s if it had not already had a run of three," said a voice at my
elbow.

It was Kennedy. The roulette-table needs no introduction 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 had 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