The Saint to the Rescue

The percentage player

There is a story, which may be apocryphal, about a certain bookmaker (of the horsey, not the literary, variety) who was making a long trip by car when towards nightfall he happened upon a hostelry which displayed an ordinary sign bearing a most unusual name, “The Even Steven.”

To a man in his business, this quaint appellation was of course doubly intriguing, and since it was in the middle of a particularly bleak and desolate stretch of country, and he had no idea how much farther he might have to drive to find a meal and a bed, he quickly decided to stop there for the night and satisfy his curiosity at the same time. The proprietor soon explained the peculiar designation of the place.

“It’s very simple, really. You see, my name actually is Steven Even. So I just decided to turn it around and call this ‘The Even Steven.’ I thought it might get a few folks puzzled enough to stop and ask questions, and sometimes it does. Like yourself.”

“That’s a pretty smart way to use the luck of a name,” said the bookie appreciatively. “I bet it brings you a lot of business.”

Mr Even, a dour and dejected type of individual, seemed glad to have someone to talk to.

“It hasn’t brought me so much luck,” he said. “The folks who stop don’t stay long. There’s not much gaiety around here, as you could see. In fact, there’s not another soul lives closer than thirty miles away, whichever way you go. Makes it pretty lonely for me, a widower. And worse still for my daughters. Three of the loveliest girls you ever set eyes on, should have their pick of boyfriends. But the nearest lads would have to drive thirty miles to pick ’em up, thirty more to take ’em to a movie, thirty miles to bring ’em home, and thirty back themselves. That’s more’n they got time to do even for beauties like these. The girls are getting so frustrated they’re about ready to do anything for a man.”

The bookie made sympathetic noises, and listened to more in the same vein until hunger obliged him to change the subject to that of food. An excellent home-cooked dinner was served to him by a gorgeous blonde who introduced herself as Blanche Even, and when he was surfeited she still kept pressing him to ask for anything else he wanted.

“A toothpick, perhaps?” he suggested.

She brought it, and said, “Would you like me to sit and talk to you for a while?”

“Thank you,” he said politely, “but I’ve had a long day and I feel like closing the book.”

He went to his room, and had just started to undress when there was a knock at the door and an absolutely breath-taking brunette came in.

“I’m Carmen Even,” she said. “I just wanted to see if you’d got everything you want.”

“I think so, thank you,” he said pleasantly. “I do a lot of traveling, so I pack very systematically.”

When he had finally convinced her and got rid of her, he climbed in between the sheets and was preparing to read himself to sleep over the Racing Form when the door opened again to admit an utterly stupefying redhead in a négligée to end all négligées.

“I’m Ginger Even,” she announced. “I wanted to be sure your bed was comfortable.”

“It is,” he assured her.

“I hope you’re not just being tactful,” she insisted. “May I try it myself?”

“If you must,” said the bookie primly. “I will get out while you do it.”

When she had gone, he settled down with a sigh of relief and was about to put out the light at last when the door burst open once more and the proprietor himself stomped in, glowing with indignation.

“What’s the matter with you?” he roared. “I got to listen all night to my daughters moaning an’ wailing, the most lusciousest gals in this county, because they all try to show you hospitality an’ you won’t give one of ’em a tumble. Ain’t us Evens good enough for you?”

“I’m sorry,” said the transient. “But I told you when I registered, I’m a professional bookmaker. I only lay Odds.”

Mr Theocritus Way, this chronicler must now hasten to establish, was not the bookie immortalized in the foregoing anecdote. He was however, a man who had concentrated on the subject of Odds with an almost comparably classic single-mindedness.

Indeed, one of his oldest but perennially profitable discoveries in the field was directly tied to the same numerical quibble between Odds and Evens. At any bar where he might be chumming for potential suckers, when the inevitable dispute eventually arose as to who should buy another drink, he would promptly suggest that they match for it. The mark could hardly refuse this, and would take from his pocket the conventional single coin. Mr Way would then say, with a skillfully intangible sneer, “The hell with that penny-matching stuff. That’s how some guys got rich making doubled-headed coins. Let’s play Monte Carlo Match.”

He always had some high-sounding name, suggestive of authenticity and tradition, for the games that he invented.

“What’s that?” the innocent would ask.

Mr Way would haul out a handful of small change, which he jingled noisily in his closed fist to leave no doubt that it was a fair quantity.

“I got a mess of chickenfeed here,” he would explain, with labored patience for such ignorance. “You grab a stack from your own pocket. We slap it all on the bar — two stacks. Suppose your stack turns out to be an odd number, and the total of our two stacks is also an odd number, you win. Suppose you got an odd number, and the total of us two is even, you lose. Or vice versa. That’s one bet you can’t fix, because neither of us knows how many coins the other’s going to have.”

