Chris Beaumont, a software engineer at Counsyl, has created some cool visualizations showing the strength of different hands in Texas hold’em. The graphs are based on Beaumont’s enumeration of all roughly 1.3 trillion hands of heads-up Texas hold’em, plus data on several million online poker hands.
The graphic on the top left shows the strength of a hand averaged over all opponent hands; blue indicates hands that win more often than lose, while the pink squares lose more often than win.
But Beaumont cautions that it would be unwise to actually make bets based on this graph. The top left graph assumes that every opponent hand is equally likely, but this isn’t true: Opponents can fold weaker hands, meaning your hand won’t perform as well as this graph suggests.
The graph on the top right shows that missing data point: the actual frequency with which each hand is played. The brightest squares indicate the hands that are played most often, and the darker squares indicate those that are usually folded.
There are some interesting trends here: For one, the brighter box in the upper-right hand corner suggests that 10s are much more likely to be played than 9s. Beaumont theorizes that this could be due to a psychological bias that overvalues and overplays face cards.
The graph on the bottom left combines those two data sets, providing a more accurate way of looking at average hand strength. Each hand is averaged over all opponent hands, but the average is also weighted by the frequency of the opponent hand. Again, blue hands win more often than lose, while pink hands lose more often than win.
Finally, the graph on the bottom right shows the strength for one particular hand, here an eight of hearts and a queen of spades. The graph now representing the opponent’s hand; the redder the square, the more likely the opponent is to win. This is an interactive: You can visit Beaumont’s site to try out the odds for different hands.