HE:Probability:Preflop

One of the most important yet difficult skills to learn in playing any form of Hold 'em is assessing the strength of your pocket cards before the flop. Beginners often overvalue certain combinations and undervalue others. In the long run, improper assessment of pocket cards will break even a player who has mastered every other skill. Although memorizing a table of probabilities is unnecessary, players should learn the relative strengths of different pairs, suited cards and connected cards before trying to improve their other skills.

Basic Pocket Strength
Given standard probability theories, calculating all the possible five card or seven card hands from a 52-card deck is simple compared to the combinations that can arise in a 10 player game of Hold 'em. There are essentially 169 significantly different possible pocket combinations (13 pairs, 78 suited pockets, 78 unsuited unmatched pockets). However, there are several quadrillion possible combinations of those pockets in a ten hand game. In addition to that, the remaining 32 cards can be combined into over 200,000 combinations. Given the sheer numbers, computers have been used to deal huge numbers of random hands where all ten hands stay in until the showdown to determine which pockets are most likely to result in the winning hand. A chart of such results can be found at many web sites, including here where hands are ranked by relative strength.

Not surprisingly, pocket aces is the best pocket, and 72 unsuited the worst (it is the lowest combination where the cards cannot be arranged into a straight with three other cards). However, against nine other randomly selected hands, all played to a showdown, pocket aces will only win about 30% of the time, and 72 will actually win about 5% of the time.

However, other important trends can be determined:

- Suited pockets are very common and, unless the cards are both high or the hand contains an ace, relatively very weak. - Small pairs (22, 33, 44, 55) are relatively weak hands. - Suited small hands (23, 34, 56, etc.) are very weak.

Conversely

- High combinations can be very strong hands, even if they are not connected (AQ, KJ, AJ) - Medium pairs are very strong hands (88, 99, TT) - High suited connectors (AK, KQ, QJ, JT and even T9) are very strong hands.

Domination
However, the odds for any particular pocket doing well on any given hand is strongly determined by the other pockets on the table, position, and the betting styles of the opponents. One of the most important considerations when assessing hand strength is the concept of "domination" - How a seemingly good hand will do poorly against even a slightly stronger hand, drastically changing its odds of winning on that particular deal. In addition, it should be noted that any pocket cards that are dominated are roughly being played at the same odds as any other dominated pocket of the same type.

Your pocket is dominated if: - Another pocket shares the same high card, but your other card is lower (e.g. AK vs. AQ); or - You have a smaller pair than another player (e.g. AA vs. KK); or - Both your cards are smaller than another person's pair (e.g. KK vs. QJ).

In either case, head-to-head, you have less than a 15% chance of winning the hand, and often less than a 12% chance, even if, for example, you have a suited hand or a possible straight draw. These odds do not effectively change for any combination. For example: - The odds of winning with KK against AA are aproximately the same as winning with 22 or any other pair against AA, or winning with 22 against KK. - The odds of winning with QT against QJ are approximately the same as winning with Q2 against QJ. - The odds of winning with KQ against AA are only somewhat better than winning with 72 against AA.

By comparison, undominated hands have a much better chance of winning. For example, a modest 72 has about a 35% chance of winning against the mighty AK, and an unmatched higher set of cards like J8 has a very good chance of beating even a good pair such as 77.

Connectors and Suited Pockets
Connected cards (e.g. 98, 87) and suited cards (J8s, 85s) often seem very tempting due to the possibility of drawing a monster on the flop. However, in serious games of Hold 'em, they rarely figure into the action. The average hand at showdown is two pair, and most Hold 'em pots are won with three of a kind or less. The odds of drawing a monster on the flop are very poor. For example, the odds of drawing a flush or flush draw with a suited pocket is about 13-1 against. The odds of drawing a straight or straight draw to a connected pocket is somewhat better.

High connectors (AK, KQ), high suited hands (AKs, AQs, KJs) and suited connectors (T9s, 98s) usually play much better as the chance of making a high pair on the flop is much improved. Actually making a straight or flush on such a hand should be considered a bonus and not a goal.