The principle of Occam’s Razor is a key device in the process of discovery, across many fields of science, philosophy and logic. Developed by William of Ockham in the early 1300s, it states that among competing hypotheses, the one requiring the fewest assumptions should be selected. In short, what it means is that the simplest explanation for something is usually the correct one.
While it is not an infallible concept and is used primarily to distinguish between equally plausible hypotheses in a given situation rather than to generate a hypothesis in the first place, it still remains extremely useful in any area of discussion where the answers to the questions we ask most often are still not proven beyond reasonable doubt. This is true across various human disciplines, from biology and medicine to theoretical physics, to law, religion and the nature of the universe. It’s also true in poker.
Applying Occam’s Razor in poker
Poker, as we are so often reminded, is a game of incomplete information. It requires us to make frequent assumptions about our opponents, and we often find ourselves thinking of situations purely in theoretical terms – we think not just about what our opponent’s hand might be in a given situation, but about his or her entire range. In tournament poker, this phenomenon is accentuated, since we often find ourselves in situations where we have no knowledge of a player’s style or tendencies with which to formulate our decision-making processes.
So how can Occam’s Razor help us in these instances? Well, it’s important to recognise that using Occam’s Razor at the poker table requires us to be aware of the difference between an assumption we’re making about how someone will play, and information we already have about that person.
If we have a large sample of hands on someone and we know he’s continuation betting 80% of the time, thinking he’ll be c-betting an Ace-high flop most of the time might be a very logical assumption, but it’s still an assumption. Knowing someone is a very good high-stakes regular with millions of dollars in profit is information that might lead us to various assumptions, but it’s not an assumption in itself.
The times when Occam’s Razor is most useful are the times when we have so little information with which to make assumptions that someone is effectively a complete unknown to us, and a situation occurs in which our traditional understanding of Game Theory Optimal or unexploitable play is rendered less useful by the specificity or unique nature of the situation.
For example, it would be extremely difficult for us to attempt to construct a GTO response to someone flat-calling a 5bet out of position with only one pot-sized bet left behind in their stack, because we can be relatively sure that a high-level player with an awareness of the concept of balance and GTO play would not make a play like that, and thus we can assume that playing GTO in such a spot would be less profitable than playing exploitatively versus an unbalanced opponent, if only we knew what the exploitative play actually was.
Occam’s Razor can help us to make reasonably reliable decisions in situations where we seek to generate further profit beyond that which GTO play guarantees us, and while it’s not a perfect tool and gets progressively less useful as you move up the stakes, it can be particularly effective at lower stakes, where recreational players often make unconventional or ‘crazy’ plays that we might not understand. Here’s a look at how it can help us in these spots.
Unusual preflop plays
The Razor can be very useful in spots where we face an especially outlandish preflop play. A good example of this might be an instance where somebody open-shoves preflop for more big blinds than most players commonly would – let’s say, a huge over-shove for 50 big blinds from middle position, something a ‘good reg’ would probably never do. Here are some possibilities for why a weaker player might do that, many of which will enter into our thinking when we try to decide on a calling range:i) The player has a weak range, and is just trying to get everyone else to fold.
(i) The player has a weak range, and is just trying to get everyone else to fold.
(ii) The player has a very strong range, and thinks his shove looks weak and will get called by worse hands.
(iii) The player has a middle strength range, with which he doesn’t want to play postflop.
(iv) The player has a very strong range, and likes to bet bigger with bigger hands.
In scenario i), we’ve made several assumptions – that the player believes a bigger bet maximises fold equity; that the player doesn’t care about the possibility of busting the tournament when he gets called; that the player is aggressive enough to be comfortable risking 50 big blinds preflop, and several more. In each of the other scenarios, we make similar assumptions to varying degrees. There are very few decisions in poker that require a small number of assumptions.
Among these scenarios, applying the Razor to the situation would probably lead us to an answer that required perhaps only six or seven assumptions, as opposed to ten or twelve. I’ll leave you to decide what you think the answer is. The important thing, though, is to be aware of the huge number of assumptions we make with every decision, and think carefully about how adding more assumptions complicates the decision-making process.
