Do You Randomize by Equity?

It is common wisdom that being predictable is a bad thing. If your opponents can easily figure out the strength of your hand from your actions, then it is all too easy for them to make a good decision with their hand, whether it’s folding their weak hand, valuebetting their likely winner or even bluffing you out of the pot. To counter this, poker players need to balance their range in most situations.

A balanced range contains a certain part of expected winners, that is, hands that are very likely to win barring some unlucky confrontations (referred to as setups in poker lingo). Sets or nut flushes are typical winners if the board texture isn’t particularly threatening — you generally want all the money to go in with these hands.

In order to balance your range, a part of bluffs is necessary. They improve your range in two ways. Firstly, they extend your betting range, creating a sort of halo around your value bets, and given the strength of your range as a whole your opponents must respect it. Secondly, they help making your good hands paid, since sometimes your opponents will try to catch a bluff. The exact ratio of bluffs to winners depends on several factors, like pot odds, implied odds or your opponent tendencies. Now, the question is:

How do you pick the hands you’ll bluff with?

Many players just go with their feelings and throw a bluff when they have a hunch that their opponent is vulnerable, while they themselves have very little or no showdown value. In order to keep a balanced range, they avoid bluffing several times in a row, trying to somewhat alternate their valuebets with their bluffs, and that’s about it.

This method suffers from two shortcomings: 1) the actual bluff ratio is difficult to control when you go with rough estimates while playing, and 2) it pays no attention to your equity when your bluff is called and there are more cards to come. That’s where Randomization by Equity comes in very useful.

The principle of Randomization by Equity, as formulated by aejones (a very strong, successful high-stakes player who coined the term) relies on the equity of your hand to help you decide when to bluff. Think of your range like this:

On this representation of your range, the lowest equity is on the left (in white), and the highest is on the right (in red). This breakdown is useful to precisely define how you use each part of your range. Naturally, you want to stack your opponent when you have the nuts or close to it, and when you have good showdown value, you want to extract some value out of your hand.

When you bluff, most of your equity comes from your opponent folding, in addition to the little equity you have when you’re called — since it is frequent in NLHE not to be drawing completely dead. When your opponent folds, it doesn’t matter what you got: it could be “air” (nothing) or the nuts, you win uncontested anyway. Therefore, if you bluff with a hand that has showdown value, you sort of waste its value, since you could have tried to extract some more chips with a tiny valuebet, or you could have induced your opponent to bluff. Now, there are times when it is correct to turn such a hand into a bluff, but we’ll leave that for another post; just keep in mind that it’s more natural for hands with showdown value to shoot for a showdown.

So, that leaves the air part of your range for bluffs. But remember that when your bluff is called, we saw that you keep some “suckout equity”, with backdoor draws or five-outers. This escape hatch is certainly not to be sneezed at; it can bring you a 20-25% equity, and when you add it to your fold equity (when your bluff works) the sum can actually turn a negative equity play into a positive one.

It is much better to bluff with hands
that maximize “suckout equity”

Consequently, it is much better to bluff with hands that maximize that “suckout equity” — you then use that part of your range to the best of its value, leaving the “pure air” for the muck. In other words, use the top of your “air” part for your bluffs, in blue-green on the graph above.

A typical example would be the call of a preflop button raise from the blinds with 56, and the flop coming K73. It is a flop your opponent will often miss, while you have a gutshot straight draw and a backdoor flush draw. A check-raise would probably take down the pot quite frequently, while if you’re called you keep something like 23% equity against top pair. Compare this with a pair of deuces, which would have only 9% equity against top pair.

How to keep a balanced range using Randomization by Equity?

The good candidates for bluffs don’t come from nowhere: some hands are more likely than others to find backdoor draws or weak pairs/five-outers on the flop. Suited connectors come to mind. Thus, you can adjust how many such hands you put in your preflop range so as to obtain a reasonable amount of bluffing opportunities.

This method is vastly superior to other randomization means, like the use of your wristwatch or the exact suits of your hole cards. If you want to learn more about it or see it in practice, you can watch videos of aejones or RedJoker on LeggoPoker.