Some Dramaha Math

Last issue we introduced the all-important Golden Rule of Dramaha, which states that starting with a strong Draw hand is essential to your survival in the game. Ignore this rule and you either require a) unlimited funds or b) David Blaine level magician ability in pulling out the exact cards you need in order to avoid going broke. Most of us have neither thus we must adhere to the Golden Rule and gain the knowledge and experience to apply it correctly.

Now that we understand the rule and are ready to implement it, we must refine our thinking and consider some possible exceptions to it. Two Pair is a strong hand in Draw, however, its value in Dramaha especially if it’s just a medium or small two pair goes way down. On the other hand a pair of aces is quite a good Dramaha hand even against a range where you think you are often up against two pair or better. So let’s examine some Dramaha mathematics to help illustrate these concepts.

Two Pair Mathematics

There is a 4.75 percent chance of being dealt two pair; however, the strength of them varies greatly. Jacks up are the median two pair hand dealt and that fact may surprise a few people. Two pair can at times be a very difficult hand to play in Dramaha because when you do not improve upon them in either Draw or Omaha you can be in quite bad shape on the final two big bet rounds.

Improving Two Pair in Draw or Omaha

Suppose we look down at 10 10 5 5 2 which is a very good starting hand in Five Card Draw and in the right situations Dramaha as well. The probabilities of improving this holding in Draw as well as improving upon our pair of tens in Omaha by the turn are as follows:

1. Hitting a Set or better on the Flop

The easiest way to approach this and many other probability calculations is to determine how often we will not improve and then subtract that result from one. For this example we will ignore the small probability of flopping trip or quad deuces. You will fail to flop a ten or a five roughly 76 percent [(43/47)(42/46)(41/45)] of the time therefore you will improve to a set or better on approximately 24 percent of flops.

2. Making a Full House on the Draw

Assuming you missed the flop there are 44 unseen cards left in the deck and four cards that will fill you thus your probability is nine percent (4/44). The times you flopped a set there is one less card to hit which lowers your chances to around seven percent although you would certainly welcome that development as your scoop chances have increased.

3. Making a Set on Turn

The turn is dealt immediately after the first draw. Assuming you failed to improve thus far your probability of hitting the turn is 9 percent (4/43). Of course, had you improved on the draw there is one less out to hit but the times you do hit both it is a nice moment that rivals looking at A-A for the very first time in hold’em.

The probability that you will not improve in any fashion after the first two rounds of betting is approximately 63 percent; (1-24 percent)(1-9 percent)(1-9 percent). Therefore the chances of improving in one manner or another are around 37 percent.

This is a relatively high percentage and all is not lost should you not improve as two pair is still a relatively strong Draw hand and there is still a chance to win the Omaha with your tens or in a more random manner using the one card you drew. However, an unimproved two pair can easily be in peril in a multi-way pot.

Getting your Two Pair Outdrawn in Draw

Assume you still hold the 10 10 5 5 2 but now there are two other players in the pot with each one of them holding a single high pair larger than tens. Depending on what happens for them in Omaha they will typically either draw two or three cards. Drawing two is relatively common as they will often hold a side card that helps them on the Omaha side, such as a flush card or if they make a high pair on the flop.

Given you don’t improve the probabilities of getting outdrawn in Draw are as follows:

Improving a pair drawing 3 Improving a pair drawing 2
Two Pair: 16.0% Two Pair: 17.2%
Trips 11.4% Trips 7.8%
FH 1.0% FH 0.8%
Quads 0.3% Quads 0.1%
28.7% 25.9%

Assuming one opponent draws three and the other one draws two the probability that both opponents will miss is approximately (1-28.7 percent)*(1-25.9 percent) = 53 percent. Thus, approximately 47 percent of the time your two pair in Draw will be overtaken when two players each hold a higher pair. Remember this is assuming you did not fill up but we are quite an underdog to do so.

When you do not improve you will be in a very difficult situation when both players appear to like their hands on the turn. Even in a heads-up pot if you bet out and get raised by a competent player you are reduced to playing for half the vast majority of time and should feel somewhat fortunate to get that.

