Introduction to polarized betting
What it means to play a GTO style of poker is to be balanced at all times. This means that regardless of the situation, in theory, we should always have a range of possible hands including both bluffs and value combos.
Preflop, our range is what is called a linear range, which means that we have good hands, and some bad hands, but all of our hands have drawing potential, and we do not play the very worst hands.
The opposite of a linear range would be a polarized range, which is one that contains our good to very best hands, and our worst hands, but not those middling hands that may win at showdown, but are not so good in the face of resistance.
With correct play, our range will very often morph from this preflop linear range, to a postflop polarized range, and our betting strategy needs to reflect this. It means both our range, and our bet size needs to be balanced and reflect each other.
For example, if you bet the size of the pot on the river, then your range should consist of 67% value, and 33% bluffs. This is the inverse of the opponents break-even call percentage, also known as polarized betting.
You may ask if this does not make us very predictable? And the answer is yes, and no. Sure, our opponents in this river situation will know that we often have value, but they will also know that we do not always have value. In theory, we are making our opponents indifferent to calling or folding. Because regardless, assuming we are perfectly balanced, then it will not really matter either way. We will simply break even, and the house will take its cut.
Is this not stupid when you do not win anything? Yes, and no again. The idea is that most of your opponents will be unbalanced. They will either fold or call too often. This in turn can be exploited, and this is where one could argue that you should make small deviations from GTO in order to exploit your opponents in a structured manner.
You preferably want to avoid the players who are good enough to also play balanced, because against such a player, you would have no edge, and competition would indeed be meaningless to all parties involved but the house.
We ultimately decide our bet size based on how we evaluate our range in terms of combos.
Continuing on with the initial river example where we bet the size of the pot. Like I said, we need 67% value, and 33% bluffs in our range, but what does this mean in practice? It means that if our range contains 100 combinations, then to be perfectly balanced, 67 of those combinations need to be value, and 33 of them need to be bluffs.
It also means that if our range is only 20 combinations large by the river, then we need 13.4 combinations of value, and 6.6 combinations of bluffs. Of course, we cannot have 13.4 combinations of anything, and this is where we need to be balanced over time to average it out properly.
It is quite simple in theory, but as with many theoretically simple ideas, it can be terribly difficult to properly apply in practice. In fact, not even machines can do this perfectly yet, due to all of the unknown variables street by street that make poker what it is. All we can do is fine tune and be as good at it as possible in order to gain an edge on our opponents.
Fun fact: If your range is ever more than 50% bluffs by that last river bet, then you are always over bluffing regardless of your bet size. Because regardless of your bet size, your opponents break-even call percentage is never above 50%.
Worth mentioning is that before the river, your range will often contain more than 50% bluffs, due to the inclusion of semi-bluffs. You may semi-bluff the turn with a draw of some kind, but you can never semi-bluff the river because there are no more cards to come to complete a draw. On the river, you are always either straight up value betting, or bluffing.
Value/Bluff ratio for different bet sizes:
As you can see by this chart, the smaller your bet size, the more value needs to be in your range. This simple fact is probably intuitive to most people, because the smaller you bet, the better pot odds your opponent has to make the call. If you are going to get called more often, then you obviously need to have more value in your range to win more often in order to not hemorrhage money.
You can also see clearly that the bigger your bet size, the more bluffs need to be in your range. This can also be explained intuitively by the simple fact that if you are bluffing, you really want your opponent to fold, which is theoretically more likely to happen if you bet big and in doing so, give your opponent worse pot odds.
Let us finish off with an example. I will make it simple by showing a small range of hands and how two different river cards will affect your range composition in terms of value/bluffs.
As you can see, your range is currently 10 combinations wide, and the current composition is 60% value and 40% bluffs – 6 set combinations and 4 flush draws. This is sort of irrelevant on the turn, but what I want to show you is how this can change on the river, and how your final river composition should affect your bet size.
If the river is or some of those draws will have changed from bluffs to value, because they make their flush. Making the flush with either card would make the composition 80% value and 20% bluffs. As we now know, this means our bet size on the river should be 33%.
If the river instead was a complete brick for our range, like , our range composition has not changed. It is still 60% value and 40% bluffs. Somewhat unintuitively to most players, this means we should actually bet 200% pot.
I hope this has adequately demonstrated the idea. In practice, this is infinitely more difficult, since you often do not know your exact range in all spots and should adjust to the players at your table.
It is important to spend a lot of time analyzing your hand history. This will allow you to slowly build up a strong foundation of intuition that will help you in future scenarios at the table. Choosing the most appropriate bet sizing is one of the major factors in differentiating a bad player from a good one.