The Facts of texas hold'em poker

The key to making intelligent poker decisions is to understand that successful poker is not about winning hands; it is about winning money. Since everyone has the same chance of being dealt a winning hand, winning hands are, in the long-run, equally distributed among the players. Over time, money is accumulated by the players who make the best decisions.

Poker decisions require knowledge of mathematical probabilities, but the game is far more complex and cannot be completely described mathematically. In blackjack, in which the dealer always plays the same way, it is possible to calculate the best decision for each hand. No such calculation is possible in poker, because you are competing against different players, all of whom play in their own ways. Not only do individual players differ, but each poker table develops its own group dynamics that changes as players enter and leave the game. The replacement of a single passive player with an aggressive one can instantly alter the mood of a poker table and necessitate changes in decision making.

The combination of mathematics, psychology, and social dynamics makes poker a rich and fascinating game. Mastering poker requires hours and hours of playing in different settings with different people. However, many people place too much emphasis on the psychological aspects of the game. They think poker is all about bluffing and reading body language. The fact is, poker has an underlying strategy that must be followed for there to be any chance of survival, let alone winning.

Correct strategy bases decisions on the knowledge available to you of the cards and your opponents. You never have perfect knowledge of your opponents, their cards, and the cards to come. Given imperfect information, you must assess what is most likely to happen. Decisions must be based on the most probable outcome of a hand, not on what you hope will happen.

Before discussing the actual play of hands, it is necessary to have the facts that intelligent decisions are based on. This section, which is meant to be used as a reference, contains tables, graphs, and summaries of important information and concepts.

The Five Decision Factors

Math Concepts for Poker

There are five factors to consider in every poker decision. After summarizing the five decision factors, each one is discussed in detail. How knowledge of these factors translates into actual play is the subject of the next chapter.

Math Concepts for Poker

Poker is inherently a game of incomplete information and uncertainty. Correct decisions do not always lead to desired outcomes. Even with the best possible play, the outcome of any single hand is unpredictable. To profit over the long-run, it is necessary to make decisions that are correct in a probabilistic sense, because events at the table are not determined. To understand the decision-making process, it helps to have some ideas and language from the mathematics of probabilities.

Your Cards

To succeed at Hold'em, you must have the ability to judge the winning potential of the first two cards you are dealt (your pocket cards). There are exactly 1326 equally probable combinations for two cards dealt from a deck of 52. However, because the suits are all equally ranked, the number of unique starting hands is reduced to 169. Not all 169 starting hands occur with the same frequency because the number of combinations required to produce each unique starting hand differs. For example, of the 1326 combinations, six result in AA, four result in AK suited, and 12 result in AK unsuited. In terms of percent, this means the chance for AA is 0.45%, AK suited is 0.30%, and AK unsuited is 0.90%.

To compute probabilities, it is useful to divide the 169 starting hands into five distinct groups. The groups and the number of hands in each group are pairs (13), straight-flush-draws (46), straight-draws (46), flush-draws (32), and no-draws (32). Each group is based on what type of hand can be built when initial cards are combined with favorable community cards. The chart below summarizes the five groups and their frequencies.

Frequencies of Starting Hands

Starting Hand Frequency

Two cards of the same rank.
Straight-Flush-Draws 13.9% (SFD)
Two suited cards that are also part of a straight. The hand 10V 8V is a straight-flush draw (the flop could come up JV 9V QV).
Straight-Draws (SD) 41.6;
Two cards that form part of a straight, but not a flush. With 10V 8* only a straight is possible after the flop.
Flush-Draws (FD) 9.7%
Two suited cards that cannot form a straight.
No-Draws (ND) 28.9%
Two cards that cannot be used as part of a straight or flush. For example QV 4*.

Subcategories of starting hands can be identified within these five groups. For example, a hand that contains two of the top five cards, such as Ace, K, Q, J, or 10, is an Ace-high straight draw. The subcategories of starting hands can be grouped into roughly four categories of strength. The strength of a starting hand, identified in the next table, is described as premium, strong, drawing, or garbage.