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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, if you happen to remember, was the dealer both times. I, who purposely sat on his right, was careful to cut the cards in accordance with his instructions. And you really must admit that no stricture can possibly attach to my deception, inasmuch as the only beneficiaries of Allen’s manipulations were Cleaver and Spotswoode. Although Allen did deal me four of a kind on each occasion, I lost heavily both times.”

      Markham regarded Vance for a moment in puzzled silence, and then laughed good-naturedly.

      “You appear to have been in a philanthropic mood last night. You practically gave Mannix a thousand dollars by permitting him to double the stakes on each draw. A rather quixotic procedure, I should say.”

      “It all depends on one’s point of view, don’t y’ know. Despite my financial losses—which, by the bye, I have every intention of charging up to your office budget—the game was most successful. . . . Y’ see, I attained the main object of my evening’s entertainment.”

      “Oh, I remember!” said Markham vaguely, as if the matter, being of slight importance, had for the moment eluded his memory. “I believe you were going to ascertain who murdered the Odell girl.”

      “Amazin’ memory! . . . Yes, I let fall the hint that I might be able to clarify the situation to-day.”

      “And whom am I to arrest?”

      Vance took a drink of coffee and slowly lit a cigarette.

      “I’m quite convinced, y’ know, that you won’t believe me,” he returned, in an even, matter-of-fact voice. “But it was Spotswoode who killed the girl.”

      “You don’t tell me!” Markham spoke with undisguised irony. “So it was Spotswoode! My dear Vance, you positively bowl me over. I would telephone Heath at once to polish up his handcuffs, but, unfortunately, miracles—such as strangling persons from across town—are not recognized possibilities in this day and age. . . . Do let me order you another croissant.”

      Vance extended his hands in a theatrical gesture of exasperated despair.

      “For an educated, civilized man, Markham, there’s something downright primitive about the way you cling to optical illusions. I say, y’ know, you’re exactly like an infant who really believes that the magician generates a rabbit in a silk hat, simply because he sees it done.”

      “Now you’re becoming insulting.”

      “Rather!” Vance pleasantly agreed. “But something drastic must be done to disentangle you from the Lorelei of legal facts. You’re so deficient in imagination, old thing.”

      “I take it that you would have me close my eyes and picture Spotswoode sitting up-stairs here in the Stuyvesant Club and extending his arms to 71st Street. But I simply couldn’t do it. I’m a commonplace chap. Such a vision would strike me as ludicrous; it would smack of a hasheesh dream. . . . You yourself don’t use Cannabis indica, do you?”

      “Put that way, the idea does sound a bit supernatural. And yet: Certum est quia impossibile est. I rather like that maxim, don’t y’ know; for, in the present case, the impossible is true. Oh, Spotswoode’s guilty—no doubt about it. And I’m going to cling tenaciously to that apparent hallucination. Moreover, I’m going to try to lure you into its toils; for your own—as we absurdly say—good name is at stake. As it happens, Markham, you are at this moment shielding the real murderer from publicity.”

      Vance had spoken with the easy assurance that precludes argument; and from the altered expression on Markham’s face I could see he was moved.

      “Tell me,” he said, “how you arrived at your fantastic belief in Spotswoode’s guilt.”

      Vance crushed out his cigarette and folded his arms on the table.

      “We begin with my quartet of possibilities—Mannix, Cleaver, Lindquist, and Spotswoode. Realizing, as I did, that the crime was carefully planned with the sole object of murder, I knew that only some one hopelessly ensnared in the lady’s net could have done it. And no suitor outside of my quartet could have been thus enmeshed, or we would have learned of him. Therefore, one of the four was guilty. Now, Lindquist was eliminated when we found out that he was bedridden in a hospital at the time of Skeel’s murder; for obviously the same person committed both crimes——”

      “But,” interrupted Markham, “Spotswoode had an equally good alibi for the night of the Canary’s murder. Why eliminate one and not the other?”

      “Sorry, but I can’t agree with you. Being prostrated at a known place surrounded by incorruptible and disinterested witnesses, both preceding and during an event, is one thing; but being actually on the ground, as Spotswoode was that fatal evening, within a few minutes of the time the lady was murdered, and then being alone in a taxicab for fifteen minutes or so following the event—that is another thing. No one, as far as we know, actually saw the lady alive after Spotswoode took his departure.”

      “But the proof of her having been alive and spoken to him is incontestable.”

      “Granted. I admit that a dead woman doesn’t scream and call for help, and then converse with her murderer.”

      “I see.” Markham spoke with sarcasm. “You think it was Skeel, disguising his voice.”

      “Lord no! What a priceless notion! Skeel didn’t want any one to know he was there. Why should he have staged such a masterpiece of idiocy? That certainly isn’t the explanation. When we find the answer it will be reasonable and simple.”

      “That’s encouraging,” smiled Markham. “But proceed with your reasons for Spotswoode’s guilt.”

      “Three of my quartet, then, were potential murderers,” Vance resumed. “Accordingly, I requested an evening of social relaxation, that I might put them under the psychological microscope, as it were. Although Spotswoode’s ancestry was wholly consistent with his having been the guilty one, nevertheless I confess I thought that Cleaver or Mannix had committed the crime; for, by their own statements, either of them could have done it without contradicting any of the known circumstances of the situation. Therefore, when Mannix declined your invitation to play poker last night, I put Cleaver to the first test. I wig-wagged to Mr. Allen, and he straightway proceeded to perform his first feat of prestidigitation.”

      Vance paused and looked up.

      “You perhaps recall the circumstances? It was a jack-pot. Allen dealt Cleaver a four-straight-flush and gave me three kings. The other hands were so poor that every one else was compelled to drop out. I opened; and Cleaver stayed. On the draw, Allen gave me another king, and gave Cleaver the card he needed to complete his straight-flush. Twice I bet a small amount, and each time Cleaver raised me. Finally I called him, and, of course, he won. He couldn’t help but win, d’ ye see. He was betting on a sure-thing. Since I opened the pot and drew two cards, the highest hand I could possibly have held would have been four of a kind. Cleaver knew this, and having a straight-flush, he also knew, before he raised my bet, that he had me beaten. At once I realized that he was not the man I was after.”

      “By what reasoning?”

      “A poker-player, Markham, who would bet on a sure-thing is one who lacks the egotistical self-confidence of the highly subtle and supremely capable gambler. He is not a man who will take hazardous chances and tremendous risks, for he possesses, to some degree, what the psychoanalysts call an inferiority complex, and instinctively he grasps at every possible opportunity of protecting and bettering himself. In short, he is not

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