“A friend of mine who was not with us, but who had had many weeks’ experience at Monaco, had communicated a little plan for an all but moral certainty of winning, which was founded on the most scientific principles, but the only defect of which was that the banks gave one no conceivable means of carrying it into practice—a defect, indeed, which I believe he himself had verified by leaving Monaco a loser, in spite of his scientific plan. His idea was this:—It is obvious that even where,—say at roulette,—the chance of the next ‘odd’ or ‘even’ is precisely one in two, or one-half, the chance of a run of any given eight results in a _specified_ order,—such as odd, odd, even, odd, odd, even, even, even,—will be only one in 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, or one in 256. If, then, my friend bethought himself, you could but steadily stake your money so as to stake it against the arrival of this highly improbable compound event, you would be sure to win. I quite agreed in this extremely sagacious principle, but the difficulty, unfortunately, was in the application of the theory. The bank gives you no chance at all of staking your money against any complex event. It admits only of your staking it in favour of or against the simple elements of this compound event. And, unfortunately, though it always remains highly improbable that any specified run of eight will take place, as you can only stake your money time by time on each single one of the eight component elements of the event, and as, in each of them separately, the chance is one in two, and not one in 256, it is simply impossible by the rules of the game so to play as to have the chances in your favour. I did, indeed, think of requesting the bank to let me stake on the result of two or three successive twirls of the roulette table, instead of on one at a time, but since my French was extremely bad, hardly adequate to protesting against the accidental raking up of my money when I had actually won, and since, had it been better, I had no hope that the authorities would comply with a request so very unsafe for themselves,—the drift of which, indeed, the croupiers might hardly have caught at the first suggestion, but would certainly have suspected,—I reluctantly abandoned my friend’s scientific receipt for winning, and was contented to lose.