The mark might win or lose the first time, on this fair fifty-fifty basis. Mr Way rather liked him to win, because that made it somewhat easier to insist on another match for money instead of drinks. And one game easily led to another, and another, for increasing stakes. If the dupe insisted on them taking turns as matcher, Mr Way would take his honest fifty-fifty chance. But after the first time, the victim never had a chance to match the total of their combined hands in oddness or evenness.

Whenever the other was trying to “match,” Mr Way simply took care to have some odd number of coins in his own stack. Therefore if the mug also had an odd number, the total had to be even, if the mug had an even number, the joint total had to be odd. Stated this way, an intelligent reader will see that the stupe would have had the same fifty-fifty chance of finding somebody with a right foot growing naturally on his left leg. But it was a gimmick which had paid Mr Way more cash dividends than Albert Einstein ever earned from the Theory of Relativity.

The fond parent who had him baptized Theocritus was only another of the human race’s uncounted casualties to misguided optimism. Even in his tenderest years, his contemporaries declined to accord him even the semi-dignified contraction of “Theo.” They abbreviated him swiftly and spontaneously to “Tick.” The record does not show whether this was initially due to his instinct for stretching credit to the snapping point whenever he was supposed to do the paying, to his physically insignificant stature, or to his extraordinarily irritating personality, or to a combination of all three. But the monicker clung to him like fly-paper into the middle-aged maturity where his path crossed the Saint’s, which is the only encounter this short story is seriously concerned with.

However, in contradiction of some recent propaganda which purports to attribute all adult crime to the cancerous frustration of the growing boy, it must be instantly said that “Tick” Way consistently collected above-average grades, and revealed an especial talent for mathematics. But instead of being thus inspired to think of a career in science or engineering, his temperament had been impressed only by the magnificent possibilities of pigeon-plucking that were opened up by the magical craft of figures.

In his middle forties he was still a runt, barely topping five feet in his built-up shoes, but broad and thick-set and now somewhat paunchy, a strutting little rooster of a man with all the aggressiveness with which the small ones are prone to over-compensate for their unimpressive size, and a toughly amorphous face which looked as if he had antagonized more than one person whose resentment was too convulsive to be conveyed without physical amplification. But if he was doomed by his chromosomes to be forever unformidable in a fight, he had a grasp of the immutable laws of probability that might have frightened an insecurely wired electronic brain.

For “Tick” Way, the comparatively obvious percentages of dice were teen-age stuff. He had nothing but contempt for the half-sharp crapshooters who knew that the true odds were three to one against a natural on the first roll, two to one against making a point of ten, and thirty-five to one against making it the hard way — only because they had read the figures in a book. He could work out all those simple chances in his own head and even knew how to project them into the more elaborate calculation which ends up showing that the shooter has only a 49.3 per cent chance of passing when he takes the dice.

The higher complexities of poker were not much harder for him. He did not have to memorize the odds of twenty-three to one against drawing two cards to make a flush, or ninety-seven to one against drawing three that would turn a pair into a full house. He could even prove on paper the paradoxical theorem that when holding two pairs against an opponent who you are sure has threes, you have a better chance of taking the pot if you discard your smaller pair and buy three new cards than if you timidly trade your maverick for just one that you hope will fill the hand.

Mr Way had long since relegated such overworked games to the category of minor pastimes or last resorts. For one thing, he had also learned a few things about the mechanical methods of loading, shaving, switching, marking, and otherwise hocusing cards and dice, to say nothing of the sleights of hand (for which he himself had no natural aptitude whatever) in their manipulation, which could nullify the most comprehensive theoretical calculations. For another, he had found that a discouraging percentage of even the most verdant greenhorns had been forewarned through the modern media of Sunday newspaper supplements, paperback fiction, B pictures and television, of the hazards of playing games with strangers. And thirdly, the relatively fractional edge that a brain with a built-in slide rule might give him in conventional gambling was too small and laborious in the payola to satisfy his driving ambitions. He would prefer to cash in any day on some proposition in which his advantage could be measured not in fractions, but in fat round numbers.

Simon Templar first saw him in action at the bar of the Interplanetary Hotel in Miami Beach. Every season during this era of seemingly endless expansion saw the opening of some gleaming new caravanserai which aspired to be the “hotel of the year” — bigger, grander, gaudier, more modern, more luxurious, and more expensive than all the jam-packed hundreds of other palaces to which it added its opulence — which for a few dizzy months would skim the cream of the traffic before it yielded to the hotel of next year which was even then in the girder stage on the adjoining lot. The period of this story is fatally pinpointed by the mere mention of the Interplanetary Hotel, which obviously staked its début on the fact that solemn citizens who once automatically dismissed science fiction as a form of juvenile escapism were currently pontificating about rockets to the moon and pondering the legal tricks that might have to be invoked to grab off the largest hunk of the lunar market. The entrepreneurs of this palatial pub had already nailed their seats on the bandwagon by having the lobby laid out on the lines of some futuristic concept, of a space port, decorating the main dining room with symbols aimed at striking a happy compromise between astronomy and astrology, branding their plushier accommodations with such labels as “The Martian Suite” or “The Venusian Suite,” and barely stopping short of putting Plexiglas bubble helmets on the bellboys. And for that season, at least, they were assured of entertaining the loudest, lushest, most ostentatious fugitives from the northern, snows who were likely to get washed up on that excessively upholstered strand. The ideal subjects, in fact, for Mr Way’s studiously honed technique.

