In part one of this article, we looked at the basics of balance as a concept. In this instalment, we will be delving a little deeper into one of the subtleties of balance, and taking a look at a concept referred to as frequency.
Last time, we discussed how exploitable a player would be if they always bet full-pot with their best hands, and half-pot with their bluffs, because they would be unbalanced. However, let’s assume that we are playing against someone who makes the same bet size with their entire range; someone who is, for all intents and purposes, balanced.
For the most part, it’s still quite easy to see which hands are good enough to call versus this opponent, and which hands we have to throw away. There is sometimes that grey area in the middle, though, wherein lie the close decisions.
You might have a hand that is better than most of your opponent’s range but still loses to some of his holdings. Or perhaps you have a hand that is a little too strong to fold, but is unlikely to win at showdown. How do you determine what to do with these types of hands?
Minimum defence frequency
There’s actually a formula to determine exactly how to draw the line, referred to as “minimum defence frequency.” It’s used to calculate exactly how much of our range we need to continue with in order to prevent our opponent from showing an immediate profit, and it’s probably a lot easier to work out than you would expect
Here’s what it looks like:
p/(p+B) = 0
Where p = pot size, and B = bet size.
Let’s keep it simple to begin with. Let’s say that there is $100 in the pot on the flop and your opponent moves all-in for exactly $100. Here’s how we break down the above equation:
pot-size of $100 / (pot-size of $100 + bet-size of $100) = 0
100/(100+100) = 0
100/200 = 0
0.5 = 0
For those who prefer percentages, simply multiply your answer by 100. In this instance, 0.5*100 = 50%
Applying frequency as a concept
So, we’ve arrived at our breakeven number of 50%. How can we apply that to our calling range? Simply enough, assuming your opponent is completely balanced, it means we need to call with 50% of our overall range.
If we folded more than half of the time, then we would be conceding equity over the long run. If we called more than half of the time, then we would be conceding equity immediately.
Sometimes, it can feel like calling 50% of your hands means you are continuing with air a lot of the time. If this is the case, then consider that your pre-flop range may be too wide. If, by folding 50% of hands, you find you would end up folding some good hands, then consider that your pre-flop range may be too tight.
With that said, it’s crucial that we don’t become too hung up on this concept. A lot of the time, decisions are still quite simple. If you flop a full house and your opponent goes all-in, don’t sit there and calculate what p/(p+B) is, just click the call button!
When you start using this concept in-game, save it for the tough spots, where your decision could go either way. Do the math, work out how often you need to call to remain unexploitable, then decide if your holding sits in that percentile.
If you’re playing against someone who isn’t balanced, then you needn’t worry about any of the above, because you can simply exploit their tendencies to prefer one action over another. Chances are, especially as your game improves and you move up stakes, you’re going to encounter more and more players who are close to, if not perfectly balanced.
Always have a rough idea of what your overall range looks like, and do your best to incorporate frequency wherever you can.
In part 3, we will use this concept, coupled with simple pot-odds, to go through a couple of example hands.
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