oduction when curious
sequences are afoot. All are friends.

"That's the theory of Sir Hiram Maxim;" commented my friend, as he
excused himself reluctantly for another appointment. "But no true
gambler will believe it, monsieur, or at least act on it."

All eyes were turned on Kennedy, who made a gesture of polite
deprecation, as if the remark of my friend were true, but he
nonchalantly placed his chips on the "17."

"The odds against '17' appearing four consecutive times are some
millions," he went on, "and yet, having appeared three times, it is just
as likely to appear again as before. It is the usual practice to avoid a
number that has had a run, on the theory that some other number is more
likely to come up than it is. That would be the case if it were drawing
balls from a bag full of red and black balls--the more red ones drawn
the smaller the chance of drawing another red one. But if the balls are
put back in the bag after being drawn the chances of drawing a red one
after three have been drawn are exactly the same as ever. If we toss
a cent and heads appear twelve times, that does not have the slightest
effect on the thirteenth toss--there is still an even chance that it,
too, will be heads. So if '17' had come up five times to-night, it would
be just as likely to come the sixth as if the previous five had not
occurred, and that despite the fact that before it has appeared at all
odds against a run of the same number six times in succession are about
two billion, four hundred and ninety-six million, and some thousands.
Most systems are based on the old persistent belief that occurrences of
chance are affected in some way by occurrences immediately preceding,
but disconnected physically. If we've had a run of black for twenty
times, system says play the red for the twenty-first. But black is just
as likely to turn up the twenty-first as if it were the first play of
all. The confusion arises because a run of twenty on the black should
happen once in one million, forty-eight thousand, five hundred and
seventy-six coups. It would take ten years to make that many coups, and
the run of twenty might occur once or any number of times in it. It is
only when one deals with infinitely large numbers of coups that one can
count on infinitely small variations in the mathematical results. This
game does not go on for infinity--therefore anything, everything, may
happen. Systems are based on the infinite; we play in the finit