Thinking through ‘levelling wars’
When it comes to situations that are more specific in nature, the number of assumptions in play actually increases further still as metagame considerations enter the equation. Let’s consider a situation where we’re in a heads-up pot against an unknown villain, deep in a tournament. We c-bet the flop, and the villain check-minraises us. Here is the progression of different ‘levels’ the villain could be on:
Level 1: He has the nuts and wants to raise, but doesn’t want to risk us folding.
Level 2: He’s bluffing, but he knows that a check-minraise looks like the nuts.
Level 3: He has a strong, non-nutted hand, and is going for value by giving us good odds to call
Level 4: He has the nuts, and thinks that we would think he would never check-minraise the nuts because it looks so obviously like the nuts.
Level 5: He’s bluffing, and knows we’re getting good odds to call with a lot of hands, so our range will be weak on the turn and he can pick up the pot with another barrel.
Level 6: He has a thin value hand, and thinks that we would fold to a larger raise but still call a minraise with a range that he is ahead of.
This could go on a lot further. In fact, many of the levels are interchangeable, since they don’t necessarily represent diametrically opposite or polarizing plays. The key here, though, is that each level requires a deeper level of assumption from us, because it requires a deeper level of assumption from the villain, and we just don’t know if he or she is capable of that.
We can’t just give all of our opponents credit for being on the highest level of thinking, so without any further information, we should assume that level 1 is the most likely scenario, with each further level becoming progressively less likely. I’ve seen players analyse hands by jumping straight to level 4 or 5 without information, and this can be a big mistake.
Establishing bluffing ranges postflop
Finally, the Razor can be especially useful towards the end of a hand, when the players’ ranges are both a lot more clearly-defined, and situations are often reduced to call-or-fold situations. Sometimes in these spots we’re faced with call-or-fold or bluff-or-check spots, and in conjunction with GTO bluffing and calling frequencies where appropriate, the Razor can help us to gain an extra edge against unknown villains.
Imagine you find yourself in an unusual river scenario. You have top pair, and the villain check-calls two streets on a dry board, before suddenly shoving his or her whole stack in on the river out of position. This might force you to re-examine your assumptions about the villain’s ranges on earlier streets, and consider whether you may have made a mistake somewhere. You might start thinking, “he can’t be bluffing here”, or “that card can’t have helped his range”, or something similar. These are good things to bear in mind, but as your confusion deepens in an unfamiliar spot, you might feel yourself edge more towards calling. You might refer back to the old adage of “if someone’s line doesn’t make sense in a hand, you should call”. Before you do that, consider the Razor.
Is it really that likely that the villain check-called two streets with the intention to bluff-shove the river? Is it really that likely that he or she suddenly decided that you don’t have the strong hand you were representing, and turned a decent hand into a bluff? When someone changes their behaviour, such as from passiveness to aggression, there’s usually a stimulus. The Razor dictates that the most likely stimulus here is that the river did, in fact, change your opponent’s hand. The simplest explanation for his or her sudden shove is the most likely to be correct – he or she suddenly had a strong hand.
A final thought
It would be easy to over-simplify the use of Occam’s Razor in poker and think that it indicated that “people always have the hand they’re representing”. Of course, that’s not the case. But while reverting to GTO and unexploitable strategies will usually be our default play in spots where we don’t have enough information to exploit our opponents, there are times when strange things happen, and we can be pretty confident that there’s a strategy somewhere out there that’s more profitable than GTO in those spots.
When we’re trying to really focus on playing maximally exploitative poker against weaker players, that’s where the Razor comes in handy. If you’re trying to “get into the fish’s head” and figure out what logic he’s using to make that crazy play he just made, the simplest answer is usually – but not always – the correct one. 700 years after William of Ockham, the Razor is still sharp.
folding_aces_pre_yo
Awsome! ty 🙂
andrebnu
Amazing post!