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Variables and Decision Making

3,387 Views 1 Comment on 28/8/15

Poker is a game of imperfect information. Sometimes the best decisions are a product of guesswork, sometimes we may not even know the correct decisions, but understand which piece of relevant information would allow us to make the best assumptions. It's simply a case of having enough skill to make better decisions than the other player.

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Decision Making

Sometimes we might imagine that the players who consistently make money have the game of poker completely figured out. It's easy to assume that they know exactly what to do in every situation. But this is not really the case. Sometimes the best decisions are a product of guesswork. Sometimes we may not even know the correct decision but understand which piece of relevant information would allow us to make the best assumptions.

Perfect vs Imperfect Games

opponentrangesPoker is a game of imperfect information. An example of game with perfect information would be something like chess. Both players know the exact condition of the game state. Every element required to make a perfect decision is already on the table in front of them. It's simply a case of having enough skill to make better decisions than the other player.

Poker is different in that there is missing information. For example we might know our hole-cards but we don't see our opponents hole-cards. We might know that there are 43 cards left in the deck but won't necessarily know which cards. We might be able to put our opponent on a range but don't necessarily know which parts of that range he is folding. 

It's this feature of games like poker which make it very difficult to find an optimal solution. Chess computers have been undergoing development for many years and are extremely strong. They have all the information needed in order to make a decision so programming them (while still admittedly complex) is a lot more straightforward than programming a computer to play good poker.

Filling in the Blanks

With a game like chess we already have all of the information required, so our ability at the game comes purely down to being able to make the best decision based on the information we have. With a game such as poker there is an extra step, both of which we must become proficient at in order to succeed at the game. The two steps are as follows,

1 – Fill in as much of the missing information as possible
2 – Use the information to make the best decision possible
Note - If either of these steps are missing, then our overall ability as a player will suffer dramatically.
Let's imagine that we can see our opponents hole-cards and know exactly which cards are going to come on the turn and river. We are now playing a game of perfect information so we can ignore step 1. Does this automatically mean we are going to be a strong player?

pokerbookWe are not going to suggest for a minute that such a setup would not confer us a huge advantage, but to realise that advantage as fully as possible we still need the skill required to make the best decisions. To take an extreme example, imagine we don't know how to read poker hands and don't understand the hand ranking system. Our ability to fill in the missing information is not going to be of any use to us whatsoever.

Or let's imagine that we are really strong at making decisions when we know what our opponent is holding. Is this going to be of help to us if we are consistently putting our opponents on ranges that are not even close to their actual ranges? This is a really common issue. Players trying to fold their opponents off hands that are not even in their range, or trying to extract value from hands which are not in their range either.

Professional vs Recreational Decision Making

So what is the main difference between how professionals make decisions when compared to weaker players? Both are presented with the same list of unknown variables. Unknown hole-cards, unknown tendencies, unknown future cards, along with many others.

The main difference is simply the number of unknown variables that a professional can fill in as opposed to a recreational player. The professional does not know everything – no-one knows everything. He just knows more than the recreational player. So if there was a list of 10 unknown variables in any given situation, the professional might be able to figure out 7 of those unknowns while the recreational player can only figure out 2. 

It's also the case that the profesional player will be aware of what he does not know in a given situation i.e A “known unknown”. The weaker player is not even aware of the existence of certain unknown pieces of information that he should be attempting to assign a value to.

Known Unknowns – Conditional Answers

As we mentioned at the outset, it's not necessarily the case that even a seasoned professional knows the correct decision in every situation. Even if his decision making ability is excellent, if he is simply lacking the required information to make the decision there is not really that much he can do apart from guess. However the difference between a professional and a weaker player is that the professional understands what the missing piece of information is and exactly how it can be used once it is uncovered. The weaker player is simply confused. This kind of thing happens way more often that we might imagine – but we tend to notice it a lot more when we are not playing our A-game and are perhaps starting to doubt or question our abilities. Here is an example.

pokercardsSingle-raised-pot, 100bb effective. We open raise from the BTN and get a caller in the BB. We skip our Cbet after flopping nothing and turn a weak 2nd pair. Villain fires 2/3rds pot on the turn OOP, we call. Villain fires river OOP for ½ pot. Hero?

Many of us won't actually know what to do here. If we think we know what to do then maybe we should ask ourselves why we are so sure we know what to do. After all, we know nothing about our opponent and we did not specify which limits we are playing. We did not specify whether this was a live or online environment and which network or casino we were playing at. So how could we possibly know the answer to this question? If your initial thought was “snap-call” or “snap-fold”, perhaps you need to strongly re-evaluate how you approach your decision making process.
Note - Rather than trying to come up with answer to this situation – this is something that weaker players do without considering the variables – let's come up with a condition.
The correct answer to the situation will be dependent on this condition. Firstly let's ask the following....

