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a straight-flush, nine chances in forty-seven of making a flush, and eight chances in forty-seven of making a straight; so that he had nineteen chances in forty-seven—or more than one chance in three—of strengthening his hand into either a straight-flush, a flush, or a straight.”

      “Exactly,” assented Spotswoode. “However, after I had drawn my one card, the only possible question in Mr. Vance’s mind was whether or not I had made my straight-flush. If I had not made it—or had merely drawn a straight or a flush—Mr. Vance figured, and figured rightly, that I would not have seen his large bet and also have raised it the limit. To have done so, in those circumstances, would have been irrational poker. Not one player in a thousand would have taken such a risk on a mere bluff. Therefore, had Mr. Vance not laid down his four aces when I raised him, he would have been foolhardy in the extreme. It turned out, of course, that I was actually bluffing; but that does not alter the fact that the correct and logical thing was for Mr. Vance to quit.”

      “Quite true,” Vance agreed. “As Mr. Spotswoode says, not one player in a thousand would have wagered the limit without having filled his straight-flush, knowing I had a pat hand. Indeed, one might also say that Mr. Spotswoode, by doing so, has added another decimal point to the psychological subtleties of the game; for, as you see, he analyzed my reasoning, and carried his own reasoning a step further.”

      Spotswoode acknowledged the compliment with a slight bow; and Cleaver reached for the cards and began to shuffle them. But the tension had been broken, and the game was not resumed.

      Something, however, seemed to have gone wrong with Vance. For a long while he sat frowning at his cigarette and sipping his highball in troubled abstraction. At last he rose and walked to the mantel, where he stood studying a Cézanne watercolor he had given Markham years before. His action was a typical indication of his inner puzzlement.

      Presently, when there came a lull in the conversation, he turned sharply and looked at Mannix.

      “I say, Mr. Mannix”—he spoke with only casual curiosity—“how does it happen you’ve never acquired a taste for poker? All good businessmen are gamblers at heart.”

      “Sure they are,” Mannix replied, with pensive deliberation. “But poker, now, isn’t my idea of gambling—positively not. It’s got too much science. And it ain’t quick enough for me—it hasn’t got the kick in it, if you know what I mean. Roulette’s my speed. When I was in Monte Carlo last summer, I dropped more money in ten minutes than you gentlemen lost here this whole evening. But I got action for my money.”

      “I take it, then, you don’t care for cards at all.”

      “Not to play games with.” Mannix had become expansive. “I don’t mind betting money on the draw of a card, for instance. But no two out of three, y’ understand. I want my pleasures to come rapid.” And he snapped his thick fingers several times in quick succession to demonstrate the rapidity with which he desired to have his pleasures come.

      Vance sauntered to the table and carelessly picked up a deck of cards. “What do you say to cutting once for a thousand dollars?”

      Mannix rose instantly. “You’re on!”

      Vance handed the cards over, and Mannix shuffled them. Then he put them down and cut. He turned up a ten. Vance cut and showed a king.

      “A thousand I owe you,” said Mannix, with no more concern than if it had been ten cents.

      Vance waited without speaking, and Mannix eyed him craftily.

      “I’ll cut with you again—two thousand this time. Yes?”

      Vance raised his eyebrows. “Double?… By all means.” He shuffled the cards and cut a seven.

      Mannix’s hand swooped down and turned a five.

      “Well, that’s three thousand I owe you,” he said. His little eyes had now narrowed into slits, and he held his cigar clamped tightly between his teeth.

      “Like to double it again—eh, what?” Vance asked. “Four thousand this time?”

      Markham looked at Vance in amazement, and over Allen’s face there came an expression of almost ludicrous consternation. Everyone present, I believe, was astonished at the offer, for obviously Vance knew that he was giving Mannix tremendous odds by permitting successive doubling. In the end he was sure to lose. I believe Markham would have protested if at that moment Mannix had not snatched the cards from the table and begun to shuffle them.

      “Four thousand it is!” he announced, putting down the deck and cutting. He turned up the queen of diamonds. “You can’t beat the lady—positively not!” He was suddenly jovial.

      “I fancy you’re right,” murmured Vance; and he cut a trey.

      “Want some more?” asked Mannix, with good-natured aggressiveness.

      “That’s enough.” Vance seemed bored. “Far too excitin’. I haven’t your rugged constitution, don’t y’ know.”

      He went to the desk and made out a check to Mannix for a thousand dollars. Then he turned to Markham and held out his hand. “Had a jolly evening and all that sort of thing.… And, don’t forget: we lunch together tomorrow. One o’clock at the club, what?”

      Markham hesitated. “If nothing interferes.”

      “But really, y’ know, it mustn’t,” insisted Vance. “You’ve no idea how eager you are to see me.”

      He was unusually silent and thoughtful during the ride home. Not one explanatory word could I get out of him. But when he bade me good night he said, “There’s a vital part of the puzzle still missing, and until it’s found, none of it has any meaning.”

      CHAPTER 28

      THE GUILTY MAN

      (Tuesday, September 18; 1 P.M.)

      Vance slept late the following morning and spent the hour or so before lunch checking a catalog of ceramics which were to be auctioned next day at the Anderson Galleries. At one o’clock we entered the Stuyvesant Club and joined Markham in the grill.

      “The lunch is on you, old thing,” said Vance. “But I’ll make it easy. All I want is a rasher of English bacon, a cup of coffee, and a croissant.”

      Markham gave him a mocking smile.

      “I don’t wonder you’re economizing after your bad luck of last night.”

      Vance’s eyebrows went up. “I rather fancied my luck was most extr’ordin’ry.”

      “You held four of a kind twice and lost both hands.”

      “But, y’ see,” blandly confessed Vance, “I happened to know both times exactly what cards my opponents held.”

      Markham stared at him in amazement.

      “Quite so,” Vance assured him. “I had arranged before the game, d’ ye see, to have those particular hands dealt.” He smiled benignly. “I can’t tell you, old chap, how I admire your delicacy in not referring to my rather unique guest, Mr. Allen, whom I had the bad taste to introduce so unceremoniously into your party. I owe you an explanation and an apology. Mr. Allen is not what one would call a charming companion. He is deficient in the patrician elegancies, and his display of jewelry was a bit vulgar—though I infinitely preferred his diamond studs to his piebald tie. But Mr. Allen has his points—decidedly he has his points. He ranks with Andy Blakely, Canfield, and Honest John Kelly as an indoor soldier of fortune. In fact, our Mr. Allen is none other than Doc Wiley Allen, of fragrant memory.”

      “Doc Allen! Not the notorious old crook who ran the Eldorado Club?”

      “The same. And, incidentally, one of the cleverest card manipulators in a once lucrative but shady profession.”

      “You mean this fellow Allen stacked the cards last night?” Markham was indignant.

      “Only for the two hands you mentioned. Allen,

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