This was one of those rare but reliable drizzling gray afternoons which the Chamber of Commerce sweeps furiously under the rug, but which stubbornly re-manufacture themselves a few times every winter — the kind of day which makes even the stiffest isolationists tend to unbend in the common misery of being done out of most of the highly advertised amenities while paying the same fifty dollar daily rent on a minimum room. Mr Way hit the bar, or the Spaceship Room, as the brochures called it, at a shrewdly calculated 4:25 pm, when the patrons were mostly solitary and vaguely disgruntled males, and few enough to be individually aware of each other and surreptitiously absorbing every audible word even if they spoke none themselves. The first bartender recognized him as an obstreperous but lavish tipper, and greeted him with the perfect blend of obsequiousness and familiarity. “Hi, Tick. What’s new today?”

“I dunno, Charlie. Gimme the usual — double.”

“Yes, sir.”

A quick and expert pouring and mixing.

“Y’know, Charlie, there are some guys in this world so stupid, I sometimes wonder how they ever learned to keep on breathing.”

“I hear plenty of ’em gasping, but who did you have in mind?”

“Just a little while ago, I get in the damnedest argument with some thick-skulled bartender.”

“You should stay out of those low-class bars, Tick.”

“Yeah? Well, it all starts from talking about this place.” Mr. Way’s voice was deliberately pitched to carry to all corners of the room, and it had the timbre of one who was not only unabashed by an audience but welcomed one. “Somehow this gets us on to astrology, see, which it seems this dope kind of goes for. So I’m only trying to show him how dumb he is. ‘Look at it this way,’ I tell him. ‘There’s only twelve signs to be born under like there are twelve months in the year. But if you read those horoscopes, any day, they’re the same for everybody born under the same sign. Now take any six guys sitting down to a poker game. You can bet two to one there’ll be at least a couple of ’em born in the same month,’ I says, ‘but would you bet there’ll always be a couple who’ll have exactly the same luck and win or lose the same amount?’ And you know what this jerk wants to argue about? Not about the intelligent reasoning I’m giving him. No. He wants to pick on my figures, and have it that it’s only a fifty-fifty chance there’ll be two guys born in the same month.”

The bartender stayed where he was, polishing glasses. At that hour he had time to chat, before the feverish cocktail rush started, and Mr Way’s obliquely insulting gambit had inevitably given him a controversial attitude towards a conversational subject that was already more intrinsically stimulating than most of the topics that get bandied across a bar.

“That doesn’t sound so unreasonable, Tick. Let’s see, if—”

“You want to take his side, Charlie, I’ll save you the brain fever. ‘People are getting born every day, all over the world,’ says this moron. ‘So there must be about the same number born every month. Now suppose you divide the year in half, six months to a half. You take six guys. Either they get born in one half or the other. So it’s fifty-fifty.’... Now I ask you, Charlie, what sort of logic is that?”

“It makes a certain amount of sense,” said the bartender stubbornly. “After all—”

Mr Way turned to the nearest listener, who had obviously been following the entire conversation, and offered him a smirking invitation to join the fun.

“Go on,” he said. “Tell him that’s why he’ll be a bartender all his life.”

“Okay, you tell me, Mr. Jacobs,” said the bartender defensively. “You’re a good bridge player — how would you figure the odds in a deal like that?”

“I don’t think your colleague was so stupid,” said the newly appointed umpire deliberately. “He’s just a fraction off. As I heard it, the condition was that two of these six men had to be born in the same month. Well, let’s go with him up to a point, that five of them were born in five different months. You want to find the chances of the sixth man being born in one of those same five months. Well, anyone can see he’s got five to choose from that’ll do it, the other seven months of the year, he misses. So the exact odds are seven to five against him.”

Mr Way regarded him with a baleful sneer.

“There must be something about bars that gets into people,” he announced disgustedly. “Now I’ll tell you the right and scientific answer. Any man’s got the same chance of being born in one month as any other, hasn’t he? So let’s take any month — January. Give the first man a shot at it. Either he’s born in January or he isn’t. It can only be yes or no. Heads or tails. There’s the fifty-fifty chance. Let’s say he makes it. So give the second man a shot. Either he hits January or he misses. Heads or tails again. And the same for the third guy, and so on. So for these five guys in a row to all miss being born in January is like you tossing a coin and having it come down heads five times running. Sure, it can be done, but I’ll bet two to one against it any time you want to play.”

