The paradox of ranges

Poker Strategy / Marcus Bateman / 19 November 2010 / Leave a Comment

Make sure you understand the equity of your hands not just in a vacuum, but against actual possible ranges – it may be you have big leaks in areas you never guessed you did.

One of the most complex aspects of Hold'em is understanding how hands which appear stronger than others can actually be much weaker than those below them, simply by comparing them to the range of hands your opponent has.

Take a set of hands like ace two off suit, king-jack off suit, and eight-nine suited. If you run any of these hands off against each other, ace two is ahead, jack king is second, and eight seven is last. If you run any of these hands one on one against each other, the one with the higher card in is always ahead - simple right?

However, this very simple and logically obvious order of things can be quickly flipped on its head by comparing these hands not against each other, but by what we actually have to compare our hands with in day to day poker decisions - ranges. Say we raise any of these hands, a tight player shoves, and we are left with pot odds of around 1.6 to 1. We know from experience that this player's range in this spot is basically always nines or better, king-queen suited or better, or ace-ten suited or better. With odds of 1.6 to 1, we need roughly at least 30% equity to profitably call - which hand plays best in this spot?

A quick glance at PokerStove, tells us that versus a range of 99+ ATs+, KQs+, and AJo+:

A2o has: 28.05% equity.
JKo has: 30.19%.
89s has: 32.35%.

In just the blink of an eye, our simple and logically ordered progression of strength that we had earlier is flipped on its head. Now the seemingly strongest hand actually plays worst, with the weakest hand actually ending up the strongest. So what causes this weird flip in events?

Although ace-two clearly plays better against a hand like eight-nine, it plays much worse versus many of the other hands in this players range (mainly stronger aces) where it has much lower equity than a hand like eight-nine, where both cards are live. This is similar with jack-king, where in so many of the hand combinations in this range it is very far behind with one dominated card, that neither of the 'stronger' hands in this example can out run the consistent decent sized equity that a live hand such as eight-nine has against all of these options.

Weak poker players often moan about bad beat after bad beat late in tournaments when skilled players end up calling with hands like suited connectors in pre flop all in situations. What the weak players fail to understand is that often this is not a mistake, and that by blinding down to an unplayable stack size they effectively force good players to start calling them with what can appear very odd hands. Make sure you understand the equity of your hands not just in a vacuum, but against actual possible ranges - it may be you have big leaks in areas you never guessed you did.

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