The Myth of Any Two Cards

Article I liked (a little old school):

The Myth of Any Two Cards
by Andrew Brokos
Originally Published in Two Plus Two Internet Magazine, December 2007 issue

By its nature, the game of poker generates tidbits of ?wisdom? that are often ambiguous and occasionally flat-out wrong. For example, many players will have heard some variation on the clich?, ?Play the situation, not the cards.?

Is this good advice? The answer depends on what one takes it to mean. There are certainly players who would benefit from the realization that a pair of Aces is a strong hand when facing a large bet pre-flop but not when facing a large bet on a JJT98 board.

But this advice has also been taken to mean that cards don?t matter and that good poker players can manipulate their opponents into folding at will. For example, many tournament players will be familiar with a move known as a re-steal, where one player suspects that another is raising pre-flop on a steal and therefore re-raises him all in so as to collect not only the blinds and antes but also the original steal raise.

When trying to learn how to re-steal profitably, many players wonder whether it is better to choose a good target, i.e. an aggressive player who is raising a very wide range of hands, or a good hand, i.e. a holding that has good equity against the range of hands with which the target will call the re-raise. In truth, a re-steal is a profitable move when the equity you gain from your opponent?s folds plus your equity against his calling range is greater than 0, which is your expectation if you fold. (For the sake of simplicity, this ignores the options of calling or re-raising less than all in.)

Theoretically, it is possible to have so much fold equity in a given situation that you can re-steal profitably with any two cards. Against good players, however, these opportunities arise only in the relatively rare situations where the payout structure of a tournament causes the target?s expected value measured in tournament chips (cEV) to diverge substantially from his expected value measured in real money ($EV). In general, good players will recognize situations where you know they are likely to have a wide range and consequently may be making a move with a relatively wide range of your own, and they will adjust their calling ranges accordingly. This isn?t to say that you can never acquire an edge against them, but making an all-in play with any two cards requires a much larger hole than can be found in the games of most good players.

In Which The Author Learns the Error of His Ways
This first hand occurred during the early stages of the final table of a $100 online multi-table tournament. I had one of the shorter stacks of the eight remaining players, with around 15 BB?s. With a stack like this, I?m just itching for the opportunity to re-raise all in. When the chipleader, an aggressive and very good tournament player, open raised on the button, I decided to move all in with anything if the SB folded.

Sure enough, the action folded to me, and I moved all in with Q7o. The button called me instantly, without the slightest hesitation, and turned over K5o. His hand held up, and I was eliminated in eighth place.

Let me emphasize again that this player was very good. He was already recognized as a top online tournament player at the time, and since this hand took place, he has had some success on the live circuit as well. His chat with a railbird after the hand illustrates his thought process:

Railbird: Snap-call with K5o? LOL.

Strong Player: I thought I had the best hand. Should I pretend I have to think about it just because it?s King high?

I got owned, plain and simple. My opponent was one level ahead of me, recognized a spot where I was going to move all in on him with a very wide range, and adjusted his calling range accordingly. Just because he was opening a wide range from the button doesn?t automatically make it a good re-steal spot for me. To re-steal profitably, I need a large gap between the range he?ll open and the range he?ll call, and in this spot that gap just wasn?t there. It is very possible, in fact, that he knew how likely I was to attempt a re-steal and was only going to raise his button with hands that could call an all in, meaning that I had no fold equity at all.

In Which The Author Learns From His Mistakes
This next hand occurred a few months after the first, during which time I?d put a lot of thought into the re-steal and similar plays. I was one of the chipleaders at my table in the middle stages of a $150 online tournament. The player two seats to my left, also one of the chipleaders, was a great tournament player with whom I?d often discussed strategy. We are both very aggressive players and had a lot of history of stealing and re-stealing from each other in past tournaments.

Blinds were 80-160. The action folded to me on the button, and I opened to 480 with ATo. The SB folded, and my friend in the BB re-raised to 1440. With these stacks, I am going to be opening a very wide range from the button, and I knew that he knew this. Consequently, I expected that he was going to re-raise me with a relatively wide range of his own.

After his re-raise, there were 2000 chips in the pot. Even with position, I?d rather move all in or fold than call with ATo. Thus, I had the option of betting my last 9520 chips or folding. I put my opponent on a range of something like 20% monsters (JJ+, AKo, AKs), 60% medium-strength hands that figure to be ahead of my button opening range (22+, A2s+, K5s+, Q9s+, JTs, A2o+, K7o+, Q9o+, JTo), and 20% weak holdings just looking to re-steal from me. If he only calls my all in with his monsters, then he is folding 80% of the time.

Even 72o has about 20% equity against a calling range of JJ+, AKo, AKs. The Expected Value (EV) of an all in with 72o is the value of my fold equity (.8 * 2000 = 1600) plus my equity from winning at showdown (.2 * .2 * 20,080 = 803) minus what I?ll lose at showdown (.2 * .8 * 9520 = 1523), or about +880 chips. Thus, if he only calls my all in with the 20% of his range that consists of monsters, then I can profitably make a move on him with any two cards.

But I knew my opponent better than that, and I knew that he knew me too well to leave himself open to such exploitation. As it happened, I moved all in for a total of 10,000, and he called instantly with A2o.

My opponent in this hand is a great player, but I don?t intend to hold up this particular call as an exemplary one. In my opinion, it is a losing call, but it does demonstrate just how dramatically a smart player may adjust his range against another smart, aggressive player, to the point where he is calling a 4-bet all in for 62 BB?s with A2o.

It is not going to be profitable to make a move on this player with any two cards. Even though including all of his medium strength holdings in his calling range actually increases the showdown equity of 72o to roughly 29%, it drastically decreases my fold equity to 20%. The EV of moving all in with 72o against this expanded calling range is -348 (.2 * 2000 + .8 * .29 * 20,080 + .8 * .71 * -9520).

ATo, on the other hand, is actually a slight favorite against that very wide calling range. As this difference illustrates, beating tough players requires more than blindly shoving chips into the pot in situations where they are likely to be on a wide range. They recognize these situations as well as you do and can adapt accordingly. Instead, you must be able to make thin value plays and stay one step ahead by adapting your range more effectively than they adapt theirs.