Pre-flop Strategy - Ace In Hand
A pair of Aces is the most powerful hand in Hold’em. Ace King or Big Slick is also a great hand. Aces become very important in head-up situations and some players will raise with any Ace in head-up action.
Pairs of Aces are dealt 6 ways (combin(4,2)). There are combin(52,2) possible hands. Therefore the chances of being dealt a pair of Aces are 6/1326 or 1/221.
The list below documents some of the math involved in hands with at least one Ace:
Ace, King or Big Slick is dealt 16 ways (combin(8,2)-6-6). There are combin(52,2) possible hands. Therefore the chances of being dealt Big Slick are 16/1326 or 1/83.
The chances that no one was dealt a hand containing an Ace are 13 percent. It is calculated as (48/52)*(47/51)*...*(29/33).
If you hold one Ace and an Ace flops, then the chances that at least one other player was dealt at least one Ace are 62%. It is calculated as 1 – ((45/47)*(44/46)*...*(28/30)).
If you hold one Ace and have not yet seen the flop, then the chances that at least one other player was dealt at least one Ace are 75%. It is calculated as 1 – ((47/50)*(46/49)*...*(30/33)).
5h 6h has a 22.87% chance to beat and a .37% chance to tie Ac As. (source twodimes.net)
The facts above are important. It is crucial to understand that in the long run you will get more than twice as many Big Slick hands as American Airlines hands. As such you must realize that this is also true for your opponents.
It is also paramount to remember that the odds of one or more of your opponents getting one or more Ace are high on a 10 player table.
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