There was barely an instant’s silence, sustained only by incredulous second-thinking, for nobody there was a mathematical prodigy, and then the first derisive retort became a fugue which became a chorus.

“You call that scientific?”

“Perhaps I’m stupid, but—”

“If that’s what you mean by logic—”

“All right,” retorted Mr Way, even more loudly and offensively. “Anyone who calls anyone else crazy should have the guts to back up his opinion. I’ll back mine with good green money.” He hauled out a roll of bills and slammed one on the counter. “I’ll still lay ten bucks to five that out of any six men here, two were born in the same month.”

The erstwhile referee sucked his cigar for a moment, and said slowly, “Well, if that’s your attitude, and you want to pay ten to five on something that any fool can see should get you seven to five against, I guess I can bear to take it.”

He was backed up by a respectable clamor of others who wanted a piece of this self-evident bonanza.

It was almost a classic example of the technique which had sustained Tick Way throughout his dubiously solvent life. First, the proposition to arouse the interest of a vast curious and inherently disputatious section of mankind, presented at a cold-bloodedly chosen hour when they would be most susceptible. Second, the channeling of their first thoughts into a fallacious pattern that they would soon adopt as their own, forgetting that he was the one who implanted it. Third, the presentation of a contrary theory so apparently absurd that the most mediocre intellect would reject it. And throughout and overall, a display of objectionable cockiness that was guaranteed to strangle the noblest impulse to show him his error kindly and disinterestedly.

For Mr Way was not one of those ingratiating swindlers who work on the softer side of their prey. The most brilliantly original facet of his art was in his development of a natural gift for making himself detestable. In a few scintillating minutes, he could inspire the mildest citizen with seductive thoughts of mayhem. But since he was too ludicrously puny for the average man to punch in the nose, most of them sublimated this healthy impulse into a willingness, indeed an eagerness, to take it out of his noisily proffered bankroll.

The fact that Simon Templar was not among the first of those who volunteered to fade him may have been due not so much to the Saint’s mastery of theoretical figures as to his appreciation of live ones, and particularly the specimen who chose that moment to make her entrance.

It should be superfluous, after that sentence, for this chronicler to expatiate at much length upon the proportions and attractions of Hilda Mason, which in cold truth were not intrinsically different from those of any other girl who gets herself into these stories. They were, however, striking enough for him to have judged her at once to be the most interesting girl on the Interplanetary Hotel beach on the first day he cased it, with an outstanding chance of defending that title against all comers from plenty of other beaches and for quite a few orbits. Let it be on the record that she had light brown hair and light brown eyes and was almost criminally young and glowing, and that the puffy balding-gray man with her who looked easily old enough to be her father proved on investigation to be her father — a phenomenon which in Miami Beach in the season was not merely epochal but had also made the Saint’s casual campaign almost effortless.

“I’m not late, am I?” she said.

“Not one second,” he smiled. “And I’d allowed for half an hour. Which gives us time for just one family-style drink together.”

“I accept with pleasure,” said her father, sinking into another chair. “But I assure you, that’s as long as you’ll be stuck with me. I only came this far to keep Hilda company in case you happened to be late. I brought her up according to the old-fashioned doctrine that punctuality is the most inexpensive of grand gestures, but one can’t count on everyone else having the same philosophy.”

Simon ordered the drinks from a waiter who was already waiting, fortunately, for more customers were beginning to seep in. But the room was still populated sparsely enough for Mr Way’s discordantly jeering voice to snag the attention of the newcomers as it rose in raucous triumph a few minutes later.

“October! Here’s another guy born in October! And he’s only Number Five. Now who says I didn’t prove my point?”

“What is this all about?” George Mason asked.

Simon gave him a factual synopsis, untrimmed with any personal comment, and Mason shook his head.

“The man must be out of his mind. Or else he’s got money to burn and he’d rather burn it than admit he’s wrong.”

The group that was gravitating towards the noise focus of the bar evidently shared this opinion, and furthermore had no scruples about taking advantage of either contingency. Nor were they discouraged by the accident that had cost them a few dollars on the first sampling of nativities.

“Any fool can be lucky,” growled the good bridge player who had been finessed into becoming spokesman for the opposition. “But that doesn’t prove he’s right. If you want to convince me the odds are what you say, you’d have to win two out of three times. With six total strangers.”

“You think you aren’t strangers?” squawked Mr Way. “You think one of you is my stooge? I’d really hate to have such a dishonest mind as to even think that. Or to be such a bad loser as to say it. But don’t make any cracks about backing down until we see who’s doing it. You want to try this again twice more, or two hundred times, I’ll give you the same odds.”

