# Strategy and Luck Play Roles in 50th Annual World Series of Poker

betting on statistics in poker goes hand in hand with a bit of luck

## The World Series of Poker is underway for its 50th year, according to the Las Vegas Sun. Its 89 tournaments will conclude in mid-July. Mathematical odds and player strategies will both influence the outcome.

The Main Event for the World Series of Poker will last 10 days, beginning on July 3, as reported by the Las Vegas Sun. It will have a buy-in rate of \$10,000 and its final table will air live on ESPN. It will host as many as 8,000 players, many of whom rely on personal strategies they follow religiously while others simply play the odds. Both methods have their own merits.

#### Texas Hold’em Rules

Texas Hold’em is arguably the most popular variation of poker, but the rules can be a bit much to take in at first. “Everyone is dealt two cards face down, then there’s the round of betting,” Dr. Arthur T. Benjamin, Professor of Mathematics at Harvey Mudd College, said. “After that comes the flop, where three cards are turned over [on the table] — these are common cards that every player is allowed to use in their hand.”

Dr. Benjamin said that once the flop occurs, another round of betting takes place. Next comes the “turn,” in which a fourth card is placed on the table and turned over. A new round of betting happens, followed by a fifth common card called the river being revealed. Finally, one last round of betting occurs. “The players who have not yet folded each have seven cards—their own two face-down cards and the five common cards—to create their best five-card poker hand,” he said. Whoever has the best hand wins.

#### The Rule of Two and the Rule of Four

So how do players know when to bet, and how much? “Suppose that after the flop, you don’t have the best hand yet, but there are some cards which, if they appear in the next two cards, would give you the best hand,” Dr. Benjamin said. “These winning cards are called your ‘outs.’ Now the Rule of Two says that if you have X outs and there’s just one more card to be shown, then your chance of winning is 2 times X percent. For example, if you have 10 outs, then the chance that one of them shows up on the last card on the river is about 20%.”

He said that this rule works because if you’ve seen six cards so far—the two you hold and the four common cards on the table—there are 46 unknown cards remaining in the deck, so your outs, in other words, are how many cards out of that 46 that could save your hand, or X/46. If you have 10 outs from the example, 10/46 is about 22%, which is close to the Rule of Two estimate of 20%.

The Rule of Four is similar, but it applies after the flop, when only three cards are shown on the table. “The Rule of Four says that if you have X outs and two more cards to be shown, then the probability that one of your outs shows up is approximately 4 times X percent,” Dr. Benjamin said. “This rule makes sense if you know five cards—two in your hand and three from the flop—then there are 47 cards left in the deck. What’s the chance that the first card is good? It’s X/47. What’s the chance that the second card is good? Not knowing the first, it’s also X/47.” He says if you take X/47 + X/47, it adds up to about four times x percent. Using the example of 10 outs, 10 divided by 47 plus another 10 divided by 47 is between 38% and 40%.

Gamblers who utilize statistics like these aren’t guaranteed to win, but they’re certainly given an advantage by knowing the odds they face.

Dr. Arthur T. Benjamin contributed to this article. Dr. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989.