“When does the interview come on?”

“Ten minutes.”

“I’ll have a look, and let you know what I think.”

The only new thing Valentine had purchased since moving to Florida was a giant-screen TV, and that was because his old TV had gotten blown out during a lightning storm. Sitting in his La-Z-Boy, he hit the power on the remote, then surfed through the hundreds of channels he paid for but never watched, until he hit upon the sports channel showing the World Poker Showdown.

To Valentine’s way of thinking, poker tournaments were the only real competitive sport on TV. No one was getting paid except the blow-dried announcers, and every player paid an entry fee. He wondered how the prima donnas in baseball and football would feel if they had to pay to play their games in the hope of winning a prize.

An announcer named Gloria Curtis appeared on the screen. She’d been a big-time sports analyst for years, then gotten sent down to the minor leagues of cable. Valentine had always liked her and turned up the volume.

“This is Gloria Curtis, reporting from this year’s World Poker Showdown in Las Vegas. I’m standing here with poker legend Rufus Steele, who was knocked out of the tournament last night and is crying foul over what happened at his table.”

The camera pulled back, and Rufus Steele entered the picture. He still looked like an advance man for a famine. He wore his usual cowboy garb—boots, blue jeans, and a denim shirt buttoned to the neck—and could have stepped straight out of a rodeo. His Stetson was held politely in his hands.

“Rufus,” Curtis said, “could you explain to our viewing audience what happened last night?”

“I was cheated,” Rufus said, staring into the camera.

“Can you explain how you were cheated?”

“I’d be happy to. The tournament starts with everyone having two hundred dollars in chips. As a result, everyone plays tight. Now, the tournament directors also move players around every hour to keep things fair.”

“I’m with you so far,” Curtis said.

“Good. The second hour into the tournament, I was up two hundred dollars, and doing the best at my table. Then the tournament director brought over a new player. This player had fourteen hundred dollars in chips, which put everyone at a disadvantage. Within an hour, this player knocked several players out, including myself.”

“How is that cheating?” Curtis asked.

“The cheating occurred at that player’s previous table,” Rufus said. “It is statistically impossible for that player—who is an amateur—to have won that much money in such a short amount of time.”

She looked flustered. “But Mr. Steele, you’re playing cards. People get lucky.”

Steele gave her an icy stare. “Ma’am, are you familiar with something called the Poisson distribution?”

Gloria Curtis shook her head no.

“The Poisson distribution is a mathematical method of analyzing rare events. One assumption of the Poisson distribution is that the chance of winning is equally distributed. Every individual should have an equal chance when it comes to a game of cards, or playing the lottery. Make sense?”

“Certainly,” she said.

“Well, I went back to my room, and used the Poisson distribution to analyze the chance of that player being the onlyplayer in this tournament to have won that much money in such a short period of time. Would you care to know what the odds are?”

“Please.”

“Six billion to one. Where I come from, that ain’t called luck.”

Valentine heard the phone ringing in his study. He killed the power, and walked to the back of the house while thinking about what Rufus had just said. Rufus looked like a bumpkin, but it was just an act. Otherwise, he wouldn’t have lasted as long as he had.

He picked up the phone, and heard Bill say, “So, what do you think?”

“I’d say you’ve got a problem,” Valentine told his friend.

9

“You think Rufus was cheated?” Bill asked.

“It sure sounds that way.”

“Come on, Tony, there’s no smoking gun, just his word against the tournament director’s. I thought Rufus might say during the interview that he saw this other player marking cards or stealing chips, but he didn’t say anything like that. Quoting some obscure mathematical equation isn’t grounds to say you were cheated.”

“It is in poker,” Valentine said.

There was a pause on the line. Valentine found a pad and pencil on his desk, and jotted down the number of players in the World Poker Showdown, then determined the likelihood of one player beating seven other players within an hour based upon the Poisson equation. Although his formal education had ended in high school, he’d become schooled in statistics and probability when he’d started policing Atlantic City’s casinos, and as a result understood the math behind the games as well as anyone. Finished, he stared at the long number on the pad. Rufus had been dead on: six billion to one.

“Would you mind explaining?” Bill said.

Poker was not a big casino game, and not a lot of people in the gambling business understood it. He said, “Sure. Poker isn’t like other casino games, where the players gamble against the house, and the house always has an edge. In those games, the house is expected to win.”

“I’m with you so far.”

“Good. In poker, every player has the same chance, especiallyat the beginning of a tournament, when players start with an equal number of chips. Now, the odds of an amateur beating seven other players out of all their chips within the first hour is off the chart.”

“But it could happen,” Bill said.

“Maybe, but not necessarily,” Valentine said.

“What is that supposed to mean?”

“It means it could happen, but probably won’t, especially in a tournament like the World Poker Showdown. There are a number of reasons. First, people always play tight on the first day, because they don’t want to get bounced out. Second, amateurs tend to be picked on by pros or more experienced players, so the chance of an amateur knocking out seven other players is slim.”

“Maybe the guy got lucky,” Bill interrupted. “That’s a big part of the game.”

“I’ll agree with you there.”

“So, the amateur who beat Rufus Steele got lucky.”

“That would be the natural assumption,” Valentine said, “only the Poisson distribution rules that out in this situation.”

“How?”

“When applied to gambling, the main assumption of the Poisson distribution is that the chance of winning is randomly distributed. Which means that every individual has an equal chance. For example, if someone won a million-dollar jackpot on a slot machine, that’s luck. Right?”

“Of course.”

“However, if someone won twomillion-dollar jackpots on the same machine within an hour, that’s probably cheating. You agree?”

Bill let out an exasperated breath. “Yeah, probably.”

“The same thing is true in poker. An amateur might beat a guy at his table out of all his chips in an hour. However, the chances of him beating twoguys is unlikely, and the odds of him beating everyoneis exactly what Rufus said during his interview.”

“Six billion to one?”

“Yeah, give or take a few thousand.”

“So the amateur was cheating.”

“That would be my guess.”

“You want the job?” Bill asked.

“What job?”

“I want to hire you to figure out how this amateur beat those seven players at his table. I’ll send you the surveillance tapes, plus the footage Gloria Curtis’s cameraman shot. Study them, and tell me what the guy’s doing. Then we can bar him from the tournament, and everyone will be happy.”