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STARTING HANDS IN HOLD'EM

This table shows the distribution of starting hands in Texas Hold'em, with the percentage chance of being dealt them in any one hand.

You can see you will get a particular pair such as AA only 0.45% of the time, equating to once every 221 hands.  But you get dealt a single ace, with any card other than another ace, 14.48% of the time, equating to once every 7 hands!

To create this table, we first need to know how many different combinations of hole cards are available.  There is a useful function on most scientific calculators, and excel, called the 'combination' or 'choose' function, denoted by a C.  This function has 2 inputs, n - the size of the set, and k - the number of choices.

nCk denotes choose k elements from a set of size n.  Therefore 52C2 is the number of ways of choosing 2 cards from a set of 52.  This gives us the answer 1326.  To do this in excel, simply type:

=COMBIN(52,2)

and it will return 1326

Now we have the number of combinations of different hole cards, we can work out the percentage chance of being dealt a particular hand by working out how many combinations there are for this hand, then dividing by 1326, and multiplying by 100.

We can count a lot of the hands simply by listing them and counting, but there are a few shortcuts.  For a particular pair, there are 4 possible cards, and we need 2 of them, so here we can use the choose function, 4C2 = 6.  (AcAd, AcAh, AcAs, AdAh, AdAs, AhAs), and for any pair we can multiply by 13 to get 78 combinations of pairs.

For hands like particular Ax, there are 4 cards for the A and 4 cards for the x, and any of them can go with any other, giving 16 combinations.  Multiplying by 12 gives us 192 combinations of any Ax.

To work out the 1 in x hands part, simply divide 100 by your percentage.

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