“There aren’t that many people here—”

“Then we go out and ask any six guys in the street. And you pick ’em. Or easier still, we send out to the office for something like Who’s Who — they must have a copy in a joint like this. You name any six names, so long as they aren’t your ancestors. Or shut your eyes and pick ’em with a pin. Just show me the color of your money first!”

The debate progressed without any diminution of temperature towards the next inevitable showdown.

“If I’d known bars were such fun,” Hilda said, “I’d have lied about my age long before this.”

“You probably did, anyhow,” said her father tolerantly. “Only you were afraid to try it on the fancy places, which are much less willing to be fooled than certain others, I’m told.”

“I wonder who told you.”

The Saint grinned.

“I must hear more about this, George,” he murmured. “Some time when the child isn’t fanning us with its big shell-pink ears. Right now, I honestly hate to drink and run, but we’re stuck with the program I sold her. At this hour, it’ll be mostly a crawl down to the very end of the Beach for Joe’s immortal stone crabs. And from there, it’s another long haul over to Coral Gables and this show she wanted to see. Until the millennium when it dawns on theatrical producers that an eight-fifteen curtain is the ideal time to ensure a hostile and dyspeptic reception from anyone who also likes a nice peaceful dinner—”

“Don’t worry about me, my boy,” said Mr Mason expansively. “I shall stay here for a little while and improve my education.”

“Just don’t pay any padded tuition fees,” said the Saint frivolously.

It was not until after he had ordered their stone crabs at Joe’s, with a bottle of Willm Gewurtztraminer, and they were toying with cigarettes and Dry Sack while they waited, that he realized that he might have been a little too flippant.

“I only hope Papa doesn’t get into anything silly,” Hilda said.

“Is he likely to?” asked the Saint. “He seems a long way from being senile, to me.”

“He does like a little gamble, though. And he can’t forget that he was an insurance company statistician for thirty years. Of course that’s only a glorified kind of bookkeeping, but he sometimes thinks it makes him an authority on anything to do with figures. He might have a hard time staying out of that argument in the bar.”

“That shouldn’t get him in any serious trouble... Well, I admit I hadn’t thought of it that way. It sounded like a typical barroom argument, with nobody really knowing the score. They were all talking through their hats, I may tell you. Let’s find out what the odds really are.”

He turned a menu over, took out a ball-point pen, and began jotting.

“Do you really know how to work it out?” she asked.

“I don’t let on to everyone, but I had one of those dreary old out-dated educations. Lots of gruesomely hard study, and no credits at all for football, fretwork, or folk dancing. But I think I can figure it the text-book way.”

“You’ll have to tell me. I even flunked Domestic Science.”

“They must have tested you in the wrong domicile. But this is how you have to look at it. The first guy can be born in any month, as somebody said. When were you born?”

“April.”

“Okay. Then the second guy has eleven months to choose from, that’ll lose for Loud Mouth back there.”

“That sounds right.”

“So the second guy was born in May. Now up comes the third guy. He has two months to dodge, out of twelve. On any of the other ten, he still wins from Loud Mouth.”

“Even I can follow that. So it leaves the fourth man nine months, and the fifth man eight months, and the sixth man seven months. But—”

“Now according to the Law of Probabilities in my school book, and don’t ask me who made it or why it works that way, to find the odds against all those things happening in succession, you don’t add them up, you have to multiply them. Like this.”

He had written: “11/12 x 10/12 x 9/12 x 8/12 x 7/12.”

“Don’t forget that eight-fifteen curtain,” Hilda said.

“It’s not so hard as all that.”

He made a few quick cross-cancellations to simplify the problem, did a little rapid arithmetic, and ended up with the fraction: 385/1728.

“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.

“Well, here’s the man who knows his arithmetic.”

Simon turned and jumped up, grinning.

“I was starting to worry about you, not seeing you on the beach, all morning, I was afraid I’d shown you one night club too many.”

“I did sleep a bit late... And then, Papa and I had a lot to talk about when I got up.”

George Mason was with her, in a gaily checkered terry-cloth robe that failed to obscure a certain haggardness in his amiably inflated presence.

“Like a dutiful daughter, she is understating the fact that I made a fool of myself last night,” he said, lowering himself into the next seat. “After you left me, I was inveigled into expressing my views on that birthday bet. Unfortunately, my reasoning seems to have been erroneous. Hilda has been telling me how you worked it out, which I now remember is the proper method — but I’m afraid this is a little late. Somehow I managed to lose almost two hundred dollars to Mr Way on various names chosen at random from Who’s Who and other directories. And then, somehow, we began playing this game of Tiger Toss, which I see he is still at.”

The girl glanced across the terrace, and down again to the scratch-pad on which Simon had been trying his creaky computations.

“Were you just working that one out?” she asked.

“Yes. And I have a headache which only another Pimm’s will cure.”

“Tell us the answer.”

