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A-A-4-K vs. A-2-3-4

I received a large volume of email requesting an explanation of a term I use quite often and have defined many times, a "Bandit." Coined by author Bill Boston, it refers to a seven, eight or nine. He goes on to explain that while the ace is the most important card in Omaha/8, the worst three cards are nine, eight, and seven, which are in more losing hands than any others.

I concur, and my charts prove it. There is not a single profitable starting hand when the lowest card you hold is an eight! If your lowest card is a seven there is only one profitable starting hand. That's 7-8-K-K double suited, and it's marginal-returning a net profit of $0.12.

Even though a starting hand beginning with nine has two marginally profitable hands, it is the worst card you want to see. In a subsequent article, I'll explain why they are the worst cards you can hold.

On the cover of my latest book, Starting Hand Rules & Charts, which is now available, I pose the question "Which one of these two hands would you rather be dealt?" The A-A-4-K and A-2-3-4 depicted are both double suited. In the book I answer the question very briefly. Following is a detailed evaluation of these two hands.

A-A-4-K vs. A-2-3-4
Hand Suit W Rate Net
A-A-4-K 1PDS 56.19% 23.30
A-A-4-K 1PHS 53.83% 18.28
A-A-4-K 1PLS 53.94% 18.57
A-A-4-K 1PBS 52.65% 15.64
A-A-4-K 1PNS 51.49% 11.87
A-2-3-4 DSHH 41.14% 22.50
A-2-3-4 DSHM 41.37% 22.38
A-2-3-4 DSHL 41.32% 22.28
A-2-3-4 H2H 38.62% 18.29
A-2-3-4 H2M 38.77% 18.48
A-2-3-4 H2L 38.81% 18.64
A-2-3-4 2HM 37.06% 14.49
A-2-3-4 2HL 37.32% 14.57
A-2-3-4 L2L 37.37% 14.72
A-2-3-4 NS 34.85% 11.19

An A-2-3-4 may be double suited in three different ways. The chart to the right indicates that the most profitable starting hand is when the ace is suited to the four, yielding on average a net win of $22.50. This is less than the A-A-4-K which commands an average net win of $22.30, or 80 cents more.

When you account for how the hand is suited, there are five ways a pair of aces may combine with a four and a king to form a unique starting hand. The hands range in profitability from $23.30 down to $11.87. The A-2-3-4 on the other hand may combine to form ten unique starting hands. Three of them are double suited, six are single suited and one is unsuited. They range if profitability from a high of $22.50 to a low of $11.19. The A-A-4-K unsuited also beats out the A-2-3-4 unsuited.

Remember, the rankings above are based on each hand played against nine other randomly dealt hands at a full table. How would they fair against each other at a full table? Would the results be any different if the hands were played to a showdown?

When these two hands are matched up against each other the outcome is surprisingly reversed. At
full table, if your opponent held A-A-4-K you would definitely prefer to hold A-2-3-4. The A-2-3-4 will win on average $19.18 per round. While the A-A-4-K is no loser, it will only earn a respectable $15.70 on average per round. Either one of these hands is well worth playing. There was also a low winner 47.1 percent of the time. The A-2-3-4 has a better chance of scooping the pot because it can complete a better low.

The above simulation allowed the players holding each hand the opportunity to fold. In a showdown all hands are played to completion. When these two hands are matched up in a showdown the results are as follows: The A-2-3-4 will now only earn on average $15.72 per round. The A-A-4-K will earn about the same, $4.26 per round. There was a low 51.2 percent of the time. Why did the earnings drop? When players who hold the second or third best low are given a free ride to the river, they will get lucky sometimes and watch the best low get counterfeited. This is a good example of why you should raise with the nut low if you can safely assume you will not be quartered.

Next time I will continue with an analysis of the bandits. Now that my new book is available at $22.95, drop me an e-mail for ordering instructions.

So what have we learned? If you had your choice of being dealt an A-A-4-K or A-2-3-4 double suited you would definitely want to be dealt the A-A-4-K unless one of your opponents happens to hold A-2-3-4.

Lastly, here are a few more terms from my poker glossary:

Flop Good-A flop that help or improves your hand.

Flop the Nuts-A flop that taking into account your hand forms the best possible five card combination that cannot be beaten.

Flush-A poker hand that consist of five cards of the same suit.

Flush Draw-A flush draw or draw to a flush occurs when there is at least one card to come and you already have four cards of a suite.

Fold-To fold is to give up on the current hand by surrendering your cards to the dealer and thereby not having to call or match any additional bets.

Fold Out of Turn-All players must act in turn whether that action is to check, bet, raise or fold. A player is said to fold out of turn when they discard their cards before it is their turn to act.

Fouled Hand-A hand deemed unplayable due to any number of reasons such as containing more than the proper number of cards.

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.

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