Poker Article
HUTCHISON OMAHA POINT SYSTEM
The purpose of this system is to provide a simple means of evaluating starting hands in Omaha poker. It was developed in several steps:
First, Mike Caro's Poker Probe software was used to determine the win percentage for various four card combinations when played against nine opponents. This was accomplished via a Monte-Carlo type simulation with a minimum of 25,000 hands being dealt for each starting hand. The assumption made in this type of simulation is that each hand is played to the finish. This is, of course, an unreasonable assumption, but , in the absence of detailed knowledge of each player's starting requirements, method of play, etc., it is the best means of approximating a hand's strength and earning potential.
Secondly, a number of components were examined in an effort to determine their relative contribution to the value of each starting hand. Eventually, it was decided that the primary determinants of good Omaha starting hands related to the rank of the cards and whether or not they were paired, suited, or connected.
Finally, a type of regression analysis was conducted to try and determine the relative weighting of each of these factors. The system that follows is the result of quantifying the contribution made by each of these various components.
Once the calculations are made, the resultant point total is an approximation of the actual win percentage for a particular hand--when played to the finish against nine opponents. The correlation between point totals and win percentages, while not representing a one-to-one correspondence is, nevertheless, quite high. In fact, in about 70% of the cases the actual win percentage will be within just one point of the total points awarded by this system. This means that if the system indicates that a given hand earns, say, 20 points, you can be quite confident that the actual win percentage for this hand is between 19 and 21 points. It is very likely to win more often than a hand with 19 points and almost certain to outperform a hand with 18 points.
STEPS IN CALCULATING POINT TOTALS
FIRST, to evaluate the contribution made by suited cards, look to see if your hand contains two or more cards of the same suit. If it does, award points based upon the rank of the highest card. Repeat the procedure if your hand is double suited.
If the highest card is an ACE award 4 points
If the highest card is a KING award 3 points
If the highest card is a QUEEN award 2.5 points
If the highest card is a JACK award 2 points
If the highest card is a TEN or NINE award 1.5 points For any other combination of two suited cards award 1 point.
If your hand contains four cards of the same suit, deduct 2 points.
SECOND, to factor in the advantage of having pairs,
If you have a pair of ACES award 9 points
If you have a pair of KINGS award 8 points
If you have a pair of QUEENS award 7 points
If you have a pair of JACKS or TENS award 6 points
If you have a pair of NINES award 5 points
If you have any other pair award 4 points
Award no points to any hand that contains three of the same rank.
THIRD, when your hand contains cards capable of completing a straight (that is, when the cards do not have more than three gaps), award points as follows:
An ACE with a King, Queen, Jack, or Ten earns 2 points
An ACE with a Two, Three, Four, or Five earns 1 point
Any two cards from TWO through SIX receive 2 points Any two cards from SIX through KING receive 4 points
Any three cards SIX and above earn 7 points
Any four cards SIX and above earn 12 points
From the above totals, deduct 1 point if a one or two card gap occurs and deduct 2 points if a three card gap exists.
FINALLY, a determination must be made as to which hands qualify as playable. This becomes a function of how many points one decides are necessary before entering a hand. My suggestion would be to only play hands that earn 15 points or more. It can be argued that, ignoring the rake, any hand with more than a 10 percent win rate is potentially profitable in the long run. Still, I have the prejudice that most players, and especially those who are relatively inexperienced, would be better advised to forsake marginal hands and to focus on those that earn 15 points or more. Recalling that a random hand will win about 10% of the time in a ten-handed game, it can be seen that playing only premium combinations of 15 points or more, insures that you will always have a hand that is 50% better than a random hand. The point total required to raise or to call someone else's raise must also be determined subjectively. I feel that 20 points is the appropriate level, but, obviously, others may render a different judgment. So, in summary, a safe generalization is
YOU SHOULD CALL WITH 15 POINTS OR MORE AND CONSIDER RAISING WITH 20 POINTS OR MORE
SOME EXAMPLES FOR CLARIFICATION
The hand that has the highest win percentage in Omaha contains two ACES and two KINGS and is double suited. A hand containing the AS, KS, AH, and KH would earn 27 points under this system--calculated as follows: under step one above, the two double suits headed by the two aces earn 4 points each for a total of 8 points; step two awards nine points for the pair of aces and 8 points for the pair of kings, or a total of 17 more points; under step three, the ace-king combination earns 2 points for its straight potential. The resultant total of 27 points closely parallels the actual win percentage for the hand which is about 26.65.
Assume you have the 9S, 8S, 9D, and 8D. Step one awards a total of 3 points for the two double suits headed by nines. Under step two, the pair of nines earns 5 points and the pair of eights earns 4 points. The last step awards 4 points for the 9-8 combination. The total of 16 points is the same as this hand's actual win rate.
With the QS, QD,8H, and 8C, no points are earned under step one as there are no suited cards. Step two gives 7 points for the pair of queens and 4 points for the pair of eights. Step three awards four points for the Q-8 combination but then calls for a deduction of 2 points because of the three card gap that exists between the two cards. The final total is 13 points and this is, again, the actual win percentage for this hand.
A hand consisting of two aces, a deuce, and a seven--all of different suits--earns 9 points for the pair of aces, and 1 point under step three for the ace-two combination. This total of 10 points indicates that this hand has no better prospects than any other random hand. In fact, the actual win percentage obtained through simulation analysis is 10.6.
Consider a hand consisting of the KS, KD, 3S, and 6D. Step one awards a total of 6 points for the two double suits headed by kings. Step two gives 8 points for the pair of kings. The 6-3 combo gets a point under step three, making a total of 15 points.
An example of a hand that tends to be somewhat overrated by novice players is AS, KD, QH, and TS. Under step one the hand receives 4 points for the suited ace and ten. Step two is disregarded as the hand does not contain any pairs. Step three awards 12 points for the straight potential of the four connected cards, before deducting 1 point for the one card gap that exists. The final total is only 15 points, making this a marginally playable hand.
NOTES
To state the obvious: many skills other than initial card selection are essential to maximizing your profits when playing Omaha. Unfortunately, these other skills do not lend themselves to easy quantification, and are thus beyond the scope of this simple mathematical approach. I do hope, though, that this system will be of help to the novice player in making the important decision about which starting hands are worthwhile.
