Mathematics | Of Poker

"I am," Elias replied calmly. "But you're giving me a discount on the variance." The dealer burned a card and turned the river: . The Royal Flush.

The table gasped at the rarity—a 1-in-30,000-to-1 longshot. Miller slammed his fist on the table, cursing Elias’s "dumb luck." Mathematics of Poker

As he bagged his winnings, he realized poker wasn't a game of cards played with people. It was a game of people who didn't realize they were just variables in a very long equation. "I am," Elias replied calmly

In his mind, a decision tree sprouted. He had an overcard and a royal flush draw. He calculated his —the mathematical share of the pot he owned based on the probability of his hand winning by the river. With 12 "outs" (9 spades for the flush, 3 non-spade Queens for the straight), he had roughly a 26% chance of hitting the best hand on the final card. Miller had shoved all-in for $400 into a $600 pot. The table gasped at the rarity—a 1-in-30,000-to-1 longshot

"Your move, Professor," growled Miller, a regular who played by "feel" and lost by the same metric. Elias glanced at the board: . He held A♠ K♠ .

Elias didn't think about whether Miller was "bluffing." He thought about . He had to call $400 to win a total pot of $1,400.$400 / $1,400 = 28.5%.