"Look at these fools," continued Delapine as he pointed at the silent players. "Watch them with their note books entering the numbers down. They all have their pet 'systems.' Some stake their money on their birthday number, or the number of black cats they have seen during the day, or a certain number they may happen to have dreamt of, or any other absurd superstition. The majority, however, cling to the Martingale fallacy." "What is that?" asked Payot. "A system based on faulty reasoning," said the professor. "It is common knowledge that the same number or colour may recur two, three, four, or half a dozen times running, and this will probably occur while we are looking on, but the players think that the chances become less and less for each additional recurrence, for the same colour has never been known to recur more than twenty-five times running ever since the Casino was started forty years ago, so the players, knowing this, watched until the same colour has turned up say six or seven times running, and then they back the opposite colour, doubling their stakes each time they lose, although each time they run the risk of Zero turning up and losing everything. The stupid players imagine that they have a much better chance if they start backing the opposite colour after a considerable sequence of one colour, under the mistaken impression that what has just happened will influence the next throw. They forget that they are playing against a soulless mechanical wheel, and not against an emotional human being, and that even after red has turned up twenty-five times, the probability that black will come up next throw is not a bit greater than for red; the chances always remain exactly the same. "Gentlemen," added Delapine gravely, "all systems have invariably failed, and always will fail, although they may often succeed for a short time." "I wonder whether Tennyson had this in his mind," said Marcel aside to Violette, "when he said:-- "'Our little systems have their day, They have their day and cease to be, They have no chance to cope with thee, And thou, O Blanc,[20] art more than they.'" "O go on, Tennyson didn't really write that, did he?" enquired Violette, looking at him with a puzzled expression of mingled wonderment and doubt. Marcel said nothing, but chuckled inwardly, and looked very knowingly. "There is only one infallible way to get the better of the bank," continued Delapine. "Oh! please, professor, do tell us what that is," they all exclaimed. "Hush," said Delapine, "not so loud. Only wait until to-morrow and you shall all see it for yourselves." "Just look at that horrid old woman," said Violette in a half whisper. "I saw her distinctly grab the winnings of another party who had placed her gold piece on the line between two squares (à cheval I think you call it.) Look, professor," and she pointed her out to him. "I will soon stop her little game," said Delapine who had already detected her at it.