“I can do that, but don’t ask me to explain it. It’s a bit more complicated than the birthday deal. If you don’t want to be bludgeoned with a lot of double-talk about sine curves and spandrels, you’ll have to take my word for it that the theoretical odds are almost exactly seven to four against the stick, or the cigarette, falling cleanly inside a stripe.”

There was the kind, of silence which is tritely called pregnant.

“And I was playing him for even money,” Mason said somberly. “It honestly looked like an even bet to me, because... Well, my stupid reasons aren’t very important, are they? However, they cost me another hundred and fifty dollars. And by that time, I had imbibed a trifle more than I’m used to — enough, I fear, to make me somewhat reckless. When he offered to let me match him for double or quits, in some simple variation he calls Monte Carlo Match, I was optimistic enough to accept. As a result, I may not be much wiser, but I am some seven hundred dollars poorer.”

“And so,” Hilda said, “this is our last day here.”

She was much too young to show the same gray deflation as her father, but young enough for an excessive brightness of eye to be betrayed by a slight unsteadiness of lip.

“Does it make all that difference?” Simon asked.

“It does to us. You see, we’re not quite like the usual people who come to these places. With a job like his, and a family to bring up, Papa could never afford it. But he always promised me that when all the others were safely on their own — I’m the youngest — and the time came for him to retire, we’d have one tremendous splurge and see what it felt like to be millionaires for a couple of weeks. And I held him to it, although I’ve got a secretarial job now and I’ll pay him back for my share eventually. I thought he should have it for once in his life, before he settles down to scraping along on his pension. But we don’t really belong here, and since this has happened we’ve got to be sensible.”

“Don’t feel sorry for me,” said the older man defiantly. “Things like this have happened to millionaires, too. And I am still not so broke that I can’t insist on you being my guest for lunch.”

The Saint nodded slowly.

“No millionaire could do more, George.”

“There’s nothing else we can do, is there?” Hilda asked wistfully.

“Not legally,” Simon said. “You haven’t been swindled — technically. Nobody sold you the MacArthur Causeway, or a submerged piece of real estate. You could accuse someone of cheating at cards, but how would you accuse them of cheating at figures, the way Loud Mouth does it? A difference of opinion is what makes bets, and how would you convince a cop who has to do his own arithmetic on his fingers that Loud Mouth is taking an unfair advantage? And even if you could charge him with illegal gambling, you wouldn’t get any bounty on his hide. All you can do is remember that you were taken by one of the most original artists I’ve come across for a long time, if that makes you feel any better. And don’t look at me with those big fawn’s eyes, Hilda, because I’m on vacation, too.”

But although she instantly stopped looking at him like that, he knew that his protestation was as hollow as it had always been, since the very first time he had tried to stick to it.

He also wished he could stop being stuck with such preposterous projects. For the one thing that he had been most solidly convinced of by his strenuous figuring was that in any straight mathematical tussle with the talented Mr Way he would have about the same prospects as a rheumatic water buffalo in a greyhound race.

He thought that if there were laws against wicked old men taking advantage of trusting young girls, there should also be laws against young girls and old men trusting merely middle-aged bandits to rescue them from grades of wickedness that a college professor might have been puzzled to cope with.

In spite of which, and with no obtrusive sign of having racked his brain and paced his room for two hours in search of an answer, he was in the Spaceship Room again before four-thirty, ensconced at a strategic corner table that was still within easy speaking distance of the bar. From there he espied Mr Way’s blustery approach from the lobby, and by the time the percentage player strutted in, he was intensely absorbed in an eye-catching experiment.

On the table-top, he had laid out three ordinary poker chips. These he was shuffling around into various small patterns, sometimes turning one over and rearranging them, occasionally closing his eyes and fumbling for one at random, and turning it over and staring at it and finally shuffling the pattern again. All of this was done with a scowl of agonized concentration, and an air of frustrated bafflement, which were an almost deafening invitation to any other solitary customer in need of a conversational gambit.

Tick Way, with a hypertrophied affinity for brain-teasers to augment his common human curiosity, resisted the bait perhaps 39.65 per cent less seconds than an average target might have held out. Thus he was comfortably ahead of anyone else to turn from his bar stool, after he had been served, and boldly accept the hook.

“What in hell,” he demanded, with his distinctive kind of bumptious bonhomie, “are you playing at, buddy?”

“I’m glad you asked me that... chum,” said the Saint, without even regurgitating. “You might be able to help me work this out. I’ve heard you talking about this sort of thing a couple of times, and it sounded to me as if you knew more about figures than most people.”

“I probably do,” admitted Mr Way, with the most affability he was capable of. “What’s bothering you?”

