“That’s fine,” she said. “But how does it give you the odds?”
“It means that theoretically, out of any 1728 batches of six people, there should only be 385 batches in which two of ’em weren’t born in the same month — meaning where Loud Mouth would lose his bet. 385 from 1728 leaves 1343. So the odds are 1343 to 385, which...”
The Saint made another swift calculation, and whistled.
“It comes out at almost three and a half to one,” he concluded. “And everybody thought Loud Mouth was nuts to be offering two to one — only a bit more than half the honest odds! A fellow could make a career out of being so crazy!”
Her face fell for a moment, in transparent anxiety, before she forced herself to suppress the thought.
“Well, after all, it’s not so different from the kind of statistics that insurance companies worry about, is it?
Papa probably knows the correct way to work it out, just like you did.”
“I hope so,” said the Saint, but for the rest of the evening only the superficial part of his attention was completely available to the conversation, the entertainment, or even the notable charms of his companion.
Now that he had belatedly been obliged to think seriously about it, his fateful instinct for chicanery and the fast double-shuffle could recognize the loud and unlovable gamecock of the Interplanetary Hotel’s Spaceship Room as a probable charter member of an ancient fraternity, with a new angle. But the most interesting novelty was not the switch from the stereotyped con man’s beguiling suaveness to Mr Way’s crude art of alienation, but the upper-class mathematics on which the nasty little man had based his act. This was an artifice that Simon Templar had never met before, and he seriously wondered if it might not prove too tricky even for him.
He had even graver doubts when he saw the obnoxious operator again the next day. Wandering up to the Futuramic Terrace in search of a long cooling potion after a couple of hours of swimming and sunning himself on the beach, he spotted the little man sitting at one of the tables by the pool, unselfconsciously exposing as much of his bulbously misproportioned physique as could not be contained in a pair of garishly flowered Hawaiian shorts, and holding forth to a pimpled and sulky-mouthed young man and two tough-looking middle-aged women with the unmistakable air of dames who had never yet lost an elbowing contest at a bargain counter.
The table, like all others on the terrace, sported a cloth patterned in red, white, and blue stripes about three inches wide, and Mr Way was flipping cigarettes a foot or two into the air so that they fell on it at various random angles.
“In Pakistan, where it’s practically the national game, they call it Tiger Toss — from the board they play on, which has black and yellow stripes. And they use carved ivory sticks instead of cigarettes. But the measurements are relatively just the same: the sticks are exactly as long as the stripes are wide. Like on this cloth, the stripes happen to be just as wide as one of these cigarettes is long. See?”
He demonstrated.
“Then you toss a stick, or a cigarette, onto the board, or the cloth, and see how it lands. It has to spin in the air and turn over so there’s no chance of controlling it. If it comes down completely inside a stripe, you win. If it falls across a dividing line, you lose. Like this... But wait till you hear the catch.”
The Saint waited, at a diffident distance towards the background, but no farther off than other patrons or passers-by whose attention had been caught and held by Mr Way’s provocatively high-decibel style of conversation.
“The pitch they give the peasants is that this is the rajah’s way of distributing charity so as to do the most good. You know — if you give a rupee to every starving slob, they’ll all be just as hungry again tomorrow, but playing Tiger Toss, the lucky ones could make a pot of money. And the guy who’s running the game — who’s got a concession from the rajah, of course — shows ’em how easy it is. ‘Look,’ he said, ‘even if a stick falls at right angles to the pattern, there’s still room for it inside a stripe. And the more it falls at an angle, the more room there is.’ ” Mr Way illustrated the fact with a cigarette. “ ‘Until if it was parallel with the stripes, there’d be room for eight or nine of ’em to lie in there side by side without touching the dividing line,’ says this official gypper. But they never got me to play. No, sir.” Mr Way’s insufferably malevolent stare swung around him like a scythe. “Before I’d buy a tale about a philanthropic rajah, I’ll believe in a big-hearted Shylock.”
Without giving anybody time to draw a deep breath, he picked up another cigarette and went on, “Right away, I can see how anybody with a grain of sense would look at it. Either the stick gotta fall at right angles to the stripes — like this — or it doesn’t. It’s as simple as that. One or the other. A fifty-fifty chance. And once it falls like this, square across the stripe, if it’s only a hair off of dead center, see, it has to touch the line or cross over the next stripe. Now, there’s so little chance it’ll fall dead center, one in a million maybe — you can forget it. So it still boils down to whether it falls square or not.”
“Now wait a minute, smarty-pants,” riposted one of the women, in an almost equally strident voice. “If that’s what you call using a grain of sense, saying it’s fifty-fifty if it falls this way or two hundred other ways—”
“At least, there are ninety degrees in a right angle,” corrected the pouty young man. “So if you said eighty-nine other—”
“Are you ribbing me, trying to sound like those other benighted heathens?” snarled Mr Way, “Or if that’s what you call your intelligent opinion, would you back it up with any more than hot air?” Even from his attenuated costume he was able to produce a wad of currency which he slammed on the table with a vehemence that almost equaled a slap in the face. “You want to bet even money with me? I’ll say the cigarettes touches the line, you can do the tossing, and we’ll see who comes out ahead. And I’ll fade anyone else who wants to come in.”
Simon adroitly evaded the contentious bantam’s challenging eye, and drifted on to find himself a vacant table, where he asked a mildly befogged waiter for a Pimm’s Cup, a pencil, and a piece of paper. “When all these items were finally delivered, he sipped the cold ambrosial drink and went soberly to work with the other articles. By that time, a “Tiger Toss” school was in full and audible session on the other side of the terrace, with Mr Way the self-appointed banker daring all and sundry to prove themselves as ignorant as the credulous Pakistanis.
The techniques of bogus backgrounding, Machiavellian misdirection, and a gadfly approach that could be relied on to make almost anyone but a lower-case saint too furious to think straight, were the same as the night before. But the specific probability problem, shorn of the artistic camouflage, Simon soon found, would be unscientifically called a snorter.
Since it is not the purpose of this story to double as a first primer of higher mathematics, which it may already have started to sound like, the reasoning by which the Saint solved this rather interesting equation must be omitted from the present text. To anyone who has not set at least one foot in the mystic realm of trigonometry it would be meaningless. Those who have studied such subjects, of course, may recognize it at once under the name of Buffon’s Problem. The Saint took much longer to wring the correct answer out of his rusty recollections, and when he had done it he had even more respect for the perverse astuteness of Mr Way.
It was quite comforting to persuade himself that such comparatively small-time improbity was not worthy of his serious attention, and that the types who paid Mr Way for improving their education would not be mortally hurt by the fees, but this consolation was short-lived. Chronologically, it lasted about two minutes, until his reverie was cut short by Hilda Mason’s voice beside him.