Let’s Talk About Balancing

Balancing is one of those super-cool sounding concepts that gets talked about a whole bunch, thought about a whole bunch and ultimately misapplied a whole bunch. The general idea of balance is that any particular betting line you take should have a mix of hands of varying strength. For example, if you 3-bet a villain preflop and then c-bet the flop you should have a range that includes monsters,bluffs and hands in between (draws and all types of value hands). Conversely, if you take a line that means you only have a bluff (or any particular hand strength) then your range is out of balance. Having a balanced range makes you very difficult to beat because you will always pose the threat of many different types of hands. Because of this, your opponent’s will have difficulty reading your hand and will then have trouble winning against you.

Notice that one of the big perks to balance is that it makes it more difficult to play against you, but it does not necessarily mean that you will be extracting the most from a particular opponent. Indeed, having balance can be looked at as a form of defense. For example, say a particular opponent folds 95 percent of the time to c-bets and will never adjust to your relentlessly c-betting against him. Should you balance your c-betting range by checking some hands instead of just relentlessly c-betting? No, because your opponent won’t do anything about it. Sure, if we decide to balance our range against this opponent, we will have a better defense set up; but against a player who will not attack when we are defenseless, it is completely worthless to invest money in defense.

Balanced ranges are often associated with playing an unexploitable strategy, such that your range includes the appropriate proportions of bluffs versus monsters, so that no matter what your opponent decides to do he will be making a mistake. If your opponent decides to always call your value bets, you will be rolling in the value dough. If your opponent decides to always fold, then your bluffs will be the extremely profitable.

Often times serious poker players come across their own unbalanced lines and realize that their opponents, who are particularly observant, could take advantage of this. They realize that an unbalanced line may leave them open for exploitation, so they resolve to plug up any holes in their strategy so that a savvy opponent can’t take advantage. The thing is, there are some situations where balance is important, and there are some situations where it isn’t. The only time that a hole in your strategy is a problem is when your opponent knows that it is there, and he can do something about it. I’m sure you’ve all heard that saying: “If a tree falls in the woods and no one is around to hear it, is there sound?” Well, the perfect application of that phrase to poker would be: “If you have a hole in your game and no one is around to exploit it, is it really a hole?” The answer, at least in poker, is “no.”

A lot of poker players get really hung up on remaining balanced in situations where, ultimately, it doesn’t matter, because their opponents will probably not pick up on their unbalance. If you consistently do not take the most optimal line because you are worried about staying in balance, even though your opponent is unlikely to do anything about it if they do notice, then you are leaving money on the table. It’s really that simple.

This is something that is best explained by example, so let’s get to it.

$1/$2 online 6-handed No Limit Hold’em. You hold 5♠4♠ on the button and everyone folds after a solid but somewhat tight regular player opens in early position to $6. You call, and the blinds fold.

The flop comes A♠8♥5♥. Your opponent c-bets $10 into $12 which you expect him to do 100 percent of the time on this board. You decide to call, figuring that you can take him off his hand on the turn or the river and you’ll have more information.

The turn is the 10♠. Your opponent checks. You bet $30 and he calls. The pot is $92 and there is $154 behind.

The river is a bricky 2♣. This card doesn’t really change anything, and that’s fine with us. He checks again. Now it’s a question of what size bet we should make. A lot of players would suggest making $70 or so. It’s a bet big enough to get some folds, and it is also a bet that you would make for value. These are both very solid reasons for making a bet this size. It’s a good bet. However, this doesn’t consider the mistakes our opponent could make. Most players in this game have difficulty making sharp hand reading decisions on the later streets when the bets get bigger. If you make a shove here, his thinking will often revert to: “That’s a really big bet. Cannot compute. I guess he has it!” and fold. Against a player like that, shoving is almost always a better play. Let’s put some numbers on it to see.

Let’s assume that his range at this time is AK/AQ (this is a little oversimplification, but honestly not too far off). Assume that if we make a $70 bet, he will fold 60 percent of the time. Since we are risking $70 in order to win $92, we are getting offered 1.31-to-1 on our bluff. We need him to fold 43 percent of the time for our bluff to be profitable, so this is a +EV bluff. Now, if we shove, we are betting $154 to win $92. Assume that when we shove all-in we will see him fold about 90 percent of the time (this may seem extreme, but in my experience it is accurate). We need this bet size to work more often. We are now laying 1.67-to-1 on our bluff. For this bluff to be profitable, we need it to work about 63 percent of the time. This is also a profitable bluff. Intuitively it seems better to make the smaller bet, since it costs us less, but let’s check the numbers.

