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'Of course, these cards illustrate with accuracy a certain average of luck; but they do more-they trace the erratic footfalls of the blind goddess Tukè.'

'Bravo, well put !'

'You would imagine à priori that if red won the last jeu, the inference would be in favour of black winning the next jeu. But such is not the case. The inference is directly the reverse, and in fact in favour of red winning again.' 'How? I don't quite follow you.' 'Look at these cards.

Only occasionally do you find the order of progression is like the goose-step-red, black, red, black, red, black, even three times following. The common order runs somewhat in this fashion: red, red, black, red, red, black, black, black, red, and so on. I cannot perhaps give a better illustration than the list of University boat-races; neither Oxford nor Cambridge expect to win and lose in alternate years; on the contrary, each anticipates runs of luck, good or bad.'

6

And so you would argue that if Oxford won the race next year, the betting would be in favour of her winning the year following?'

6

That is my principle, and now for its application. Under ordinary circumstances, I quite perceive that at trente et quarante it would be insane to double. You would risk hundreds or thousands in order to recover a miserable thaler. But on my principle you need not hesitate, provided of course that your purse will stand it. For this reason, viz.: that you will be compelled to double as often as three times is unlikely, four times improbable, five times beyond the range of probability, six times virtually impossible, inasmuch as such a sequence could only occur about once in a month. Therefore, by always backing the colour which won last, and by doubling when you lose until you win, I maintain you reduce loss to a vanishing point, and render gain a dead certainty.'

Mr. Dark was not convinced. He objected that his friend was too dogmatic. This led to a hottish discussion, the outcome of which was an experiment with a pack of cards, when, to Mr. Fair's astonishment, the order red, black, occurred no less than five times in succession.

But although he felt the force of his argument weakened, he would not yield his point.

6

'You see,' he urged, if you did lose ten times, that is, if the sequence was red, black, five times, and you began with a thaler, your total loss would only be 153l. 9s.'

'Only!'

'Well'—petulantly—' you would not mind putting twice as much on the favourite of the Derby.'

'My dear boy, I never in my life offered to bet 153l. 9s.

against 3s., which is in effect what you propose. Besides, your next venture would entail the total loss of 460l. 7s.'

'So it would. Yet I am satisfied that I am right in theory if not in practice. Just put your back into it and find out how it will work, old fellow; you can generally see your way when others fail.'

Thus appealed to, Mr. Dark began to exercise his wits, which were of no contemptible order. He criticised severely a system which entailed the possible loss of several hundred pounds with the minimum advantage of saving a paltry three-shilling stake. But he could not propose an alternative system.

'I have it!' cried cheery Mr. Fair, after much cogitation. 'I'll always back the winning colour, but I won't double, and you shall always back the losing colour, but not double, and we will see which wins; one or other must.'

'I'll back myself for an even pony,' remarked Mr. Dark as he accepted the challenge.

Good!' was the response.

After a heavy breakfast on the morrow they marched to the Kursaal, with no small trepidation of soul, to try their experiment. Being early, both were accommodated with seats. Thus both had fair-play, and were in a better position for making the game than when in the gallery, besides being able to catch the eye of the croupiers. Not to weary with the various vicissitudes of the play, let it suffice to relate that they kept their seats till late in the afternoon, when by mutual consent they adjourned.

'I haven't lost,' observed Mr. Dark dubiously enough.
'I haven't gained,' rejoined Mr. Fair positively.

Then they set to work to count their money, and it soon appeared that somehow they had contrived each to a small extent to contribute towards the Kursaal profits. They were only singed, however, not burnt.

6

'Hang it,' remarked Mr. Dark, this loafing about Pandemonium is rather slow! I want some exercise for my muscles.' 'Done along with you,' observed Mr. Fair. 'Let us make tracks for the Righi.'

They made them on the next day.

COMPTON READE, M.A.

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