With the rise of Hold’em as the game of choice by far for most poker hobbyists, most people have come to rely upon different programs and charts to tell them what the chance is of being dealt specific starting hands. The problem with referring to a chart is that it doesn’t really teach you anything, and it doesn’t provide you with many skills that you can translate over to other forms of poker. So here we’re going to look at how to actually figure these things out.
In Hold’em we are dealt with two-card starting hands, and we classify those starting hands in two key ways. First, we have the difference between pocket pairs and unpaired starting hands. Second, we have suited and unsuited starting hands. These two differences in starting hands make things only slightly a little more complicated than our 1-card example above.
So first thing’s first, we need to know how many different starting hands there are. When we pick our first card, there are 52 possibilities, and when we pick our second card, there are 51 possibilities, so there are 2652 ways to be dealt two cards, but that’s not the end of it. Since we think of the hand Ace of Spades + King of Hearts as being the same thing as the hand King of Hearts + Ace of Spades, this effectively cuts our number of starting hands in half to 1326. What’s interesting to notice is that when you compare this result to our one-card starting hand example, our possible starting hands increase by a factor of 102. With that out of the way, now let’s look at some specific starting hand examples.
From our previous discussion of the combinatorics of starting hands in Hold’em, we know that there are 6 ways to be dealt pocket Aces. So what is the percent chance of being dealt pocket Aces? The answer is 6/1326, which is about 0.45%. Since the chance of being dealt pocket Aces is the same as being dealt with any other pocket pair, we now know that the chance of being dealt say pocket Fours is also 0.45%. Then the chance of being dealt any pocket pair is 13 times that result (since there are 13 pocket pairs), or about 5.88%.
From common sense, we realize that there are 4 different ways of being dealt with 76s since there are four suits. So what is the percent chance of being dealt any suited-connector from JT’s down to 54s? That comes out to be 6 different hands (JTs, 98s, 87s, 76s, 65s, 54s) times 4 different ways to be dealt with each or 24 total possible ways to be dealt with one of those suited-connectors. Since there are 1326 total starting hands, the chance of being dealt with one of those hands is 24/1326, which is about 1.81%.
Now you can figure out the chance of receiving specific groups of Hold’em starting hands, which is one of the most useful skills in creating starting hand charts and formulating early-street strategies. In order to practice all these different combinations and strategies, you should try Poker online so that you can improve these skills further and get the best results from your poker games.
