How can we value or rate the affect of the second pair on our pair of aces? Although there are many ways a statistician can accomplish the task the method we select must be simple enough to use and apply at the tables.
Let's take a look at the chart below and see if we can formulate a simple point count system. The data if from the graph we plotted last time. The first column entitled "2nd Pair" is the 2nd pair that accompanies our pair of Aces. The next column "Net Win" is the net win for each combination of starting hands consisting of Aces and the pair in column 1.
PF is short for what I term the Performance Factor. Any attempt to build a numerical rating system must take into account how much one starting hand or group of hands is better than another. The performance factor is an inverse measure of such performance. It is "inverse", because it assigns a higher value to the worst possible hand. It is calculated by dividing the net win of each hand into the net win of the best hand. In other word, the 2-2 is 3.4 times better then the 9-9, (37.78 / 11.06 = 3.42).
In the "Rough" column I simply take the PF and reverse the order. I then multiply the PF by a relevance or importance factor which I shall term "Impact Factor" or IF for short. The factor I chose here is 2 for simplicity. Therefore, looking at the 2-2 we take the 3.4 of the 9-9 and multiply it by 2 to arrive at 6.8. The "Points" column is simply the "Rough" column rounded for simplicity of use.
The purpose of the Impact Factor is to establish how important one factor is in comparison to other factors. The following example works best to show what I mean. We know that having our cards double suited improves our chances of winning a portion of the pot. We also know that having pocket aces are good as well as holding an A-2. We need to relate the various classifications to the way they affect performance. For example if being suited improves a starting hand by 20% then the PF factor must take this into account when balancing the values derived for suited hands versus those for pairs. Simply adding net wins or multiplying the points assigned to aces by 20% would not be appropriate. The value of having a pair of aces suited to any card is certainly more superior to having a pair of 9's suited to anything less then an ace or king. This is the kind of juggling that must go into the PF.
The goal of a system is to develop a numerical ranking that will value two card combinations. All 6 possible combinations must be valued and totaled to develop a point count for each starting hand. There will be short cuts to eliminate the need for valuing completely worthless hands. An example of valuing a hand may consist of the following logic. Let's take a simple two card combination, probably the most important 2 card combination in Omaha H/L, the A- 2. The aspects to consider about the A-2 are:
a. It's value as a low winning hand. A-2 is certainly better then an A-4 or a 2-3. The question we need to answer is how much better? Another question may be is the A-4 better then the 2-3? A point count system should answer all these questions.
b. Turning our attention to the high side an A-2 that is suited is better then one that is not. How much should we increase the point count based on whether it is suited or not? Note, in evaluating this we do not care about the value of the second card. Our attention is simply focused on the high card as it represents the highest flush we can make. Common sense tells us that having an ace suited is better then having a ten suited.
c. The A-2 also provides us another high hand type, a straight. Anyone who has played any form of poker knows that know that a Q-K has better straight potential then a Q-J or Q-T. This may be proven mathematically. There are more possible straights that may be made when there is no gap between the cards.
d. We have all seen a showdown where the best high hand is simply the best high card. We therefore would assign a value to the highest two cards held.
Next we would assign a numeric value to each of these categories for this two card combination. We would add the point thus derived to those for the other possible 5 combinations eliminate any duplicate prospects. For example; if we held A-2-A- 2, we would not count the low points for each A-2 as we would have only one straight draw and not two. If our hand was double suited we would have two flush draws to count.
There is one other high category that is not represented by the A-2 combination that needs to be taken into account, pairs. If two of our cards form a pair we must also assign them a value. Clearly a pair of aces would be worth more then a pair of deuces. How much more do we value them is the issue.
The chart to the left portrays data that to the best of my knowledge has never appeared in print before. It is not a trade secret or anything like that; it just requires an enormous amount of data and the ability to analyze it. The data does clearly show the advantage of suited cards.
Double Suited, (DS) clearly outperforms the Non- Suited, (NS) $1.09 average net win to an average net loss of $0.98. The only category of non-suited cards to show a profit is 2 Pair. The DS still maintains a better than 13 to 1 advantage.
The 715 hands that do not form a pair or two pair also reveal good insight. The NS version clearly is a looser. How a hand is suited is equally important. The double suited high to low, (DSHL) slightly outperforms the double suited high to medium, (DSHL). They both are more profitable then the double suited high to high by roughly 38%. Those of you who have followed my columns have been made aware of this fact before.
What would the results be if we were to view just the profitable hands? What would the results be if we just looked at hands that contained an ace? What if we applied a simple formula that eliminated the majority of the unprofitable hands? Stay tuned and next time we will further analyze the chart above and explore some of the possibilities just mentioned.
So what have we learned? We learned that there is a way to rank a set of hand types. We've seen that suited hands are better and more importantly how they are suited makes a difference. You may not be able at this point to utilize all the information above. You should however be able to factor into your decisions that you are better off when your two high cards are suited to your two low cards.