What does our decision depend on here?

We would be investing roughly 28% of the total pot, so essentially we need our opponent to be betting a worse hand 28% of the time. When holding a weak 2nd pair there is a decent chance he is not value-betting worse so we can simplify this by saying that he needs to be bluffing 28% of the time or more for us to have a call. So essentially we still don't know whether we have a call or not, but we can answer the problem with a conditional statement.
“If he is bluffing more than 28% of the time we have a call whereas if he is bluffing less than 28% of the time we have a fold."
Initially this might not seem that much more valueable than the weaker player's thought process here.
“Not really sure what I should do here so I'll just fold” or “Easy call” or “Easy fold”
The difference is that as more information comes to light the professional is going to be making increasingly strong decisions. The weaker player is going to continue making decisions on the same level that don't vary as a result of changing conditions. 

Our ability to understand the likelihood of certain conditions being true will also be refined with experience allowing us to make stronger decisions in unknown situations. For example in the above situation it's pretty likely that at lower limit online games our opponent is not going to have a bluff-frequency which is above 28% on average. We can make a pretty good decision to fold by default. 

Default Choices

confusionRegardless of our experience there will come another time in our career where we simply have no clue what to do because we are struggling to fill in some important pieces of unknown information.

Thankfully there is still one last alternative before we resort to flipping a coin which is to try taking a game-theory-optimal approach. Unfortunately this is a lot easier said than done. It requires us to be aware of our entire range at any given point (frankly most players can't do this), and also involves elements of maths and combinatorics. Naturally in game we are unlikely to delve into combinatorics unless our range is very narrow so we will usually resort to estimates based on how high up in our range we consider our holdings to be.

But by the time we have reached the stage where we are looking at our overall range trying to make a balanced decision we have essentially resigned ourself to our fate of not being able to make the absolute best decision. We have simply accepted that there are some unknown variables regarding our opponent that we have not been able to fill in. If we'd been able to make an educated guess regarding these unknown variables we would be in much better shape than attempting to make a GTO based decision.

Naturally we spend a lot of our time playing against unknowns, but in these instances we need to resort to population reads where possible. Keep in mind that a population-based play is nearly always stronger than a GTO-based play when readless. GTO is essentially a last resort when all other exploitative options have been exhausted.

The longer we play certain players and certain limits the stronger our awareness of what our default choices should be in certain situations without having to resort to a maths-based balanced approach.

Application

The important thing to take from this article is that if we want to excel we should be looking to go one level deeper. We are not interested in whether individual hands are calls or folds. We are interested in the relevant variables that effect our decision making. We can then make “conditional rules” which are a lot stronger and more flexible than “static rules”.

pokerthinkingFor example a weaker player might have a “static rule” such as “never fold an overpair on the flop”. In some situations this will be a good rule, in other situations it will be terrible. We need to make such a rule more effective by specifying certain conditions where it either does or does not apply. To add two additional conditions to that rule as an example “never fold an overpair on the flop UNLESS opponent has a raise-flop stat of less than 8% or has a stack deeper than 100bb”. This is by no means a complete rule – the complete version would have many other conditional exceptions attached to it.

Thinking in such a way will allow us to strengthen our overall decision making process and make decisions that are based on specific features of the particular game we are playing. We should also keep in mind that even in situations where we don't understand what the correct play is, we should nearly always be able to provide a “conditional answer” regarding the best play. So we might not know whether to call of fold but we should be able to say something like “call IF y but fold IF x”. Then our future thought processes can be geared around establishing how to recognize whether “y” or “x” is true in a certain situation. In some cases this might involve DB analysis, looking to see if the situation is covered by a population read. We might establish that “y” is most frequently true and can then add calling as one our default choices in this situation rather than being forced to resort to a more GTO based approach.

This is far more useful than simply acknowledging we do not know what the correct decision is and moving on. If we take this outlook there is a pretty decent chance that we will never know what the correct decision is here and will not improve.
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w34z3l

I am of British nationality and go by the online alias w34z3l. I am considered one of the top consultants in the field for technical analysis (i.e. database work) and application of game theory concepts to various card games. I make a range of educational content ( ... Read More

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Pwll

Pwllon 28/8/15

This was a nice article to get me thinking about thinking; much appreciated.

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