EV of a $70 bluff:

EV = (amount won when bluff succeeds) x (probability of bluff succeeding) + (amount lost when bluff fails) x (probability of bluff failing)

EV = ($92) x (.60) + (-$70) x (.40)

EV = $55.20 – $28.00

EV = $27.20

EV of a shove bluff:

EV = ($92) x (.90) + (-$154) x (.10)

EV = $82.80 – $15.40

EV= $67.4

So a shove bluff is far more profitable than a smaller, “normal-sized” bluff. This is a bit counter-intuitive, as most would hazard a guess that a bet of $154 should have to work twice as often as a bet of $70; but that isn’t the case here. Here’s the math for finding out how much more often a bet of $154 must work to be as equally profitable as a $70 bet.

We already know that the EV of a $70 bet is $27.20, thus we use a little algebra. We set c to the percentage of time the bluff succeeds and solve for c when our EV is equal to $27.2o using the EV equation for a shove bluff.

($92) x (c) + (-$154) x (1-c) = $27.20

$92c – $154 + $154c = $27.20

$246c = $181.20

c = 0.7366 or about 74%

So if a $70 bluff works 60 percent of the time, then an over-bet shove of $154 has to work about 74 percent of the time to have the same EV. If the shove works any more than 74 percent of the time, it is the superior play. Often times you pick up way more than 14 percent more fold equity by making a move like this.

However, when we make plays like this, we have to be aware of what our hand range is and how our opponent perceives our play. Against an opponent who plays like the one described above, it would be silly to value bet all in because we get called significantly less often. So in this spot, our range would be exclusively bluffs; and thus out of balance.

A sophisticated player can really use this unbalance to his advantage. A lot of players would use this as a reason not to make this play. They reason that their opponent will know that they will never do this for value, and they make a call. This is often too much credit to give many players. Firstly, he may not know that you will only do this as a bluff. He may just see a big bet and say: “Wow! I can’t call that!” and then fold. Also, even if he does see that you would rarely make this bet for value, he will not often have the confidence in this read to make the call.

Now, let’s say that a particular opponent is strong enough, such that he will make some extra calls in this spot because he believes that we will not take this line for value. What do we do? Now we balance. We need to make sure that our range has such a good mix of bluffs and value hands that our opponent is making a mistake. Nash Equilibrium tells us that there’s a way for us to make our opponent do no better than a 0.00 EV (and the same for us). We are offering our opponent 1.59-to-1 on a call. This means that our opponent needs to win 39 percent of the time to break even. If he wins any more than that, he has a +EV call. If he wins any less than that then he has a -EV.

Imagine in this spot that we will only shove with either the nuts or a complete bluff. If we bet in such a way that we have a bluff, exactly 39 percent of the time, and the nuts the rest of the time our opponent can do no right. Since we are laying 1.67-to-1 on a bluff he needs to call about 37 percent of the time. If he calls any less than 37 percent of the time (like in the first example), we profit from our bluffs. If he calls any more than 37 percent of the time (like a sophisticated player might), then we profit from our value bets. If he calls exactly 37 percent of the time, we both break even. Knowing where the line is for unexploitable play is helpful because we then know what adjustments to make to beat our opponent. If our opponent makes too many calls, then we bluff less that 39 percent of the time. If our opponent doesn’t make enough calls, then we bluff more than 39 percent of the time. However, do recognize that when we aren’t bluffing 39 percent of the time, we potentially can be exploited ourselves.

Against a sophisticated player who might conclude that we are bluffing with a bet size like this, it might be a good idea to bet with a range that has an air-to-value ratio (AVR) of something like 20:80. This would put enough bluffs in our range to leave him unable to simply start folding and give us enough value hands to make him incapable of just clicking the call button. Sorting our range out like this exposes our opponents to difficult decisions because we are putting big bets in, and they are going to have to take a guess as to what the correct response is. If we are in balance, or even very close to it, it is going to be very difficult for them to do much about it. Certainly, having a strategy such as the one described, will take some effort in reading our own hands. But the benefits are important and necessary against strong players.

Note that I’m not suggesting that when up against a strong player you should just leave out over-bets. I believe that doing so leaves money on the table. If you have a player that is willing to call and over-bet with a smaller hand, then you should be over-betting for value more often. This simply brings more money in with our big hands. Additionally, it is nice to have options in our strategy. It gives us more opportunities to confuse our opponents’ hand reading, and it may cause our opponents to play more timidly against us.

Having a good understanding of balance is crucial for long-term success in poker. However, understanding balance is not as black and white as the understanding that you need to be in balance at all times. Sometimes it simply doesn’t matter that you are out of balance. Sometimes being out of balance is the correct play. Don’t reject unorthodox plays because you are going to be out of balance. Ask yourself whether or not your opponent is actually going to pick up on this and exploit it. Many players will not. Only if you’re confident that they will, should you begin to balance your play.

March 2010