My turn =o)

Note that this is an illegal and unregulated gambling house; otherwise he'd never be able to bet more than a few hundred dollars at a time, at most. It's an excerpt, so forgive the lack of context.
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“Betting is now open,” the croupier obliged, and as everyone fumbled in their chips Mike smiled and decided to play the eccentric, with a little help from the dragon. He looked and tweaked the flight path as he tossed his only chip so that it bounced once and landed squarely in the middle of Black 13. Everyone stopped, stared, blinked.

The young man in the tuxedo broke the silence with a soft contralto. “Since you’re here I assume you understand the game, but for the benefit of the peanut gallery, please tell them that you do in fact understand that (one) you’ve placed your chip on a square that can only win if the ball lands exactly on that one single space, that (two) the odds are thirty-eight to one against you, and (three) that if you win you’ll collect three hundred fifty thousand dollars?” He said this in a tone that reminded Mike of someone telling him he had dandruff.

“Wow,” said Mike. “Actually, no, I hadn’t taken the time to look it up. Thanks!” He grinned, and straddled a chair. They all stared another moment, then the old Texan burst out laughing.

“Boy, I’m gonna miss you after this roll. You got balls.” He plunked down $10k of his own on each of Black and Odd, and added, “An’ I hope like hell you hit it.” He winked. Mike tipped his hat, and leaned his own elbows on the edge of the table. Blue jeans dropped a $10k bet street on the far column from thirteen, and the young man who’d spoken shrugged and bet $16k, carefully counted out, on red. Mike wanted to tell him to change it, but didn’t think it would matter. The man had the air of someone with a system, who didn’t really care if he lost a few hundred thousand dollars as an entertainment expense. He sighed and concentrated on the ball.

“Last call,” said the croupier, and waited a moment, but everyone was done. “Very well, betting is now closed.” He paused again, just a moment out of protocol, then vigorously spun the wheel. He picked up the ball and set it spinning in the opposite direction.

Mike looked for the odds – 38:1 he thought, this is gonna be a cake walk, but then he saw the swirls.

There’s an old saw in statistics: flip a coin ten times. If the first nine all come up heads, what are the odds of the tenth flip coming up heads? People will grab pen and paper and start scribbling. The smart ones will start doubling and try to figure whether they should include nine or ten iterations, and get all impressed with the enormity of the number.

The correct answer is 50/50. The coin has two sides, and the question wasn’t the odds of getting heads ten times in a row; it was the odds on the tenth flip. A lot of people can’t separate the two. That always amused Mike. Now, though, he began to doubt the purity of the question.

Looking at the roulette wheel he saw the probabilities spinning out of it, all the numbers equally likely…but he also saw the expectations of everyone present, nudging and polluting the pure probabilities. He concentrated, and selected Black 13. Other possibilities fell away.

The ball lost momentum and struck one of the barriers there to randomize its motion, and Mike had a moment of panic, but his selection held, and though the ball danced and hopped merrily about, it settled quite finally onto Black 13.

Everyone, even the croupier, stared. Cappy let out a stupendous yowp and began to dance an undignified jig, and after a few moments the old Texan burst out with a great, raucous bray of his own, took off his hat and slapped his thigh with it repeatedly. Jeans opened his mouth with unvoiced indignation, but Tuxedo just sighed and started counting out chips for his next bet.

The croupier regained his professionalism, and sounded off. “Black Thirteen,” he said loudly, “We have a winner. House pays, three hundred fifty thousand dollars to Black Thirteen.”

“WHAT?” Nick came pushing through the crowd, roughly shoving girls in green and blue gowns aside to bounce off tables and other gamblers. “What the...!?”

The croupier counted out three $100k chips and a $50k, raked Mike’s $10k to himself, and pushed all four to the area in between Mike’s elbows. Nick arrived and glared, but realized everyone at the table was staring at him. He wiped the sweat on his forehead through his hair and rubbed his face, took a deep breath, and watched Mike put the $50k chip in his pocket. The other three he leaned out and stacked again on Black 13. “Let these ride,” Mike said quietly, and settled back into his seat.

Nick goggled for a minute, then burst out laughing. “Sure,” he said, trying to relight his cigar and regain some composure. “I appreciate that. It’s a nice gesture. You’re an ok guy.” He puffed for a minute, then looked around. “Tina,” he said, “get these gentlemen some drinks, on the house. Hang around, be nice to them.” He chuckled as she skipped toward the bar. “Catch her before she gets too drunk and she can be very nice, if you know what I mean.” He stuck his tongue out to meet his incoming cigar, and even Cappy had to clamp his mouth shut. Nick wandered off again, but some of the crowd from the adjacent craps table began to drift over, what appeared to be a suburban married couple congratulating Mike on his win.

Tuxedo grinned. “For the record, since you ‘haven’t done the research’, the odds are still thirty-eight to one, but this time the payoff would be ten and a half million dollars.” He turned laconically to the croupier. “Do you even have that much here at the table?”

The croupier blanched. “I’m sorry, sir, I’m not allowed to discuss such matters.” Tuxedo just laced his fingers and waited.

“Bidding is now open,” said the croupier nervously. Jeans pushed another $10k onto the same column. Tuxedo slid his carefully counted $32k stack onto red again.