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The following is the second part of an excerpt from our next book, The Intelligent Poker Player by Philip Newall. We expect to have the book for sale by either late March or early April 2011. The first part of this excerpt appeared in last month’s magazine.

Poker would be a trivially easy game if every player’s holecards were face up on the table. Uncertainty about what hands other players are actually holding is what makes the game interesting and difficult to play well.

The first usage of the term “information hiding” that I can find is in Bill Chen and Jerrod Ankenman’s The Mathematics of Poker. They say:

Strong strategies play many hands in the same way, making it difficult for the opponent to read the distribution of hands remaining. Hiding information is the most important part of avoiding counter-exploitation.¹
 
As they explain, the reason for hiding information is to prevent opponents from exploiting us. As was shown in the last chapter, the way to play “game theory optimal” (GTO) poker is to reduce, as much as possible, the profit an all-knowledgeable super opponent (the nemesis) would be able to extract from us through exploitive poker.

The Ankeny example illustrates this concept perfectly. Suppose we draw two cards against an early position raiser. Since our pre-draw hand must be three of a kind, a super opponent could deduce that our post draw distribution is exactly {four of a kind (4.2 percent), full house (6.2 percent), three of a kind (89.6 percent)}.² With such intimate knowledge about our range of hands, the nemesis would be able to play perfectly on the final round. This would include letting weaker hands go and knowing exactly how many bets to put in with hands that do well against that range, or he might conclude that his starting hand is not strong enough to continue against that range, given the bet and pot size, and fold immediately.

Chris Ferguson, winner of the 2000 WSOP Main Event, is another poker theorist who strongly believes in the virtues of information hiding. In The Full Tilt Poker Strategy Guide he writes:

To conceal the strength of your hand, you need to play different hands the same way. Once you decide you are going to play a hand, make the same bet whether it is the strongest hand you would play in that situation, like AA, or the weakest, like 76.³

Ferguson’s advice is for the game of no-limit hold ’em, but you can see that it’s exactly the same principle at work as the one behind Ankeny’s rule in five card draw. Playing a variety of different hands the same way benefits every hand since it increases the likelihood of gaining additional action with strong hands, and weak hands are provided cover to win uncontested pots.

Note that playing different hands the same way is a much more efficient way of concealing information than playing the same hand different ways. That’s because in practice, playing the same hand different ways is immensely difficult to do right. Technically, playing a hand different ways is known as a mixed strategy, and in order to play a mixed strategy correctly, we should randomize perfectly between the different options. But unfortunately, humans are bad at predicting true randomness. For example, when predicting a string of coin tosses, we predict too many reversals and not enough streaks of either heads or tails.⁴

In many games, the benefits of raising on the opening round, especially first-in, are enormous. Calling allows players either to isolate with position or the opportunity to profitably play many hands out of the blinds. This means that in many situations on the opening round, in order to play our hands well, and to hide information by doing so, we should use a strategy of either raising or folding, and never calling. Since the majority of our strong hands would much rather raise than call, it makes sense to hide information by choosing to always raise with a playable hand. In the next chapter, I will explain my strategy for preflop limit hold ’em where information hiding is the core concept behind my decisions, and in many situations my advice is to play a strict raise-or-fold strategy.

Here’s an example of information hiding that often arises in full-ring limit hold ’em. You join a table and post a blind in the cutoff on your first hand; the action folds to you. The best course of action is to raise every time. Since it costs just one big blind to raise, all except for the very worst hands will want to automatically raise. Since checking would reveal a tremendous amount of information — it will indicate that your hand is terribly weak — the best play is to always raise.⁵

Later on in his chapter in The Full Tilt Poker Strategy Guide, Ferguson presents three different flavors of his never-call strategy preflop in no-limit hold ’em.⁶ Chen and Ankenman take a similar approach to first-in play in no-limit hold ’em. They will only raise-or-fold, varying their raise size by position only.⁷

Although the most critical demonstrations of the information hiding concept occur on the opening round, it’s also a key factor during decision points later in a hand. This is particularly evident in big bet games, where, potentially, the size of your bet could reveal information about the strength of your hand. In Winning Strategies for No-Limit Hold ’em, Nick Christenson and Russell Fox describe their approach to this problem.⁸ They vary the size of their bet by a number of factors, including the pot to stack ratio, the number of players, position, board texture, and their opponent’s hand range. Once they have decided on an appropriate bet size in a particular situation, they will bet the same amount with every betting hand. This is a textbook application of information hiding. Since they will be playing a number of different hands in exactly the same way, there should be no additional information an opponent is able to glean from the size of their bet. Put another way, if the size of our bet was correlated with our hand strength, an opponent could exploit us. Instead, by always betting a consistent amount, bluffs will look exactly like value bets, and both types of hands should benefit from being played this way.⁹

The importance of information hiding is affected by two factors: the number of betting rounds remaining, and the strength of your opponent’s range. In extremely short-stacked no-limit hold ’em, there are still four notional rounds of betting. Effectively, there is only one round of betting as players will either move all-in or fold preflop. In this game, there is no room for information hiding, as players move all-in and call all-ins to maximize EV.

The stronger your opponent’s range, the more information you give away by splitting your betting into two parts — raising some hands and calling with others. Against a range of AA, KK, and AK, the only hand with above 50 percent equity is aces. By raising on an early round against such a tight range, you would completely give away that your hand is aces; it would be much better to play the aces deceptively until a later street. At the other extreme, against someone who is playing every hand, you can raise with some hands on the opening round, and call with others, since the range of hands that you can profitably raise is very wide.

Hopefully, you can fully appreciate the importance of this concept in poker. I’ve shown applications of it in limit and big bet hold ’em, and five card draw, and it’s set to reoccur in the later chapters. Hiding information is an important part of GTO poker, but we can always flip the concept around and attempt to exploit players who fail to play their range of hands in a consistent manner.

There is also another advantage to making our strategy simpler through information hiding rules such as never calling first-in. By doing so, we make the game of poker easier to play since there are many possible scenarios which will never arise once we begin to restrict our strategy. In the first chapter, I explained how even the simplest popular forms of poker are far too complicated for the fastest computers to solve today. But by never doing certain things, we transform the game into a slightly less complicated version which makes the job of playing well a little bit easier for ourselves.