We completed our analysis of all starting hands that do not contain an ace. Now we'll tackle starting hands that contain a single ace. This is the most difficult category for which to form broad generalities. Aces are unique because they help both high and low hands.
We begin with 2,777 unique starting hands. Less than half, 46.2 percent or 1,282 are profitable. Six percent or 167 are marginally profitable while 1,328 or 47.8 percent are not profitable.
Rule 30-Eliminate any starting hand containing a single ace and any other three cards of the same rank. When you are dealt a set, except for those few that contain three aces, muck the hand. As a group, sets containing a single ace will lose on average $1.78, ranging from A-2-2-2 suited the only marginally profitable at $0.21, to the A-3-3-3 suited with a net loss of $4.26! This rule eliminates 22 starting hands. One is marginally profitable and 21 are unprofitable hands.
Rule 31-Eliminate any starting hand that begins with an A-6 through A-J, and includes a pair of sevens through jacks-except A-J-J-K double suited, 1PDS. This rule drives home two important points about pairs. Medium pairs need the help of a prime card to go with their ace and not just any other low card. Kings and queens may get by with the aid of an ace to form a nut high straight.
This rule eliminates 174 starting hands. Five are marginally profitable and 169 are unprofitable. The one exception to this rule, A-J-J-K double suited has a net win of $1.21.
Rule 32-Eliminate all non-suited, 1PNS and low suited, 1PLS pairs, of queens and kings if not combined with two prime cards. This rule is easy to remember and eliminates one marginally profitable and 23 unprofitable starting hands. This clearly demonstrates that pairs need the help of a low draw and a decent flush draw. Remember when evaluating how a hand is suited, always think of its flush potential. You want the two highest cards suited to the lowest cards.
Rule 33-Eliminate all non-suited pairs containing a seven through jack except for A-2-9-9, A-2-T-T and A-2-J-J. This rule eliminates another 37 pairs. Four are marginally profitable and 33 are not. An A-2 is a powerful holding when combined with almost any two cards. Here it helps the pair of nines through jacks, even when non-suited.
We will now divert our effort from pairs and concentrate on the various ace combinations starting with A-8.
Rule 34-Eliminate any hand beginning with A-8 except for A-8-Q-Q and A-8-K-K, 1PDS and A-8-K-K, 1PHS and A-8-9-T. This rule may be a little complicated and we are eliminating two profitable hands for simplicity. For the purist out there, please refer to the chart below. It shows the two profitable hands which are both A-8-T-J as well as the four exceptions to the rule.
Both K-K and Q-Q will appear in a number of exceptions. These hands play rather well when the flop is void of low cards. The A-8-9-T is definitely helped by all of its possible straight draws ranging down from Broadway to 5-6-7-8-9. This rule eliminates 102 starting hands consisting of two profitable, nine marginally profitable, and 91 unprofitable hands.
Rule 35-Eliminate any hand beginning with A-7 except for A-7-K-K or A-7-T-K, DSHL. Here again we exclude the pair of kings. If we averaged the net wins of all possible pair combinations we would find that without a doubt A-A is the most profitable. The second most profitable is the
K-K, followed by 2-2.
Keep A-7-T-K when double suited high to low, (DSHL). It has a net win of $1.48 but exclude the double suited high to middle, (DSHM) version with its net win of only $1.05. The other varieties of A-7-T-K all have net losses ranging from $0.28 to $2.29. I only keep the one profitable hand because it is the best suited version and therefore easy to remember, and the DSHM version is just barely profitable. This rule eliminates another 152 starting hands. They consist of one profitable, nine marginally profitable and 142 unprofitable hands.
The rules we are establishing build upon one another. They need to be understood and memorized in the same numerical order as presented. The reason for this should be obvious, but an example always helps. If stated in a prior rule to "eliminate all non-suited pair of Queens," then when I say in a later rule "except for a pair of queens" as the exception, it does not mean except for a pair of non-suited queens. They don't exist any more having been previously eliminated.
Next time we will continue with our analysis of A-6 down to A-3.
We have now gone from 2,777 starting hands consisting of 1,282 profitable, 167 marginally profitable and 1,328 unprofitable down to 2,266, 1,279, 138 and 849 respectively.
So what have we learned? There are little exclusions containing an A-2.
Sam Mudaro, BA, MBA, is a practicing tax accountant and financial executive with 35 years of analytical business expertise. He uses simulation software to analyze and develop strategies for Omaha/8 and other forms of poker. Reach Sam at: realguru2003@yahoo.com.