“It’s this silly game,” said the Saint. “A chap showed it to me in the club car, on the train coming down here. He told me it was something the rich mandarins used to play in China, for concubines — Dong Hai, or something like that, he called it. You’re supposed to have three plaques like this, all exactly the same. One of them has some Chinese character painted on both sides. The second has the identical character on one side only. And the third is blank on both sides. Instead of Chinese characters, we just made an ‘X’ with a pencil, the way I’ve marked these.”

The connoisseur of hazards was already moving over to the table.

“Okay, what’s the game?”

“Well, you drop the three chips into a bag, or a box — or a hat.” Simon did that. “You shake ’em up under the table, where nobody can see what happens to them. Then if it’s your turn, you pick out any one of ’em, without looking. Go on, you try it. You take it out and slam it on the table, so that anyone can see what’s on the top side — whether it’s marked or not — but nobody knows what’s on the under-side. Then you try to guess what’s underneath, an ‘X’ or nothing.”

Mr Way thoughtfully turned over the chip he had put down. Simon spilled out the other two beside it. The little man picked them up and examined them. A newcomer would have wondered why anyone ever called him Loud Mouth.

“Here’s how this chap explained it to me,” said the Saint, reaching for his pen and a handy piece of ash-tray advertising. “And it might help you to visualize it quicker. Let’s pretend we can see both sides of these chips at once. I’ll draw both sides of each chip and tie them together. Here’s the one with a cross on both sides, for a start...”

He drew it, followed by two similarly attenuated dumbbells.

“... and the one with a cross on one side only, and the double-blank. Now, as this chap says first, anyone can see there are three crosses and three blanks, altogether, so if you just shut your eyes and guessed what side was down — or up, for that matter — you’d have an even chance.”

“Yeah, if you’re guessing—”

“But suppose you’re looking. Suppose the chip on the table shows a cross. Then you know it can only be one of these first two, don’t you? In other words, the underside is either a cross — or a blank. An even chance... On the other hand, if the side that’s up is blank, you know the chip must be one of these second two. So the bottom either has a cross — or it doesn’t. Again, it’s fifty-fifty. Or it seems to be.”

“What d’ya mean, it seems?”

“Well, that’s what was bothering me. Because when I was doing the guessing, I was right about half the time. But this other chap guessed right much more often than not. I lost quite a packet playing with him. So I’ve started wondering if I was unlucky, or whether there’s some trick to it that I haven’t seen. I’m sure that the crosses were all exactly alike, and there was nothing on the chips that you could find by feeling them — I thought of that. And the way we played, he couldn’t have done any sleight of hand. But if it’s legitimate, why go through such a complicated business to set up an even chance?”

Mr Way fiddled with the chips and frowned over the diagram for a full minute, which is quite a long pause in a conversation. And if his had been an electronic brain instead of the old fashioned variety, one would have sworn that one could feel the churning incandescence of his tubes.

It had been manifest from the start, to his practically single-minded instincts, that some deceit was involved. But the same ingenuous presentation which had caught his interest had also effectively nipped off any branch lines of thought which might have led towards mechanical props or common legerdemain. He knew that he was confronting some subtle trick of skillful misdirection from the same family as those which had long provided him with a fairly painless livelihood, but a trick which he had somehow failed to master before. It had given him a twinge of professional jealousy to discover that some cheesy plagiarist must be exploiting a colorable imitation of his own method in positively overlapping territory, but this pang had been rapidly alleviated by more constructive thoughts of the profits he might derive from swiping this Dong Hai routine for his own repertoire. All he needed was to twig the trick, and he even had a self-confessed pushover already set up and waiting for the shove.

It may be cited as some kind of testimonial to his misguided genius that he found the solution in those sixty seconds of seething cogitation — a par for the problem which only the most razor-witted reader is likely to have equaled, although in this case no abstruse mathematics whatever were involved. Perhaps it was only the gigantic blatancy of the logical pitfall that made it so hard for a devious mind to see.

But when it did dawn on him like a blast of lightning, it was purely to the credit of Mr Way’s personal discipline that he did not emit a screech of triumph like the orgasm of a banshee, or even exhibit the faintest furtive smugness. He merely wagged his head, with a disillusioned and contemptuous weariness.

“There’s nothing wrong with the game, bud,” he said. “The only thing wrong is that some bum sports always think they’ve been robbed if they don’t win.”

“But why go to all that trouble to invent a game like that when you might as well flip a coin?”

“Don’t ask me, my friend. Maybe these mandarins were too rich to carry small change. Maybe the concubines would’ve been offended about being flipped for. Maybe they got bored with flipping coins and had to think up something different. How do any betting games get started?”

“But an even chance—”

“What’s more complicated than a roulette table? — And yet half the people you see in a casino are playing the even chances — red and black, odds and evens, high and low. It just seems more glamorous, or something, to do it that way. I could get bored with tossing heads and tails myself. I’m a sucker for a new game. Why don’t we try this one? This time, you might be lucky. That’d prove it was on the level.”

