Home > Features > Five Texas Hold’em poker probabilities it’s probably worth memorising

Five Texas Hold’em poker probabilities it’s probably worth memorising


7 Apr 2017

Between 2003 and 2006, the card game poker enjoyed an obvious boom period.

The growth had previously begun upon the release of the film Rounders, but it was the wider launch of the game online that ultimately saw the take-off of the Texas Hold’em variety.

Chris Moneymaker’s victory in the 2003 World Series of Poker Main Event, having qualified for a small fee online, also heightened the interest of a global audience who at the time were a predominantly untapped market.

Exact numbers are not known, although the World Poker Tour has previously indicated that there are now over 100 million poker players worldwide, with Hold’em comfortably the most popular variety.

The aim of the game is to end up with the best five-card hand, using any of a player’s two personal cards dealt face down and five community cards, dealt in stages, that anyone can utilise, which are laid face up.

With four separate betting rounds in total across a hand, players face regular decisions as to whether they are in the box seat holding the dominant cards.

Even if a player is losing at a particular stage, they may still feel it is worth playing on if their hand has considerable potential. Below are a selection of such hands and a breakdown of a player’s percentage chances of improving their position.

Being dealt AK

The opening betting round, which takes place between a player being dealt their two cards and the first three community cards being shown, is widely referred to as pre-flop.

The strongest hand to hold at this stage is two aces (pocket aces), but also among the best is an ace and a king (AK).

Effectively, there are 50 unknown cards that will help a player improve their hand to either a pair or better, with six of this selection being either a king or an ace.

The Wizard Of Odds website is incredibly helpful for many casino-related odds queries and it determines that the chances of obtaining a pair in this situation is 48.74%, which is pretty much a one-in-two chance.

Being dealt a pocket pair

Obviously if dealt a pair of any kind, a player already has any hand with a best of a high card beaten at final showdown. But again there is potential to improve to three of a kind or, in less typical circumstances, four of a kind.

Taking all of the combinations into account, The Wizard indicates that a player has a 10.78% chance of turning their pair into three of a kind, while the likelihood of getting four of a kind from pre-flop pair is lower than 1%.

Of course, whether a player remains in a hand or not through the turn (the fourth community card) and the river (fifth community card) will hinge on the size of the bets going into the pot.

Having four to a flush

If dealt two cards of the same suit, seeing two further cards of this suit come down on the flop makes for pleasant viewing. This leaves two community cards to unveil a fifth card of the suit to complete the flush.

On the turn, the chances of hitting, for example, a fifth diamond, is calculated to be better than one in three (34.97%) with either of the final pair of community cards, while this drops to 19.57% if a player holds four to a flush ahead of the river card being revealed.

Having four to an outside straight

Just below the flush in the poker hand rankings is the straight, consisting of five cards running simultaneously in number sequence, such as 8, 9, 10, jack, queen.

An outside straight is when you have four cards in sequence and need one to add to either end, with one example being holding 3, 4, 5, 6 and needing a two or a seven to complete a straight.

In contrast, an inside straight is something like 3, 4, 5, 7 and it is a middle card, in this case the six, needed to complete a sequence.

At the flop stage, a player has a 31.45% chance of completing an outside straight, with this lowering to 17.39% when only the river card is to be revealed.

Having two pair chasing a full house

Occasionally, players can find themselves in the enviable position of holding two pairs after the flop, whether this be being dealt a pocket pair and another pair featuring among the opening three community cards or both dealt cards pairing up on the flop.

The next hand upgrade from here is to seek a full house consisting of a three of a kind and a pair. The Wizard of Odds highlights that there is a 16.47% chance of this being accomplished on the turn and 8.7% on the river.