|
ove)are 1,287 in number. But, as in dealing with common sequences, we must multiply these by 4 times 4 times 4 times 4 times 4, or by 1,024, getting 1,317,888. Subtracting thence the flushes and sequences, 15,348 in all, we get 1,302,540 as the total number of common hands (not containing pairs or the like)--as above.
It will be seen that those who devised the rules for poker play set the different hands in their proper order. It is fitting, for instance, that as there are only 40 possible flush sequence hands, out of a total number of 2,598,960 hands, while there are 624 ' four' hands, the flush sequences should come first, and so with the rest. It is noteworthy, however, that when sequences were not counted, as was the rule in former times, there was one hand absolutely unique and unconquerable. The holder of four aces then wagered on a certainty, for no one else could hold that hand. At present there is no absolutely sure winning hand. The holder of ace, king, queen, knave, ten, flush, may (though it is of course exceedingly unlikely)be met by the holder of the same cards, flush, in another suit. Or, when we remember that at whist it has happened that the deal divided the four suits among the four players, to each a complete suit, we see that four players at poker might each receive a flush sequence headed by the ace. Thus the use of sequences has saved poker-players from the possible risk of having either to stand out or wager on a certainty, which last would of course be very painful to the feelings of a professional gambler.
We might subdivide the hands above classified into a much longer array, beginning thus :-4 flush sequences headed by ace; 4 headed by king, and so on down to 4 headed by five; 48 possible four-aces hands; 48 four-kings hands; and so on down to 48 four-twos hands; 24 possible ' fulls' of 3 aces and 2 kings; as many of 3 aces and 2 queens; and so on down to 24 ' fulls' of 3
|