“I could use a bit of luck,” Simon grumbled, declining the gibe. “How much d’you want to play for? Would five bucks be too high for you?”

“I thought you told me you’d lost a packet,” sneered Mr Way. “How long did it take you, at those prices? Or how much do you call a packet? Most times, I’d say that any bet less than a ten-spot wasn’t worth the effort, but if you’re strapped—”

“Okay,” said the Saint. “Make it ten dollars.” He scraped the chips into his hat and shook it under the table.

“Who goes first?”

“After you,” said Mr Way.

Simon brought out a chip and slapped it down. When he took his hand off it, it revealed a penciled “X.”

“Blank,” said the Saint, and turned it over.

The other side was blank. Mr Way pulled out his roll, peeled off a bill, and handed it over. Simon threw the chip back in his hat and passed it to Mr Way under the table. Mr Way took out a chip, laid it down, and exposed a cross.

“Another cross,” he said, turning it over.

He was wrong. The other side was blank again.

On the next draw, Simon showed a blank, called for a cross, but turned up another blank. Mr Way also picked a blank, called it blanks back-to-back, and lost — when the chip was turned over, it showed an “X” on the other side.

Mr Way paid off with equanimity. He was betting on a cast-iron percentage, and he could afford to wait for the dividends.

Several plays and some three hundred dollars later he was still waiting. He had won a few times, but not nearly so often as his opponent. That was when, convinced that the laws of probability could not be defied indefinitely, he made the utterly amateurish mistake of suggesting that they should double the stakes to speed up the action.

The Saint let himself be cajoled and insulted into that with the most irritating reluctance, and had soon taken another five hundred and forty dollars of Mr Way’s cash. They doubled the stakes again, and Simon won another forty dollars on his correct guess and another forty on the little man’s incorrect one.

“This can get damn monotonous, after all,” Mr Way conceded. “Let’s try some other game.”

“But I’m just getting lucky at this one,” Simon protested. “Don’t be discouraged because I’m having a winning streak. Let me have my fun. It probably won’t last long.”

Mr Way thumbed through the very thin sheaf of currency that was still left to him.

“You’ll have to take my check, then. I don’t have any more folding stuff on me—”

“I’m terribly sorry, dear boy,” said the Saint earnestly. “But that’s against the vow I made to my dear old grandmother on her death-bed. I can see her now, with the setting sun lighting up her nose, and her poor tired trembling fingers hardly able to hold on to the gin bottle. ‘Promise me,’ she burped, ‘that whatever the bet is, you’ll never take any chiseling bastard’s IOU. Always make ’em lay it on the line, son,’ she said, and—”

“I’m just wondering,” snarled Mr Way, “if I should have another look at those chips.”

“Help yourself,” said the Saint aggrievedly. “But don’t forget, you were the one who said that some bum sports always think they’ve been robbed if they don’t win.”

What Tick Way had to contribute to the remainder of the debate is perhaps largely unsuited to verbatim quotation.

“But how did you do it?” pleaded Hilda Mason.

“I simply conned him into playing strictly by the odds,” said the Saint. “With a mentality like his, he was wide open.”

“I am probably nearing my dotage,” George Mason said, “but I still don’t see the catch.”

Simon reproduced the diagram he had drawn for Mr Way.

“It’s built right into the rules. As you see, there are two chips which you might call ‘doubles’—that is, if there’s an ‘X’ on one side there’s an ‘X’ on the other, or if it’s blank on one side it’s blank on the other. There’s only one chip that has two different sides. Now, the three chips are thrown into a hat and one is drawn at random. Therefore the odds are two to one that it’ll be a ‘double.’ So if you see a cross, you call a cross, and if you see a blank you call a blank, and two out of three times you’ll win. What you have to think of isn’t the chance of what could be on the other side, but the odds on which chip has been drawn. Your pal Tick was sharp enough to spot that.”

“Then why did he lose?”

“Because I cheated,” said the Saint proudly. “I changed the odds. Since he relies on his gift for figures instead of manual dexterity, I thought he might have a blind spot for physical hanky-panky — which I’m rather good at. I made him a bit blinder with his own technique of misdirection, rubbing it in about how there couldn’t be any funny juggling. But I was palming an extra chip with a cross on one side and blank on the other. I rung that in, so that there were two of that kind, and took out one of the doubles. Sometimes I changed them back, so he wouldn’t notice that there was one double that never showed up. But most of the time, the odds were the exact opposite of what he was counting on.” Simon began to peel layers off a thick bundle of green paper. “Now, it was about seven hundred dollars you lost, wasn’t it?”

“But we can’t take that,” Hilda objected, half laughing and half crying.

“Why not? It’s your money, isn’t it? And I made a small profit for myself. Besides, I only did it because I couldn’t let you pack up and go home before we got to know each other a lot better,” said the Saint.