Five-Card Poker Probabilities

Elsewhere on Pokerglobal, we discuss the odds of different pre-flop combinations when playing Texas Hold ‘em. But what are the odds when dealt five cards at once in games such as a five-card stud or five-card draw? With two fewer cards in total to make your hand with, compared to the seven in play in Texas Hold ‘em, there are fewer possible combinations, and one of these throws up an interesting anomaly.

Unfortunately, there is nothing you can do to improve the odds when dealt a good hand in poker. However, you can significantly increase your chances of making a profit by playing with the casino’s money, using one of the many free cash bonuses available. However, be sure to read the small print so that you understand how to get at your winnings if you do get a great hand.

A Poor Hand is Odds On

Sadly, the most likely hand in five-card poker is a high where there are no relationships between your five cards, and the value of the hand is the result of the highest one. The odds that this is all you have are 0.995 to one or slightly more than half of all hands dealt. Slightly less than half the time, around 42 percent of hands, you’ll get a pair. There are 2,860 possible pairs (or over a million if you count the different suit combinations). Combine the two, and the mathematics of poker show that despite what you see in the movies, the chances of you having nothing more exciting than a pair in your hand are more than 92 percent.

Counterintuitive Rules

In most cases, the lower the odds of being dealt a hand, the higher that hand ranks. For example, there is a one in 693 chance of drawing a full house, which is far less than the one in 508 chance of drawing a flush, and so it makes sense that a full house has a higher ranking and will take the pot from a flush. However, this isn’t always the case. A seven high is 120 times less likely than an ace high but ranks lower. There are only four ways to make a seven high, without ending up with a pair or a run - if you are missing the six, five, four or three. Still, there are lots more ways to make an ace high, making it much more likely despite its higher value.

A Great Hand is Way Less Likely

Anomalies aside, the chances of being dealt a better hand are clearly slim, and the better the hand, the slimmer the odds. You’ll get a pair, on average, only 4.75 percent of the time, and three of a kind in 2.11 percent of deals or about one in 46 hands. Of course, with the chance to swap cards in a five-card draw, those odds increase somewhat, and the more cards the house allows you to trade in, the better your chances of getting a hand you can play.

Once in a Lifetime

We all dream of getting the “daddy” of all hands, the invincible royal flush, but you shouldn’t get your hopes up because you could wait your whole life to get one - literally. A player who enjoys 20 hands a day every single day for 89 years can expect a royal flush only once on average. That’s because there are 2,598,960 possible combinations of 52 cards, but four possible royal flushes, one for each suit. So, the odds of getting your dream hand are an enormous 649,740 to one.

What’s more, whatever some gambling strategies such as Martingale may suggest, the odds will not change during this time, so even after 88 years of 20 hands a day, your chances of getting that dream deal are still two-thirds of a million to one.

The Longest Odds in Cards

While the odds of being dealt a royal flush are eye-watering high, they are nothing compared to the odds of any single random order of a pack of cards. Take your pack and shuffle them, then spread them out. Rational Wiki has calculated that the chances of 52 different playing cards laid out in the specific order you created are a mind-boggling 52^!, which is 52 x 51 x 50 X 49....x1 or to put it another way, 80658175170943878571660636856403766975289505440883277824000000000000 to one. Suddenly, the odds of that royal flush don’t seem so bad after all.