Digging into the Monte Carlo Algorithm

After hearing about the Monte Carlo Algorithm over beers with friends one night, I decided to get a better understanding of how it works and learn a bit more about poker along the way. For me, there is no better way to understand a problem than coding up  and launching a product around it.

Have you ever watched a Texas Hold ’em Poker Champion on T.V.? Every time a set of cards are laid out on the table the odds of each player’s hands is provided to the audience (for example, Lindh has a 75% chance of winning with his K and 9 of clubs above). Advanced poker players have become quite good at predicting the odds as a gut instinct and is partly why mathematicians enjoy the game so much.

In order to practice my ability to develop a second-sense for poker odds, I figured repetition was the key. The game I set out to create would lay out a set of cards and allow the user to predict the percentage probability of converting that to a winning hand, quickly, over and over again.

Of couse, there are far fewer total combinations of game-plays for a poker game as compared to a game of chess; so it isn’t rocket science. However, the variation in the number of players combined with a 52 card deck does create enough variation to make things interesting.

In order to make the solution robust, I used a Monte Carlo algorithm to generate thousands of possible outcomes randomly and recorded the statistical output for “player 1” to win.  Once the algorithm was completed in Python, I built a Google Polymer app to present the probability guessing game.

You can test your ability to guess your probability of winning a text hold ’em hand in the  game here.

pokerodds

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