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 finite.”

“You talk like a professor I had at the university,” ejaculated DeLong contemptuously as Craig finished his disquisition on the practical fallibility of theoretically infallible systems.  Again DeLong carefully avoided the “17,” as well as the black.

The wheel spun again; the ball rolled.  The knot of spectators around the table watched with bated breath.

Seventeen won!

As Kennedy piled up his winnings superciliously, without even the appearance of triumph, a man behind me whispered, “A foreign nobleman with a system—­watch him.”

“Non, monsieur,” said Kennedy quickly, having overheard the remark, “no system, sir.  There is only one system of which I know.”

“What?” asked DeLong eagerly.

Kennedy staked a large sum on the red to win.  The black came up, and he lost.  He doubled the stake and played again, and again lost.  With amazing calmness Craig kept right on doubling.

“The martingale,” I heard the man whisper behind me.  “In other words, double or quit.”

Kennedy was now in for some hundreds, a sum that was sufficiently large for him, but he doubled again, still cheerfully playing the red, and the red won.  As he gathered up his chips he rose.

“That’s the only system,” he said simply.

“But, go on, go on,” came the chorus from about the table.

“No,” said Kennedy quietly, “that is part of the system, too—­to quit when you have won back your stakes and a little more.”