card, in a 

 well shuffled pack, this identical arrangement is 

 no more likely to recur than the arrangement of 

 the fresh pack. Nevertheless, while the number 

 of possible well-sorted or easily describable ar- 

 rangements is very small, there is an enormous 

 number of arrangements of a nondescript char- 

 acter. As the shuffling continues the arrange- 

 ment constantly changes; there is no approach 

 to any one particular arrangement, but on the 

 other hand it rarely happens that a remarkably 

 distinguished arrangement occurs. If one of you 



