“Since the exact situation is never likely to occur again, the least I can do, by way of showing my appreciation of your remarkable perception, is to gratify your curiosity.—I held nothing.”
Spotswoode put down his hand and extended his fingers gracefully toward the upturned cards. There were revealed a five, six, seven, and eight of clubs, and a knave of hearts.
“I can’t say that I follow your reasoning, Mr. Spotswoode,” Markham confessed. “Mr. Vance had you beaten—and he quit.”
“Consider the situation,” Spotswoode replied, in a suave, even voice. “I most certainly would have opened so rich a pot, had I been able to, after Mr. Cleaver and you had passed. But since I nevertheless stayed after Mr. Vance had opened for so large an amount, it goes without saying that I must have had either a four-straight, a four-flush, or a four-straight-flush. I believe I may state without immodesty that I am too good a player to have stayed otherwise. . . .”
“And I assure you, Markham,” interrupted Vance, “that Mr. Spotswoode is too good a player to have stayed unless he had actually had a four-straight-flush. That is the only hand he would have been justified in backing at the betting odds of two to one.—You see, I had opened for the amount in the pot, and Mr. Spotswoode had to put up half the amount of the money on the table in order to stay—making it a two-to-one bet.—Now, these odds are not high, and any non-opening hand smaller than a four-straight-flush would not have warranted the risk. As it was, he had, with a one-card draw, two chances in forty-seven of making 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 fool-hardy 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 almost 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 high-ball in troubled abstraction. At last he rose and walked to the mantel, where he stood studying a Cézanne water-color 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.