The fragility of two medium or small pair is an extremely important topic as they are one of the biggest money losers in Dramaha. As Mark Twain once said, “Learning to play two pairs is worth about as much as a college education, and about as costly.”

Sample Equity Calculations

Since Dramaha is a split pot game any hand’s estimated overall equity is simply a 50 percent blend of its Draw and Omaha equities. Online equity calculators are readily available for Five Card Omaha, however, since none could be found for Draw these equities are obtained through spreadsheet work.

Let’s start out by examining some matchups when holding a pair of aces which is a hand you will often be playing. The equities for both the Omaha and Draw side are based upon three cards being drawn. Sometimes you may draw less which would slightly lower your Draw equity, however, that indicates more prospects working on the Omaha side which helps offset that loss. For this reason we will simply assume the maximum amount of cards drawn and feel it will not unduly skew any results.

Omaha Draw Final
AA 60% 25% 43%
TT99 40% 75% 57%
AA 63% 77% 70%
KK 37% 23% 30%
AA 74% 11% 43%
888 26% 89% 57%

As you can see, Aces more than holds its own against very strong Draw hands. They have approximately 43 percent equity against both two pairs and trips which is approximately the same as holding A-K off-suit versus pocket queens in hold’em, a match-up often referred to as a classic coin flip. And in an A-A versus K-K situation the aces is in a power position with clear equity advantages on both sides and are a 70 percent favorite overall.

When holding aces there are few hands that you fear so even when a tight player opens from early position and you suspect he may be very strong you have an easy call with aces to see what happens on the board and the draw. Should you get lucky and improve on the draw your odds of scooping are very good as aces has a distinct advantage over two pair and trips hands in Omaha. Your implied odds are very good as you will often have the opportunity to raise the turn and have your opponent call you down.

Let’s move on to some matchups involving medium and small two pairs:

Omaha Draw Final
AA99 63% 92% 78%
5533 37% 8% 22%
777 54% 93% 74%
5533 46% 7% 27%
777 31% 92% 62%
TT33 68% 8% 38%
98765 44% 91% 68%
TT33 56% 9% 33%
777 29% 92% 60%
TT99 71% 8% 40%

Two pair is often the best hand before the draw but should you run into a better holding the situation is quite bad. Should you highly suspect that you are up against a better Draw hand and have nothing special for Omaha it is typically a losing play to call down the two big betting rounds. Your best hope is that you are up against low trips and the random two cards your opponent drew did not connect for Omaha and thus you will get half.

Two medium or small pairs are hands you would probably never fold in straight Five Card High, however, Dramaha, is a completely different animal. In Dramaha, many more pots are multi-way because most players will enter the pot with any holding with a semi decent pair along with Omaha potential. The looseness of the other players hurts the value of your holding and is often referred to as the “schooling effect”.

So whenever you fail to improve upon your two-pair you are very vulnerable as you hold what is a relatively strong Draw hand and have to rely on the hope that other players may be going to war with Omaha hands. This is typically a very costly reverse odds situation. And flopping bottom set may not be the salvation that it may seem as that really isn’t a monster holding in Five Card Omaha. Losing the maximum amount of money on the hand just became much more likely.

One last matchup to look at is a small pair with a suited ace kicker versus a bigger pair:

Omaha Draw Final
KK 54% 78% 66%
5(5A) 46% 22% 33%

Make no mistake, when we open up the button with a pair of fives and a suited ace we are hoping to simply win the blinds without a fight. When the big blind simply calls they can hold other things including flush draws or Omaha rundowns, however, their most likely holding is a pair with some Omaha potential. Against a higher pair such as kings you are around a 2:1 underdog, however, your odds as well as post flop fold equity will improve as the villain’s pair gets lower.

Hopefully the first two articles helped indicate what types of hands you want to play and those situations your bankroll wishes to avoid. This sets the stage for next issue where we will present a suggested set of detailed starting hand openings by position. ♠

Kevin Haney is a former actuary of MetLife but left the corporate job to focus on his passions for poker and fitness. He is co-owner of Elite Fitness Club in Oceanport, NJ and is a certified personal trainer. With regards to poker he got his start way back in 2003 and particularly enjoys taking new players interested in mixed games under his wing and quickly making them proficient in all variants. He can be reached at [email protected].