Raw Power (RP) Hand Ratings

About 10 years ago, I proposed a method for numerically rating hold'em and Omaha starting hands that I called Hand Power (Card Player, Nov. 17, 1995). Hand Power is a number that's obtained for any given starting hand by pitting it against one, three, and seven random opponents and then averaging the results. The Hand Power of a perfectly average hand is 1.0. The best hold'em starting hand, pocket aces, has a hand power of 2.55; pocket queens, 2.05; and A-K offsuit, 1.56 (other hands are reviewed in the chart). The actual mathematics used to calculate Hand Power are described in the note at the end of this column.

In response to requests by Internet software designers and programmers, some poker friends of mine who write poker software to simulate certain poker situations and I recently came up with a new numerical starting-hand rating method called RP, which stands for Raw Percent or Raw Power. The RP number itself can be thought of as any given starting hand's average percentage edge over any random hand. For example, pocket aces wins about 34.8 percent more frequently than the average random starting hand, and an A-K offsuit wins about 12.4 percent more frequently. Software producers use these approximate percentages to estimate the expected value of various starting strategies.

Are these RP numbers of interest to ordinary poker players? Like my Hand Power ratings of 10 years ago, these RP ratings do give you some feel for the relative strengths of various starting hands. The chart gives a numerical comparison of various hold'em starting hands. Note that the numbers seem to emphasize the value of pairs and suited cards.

Ten years ago, I might have been a bit surprised to see that pocket queens rated considerably higher than A-K, even when suited. But after playing several tournaments each night for the last several years, I was no longer surprised to see that pocket queens scored much higher than big slick in this method, also. It should be noted that pocket queens have a big edge over smaller pocket pairs, and a much bigger edge over any two undercards than A-K does.

The RP numbers also confirm numerous other concepts, such as the fact that suited connectors (for example, the 7 6) are indeed very marginal hands, even though many of us play such hands occasionally.

Even though both RP ratings and Hand Power ratings are essentially obtained from simulations that are made against "virtual opponents" playing random hands (instead of real opponents playing "playable hands"), it seems that the winning-percentage numbers obtained are quite similar and proportional to what might be considered more accurate numbers. All of our efforts with more sophisticated simulations in which the opposing hands are mostly better "playable" hands have led to similar results, as long as all the hands are played to completion. Thus, using simple random simulations seems to be the most straightforward measure of the natural strength of a hand.

Note: The new RP ratings are computed by first simulating a given hand against one, three, and five random opponents. From those three percentages, 50, 25, and 16.67 are subtracted, respectively. Those three differences are multiplied by 1, 3, and 5, respectively, then added together, with the sum divided by 9.

Hand Power ratings are computed by first simulating a given hand against one, three, and seven random opponents. Those three percentages are each then divided by the average win percentages – that is, by 50, 25, and 12.5, respectively. The eight-player quotient was weighted by multiplying it by 1.5; then, the other two quotients were added and the sum was divided by 3.5.