First of all, you won't calculate everything
No matter how powerful your computer or your formulae, it is simply not possible to develop an effective game optimisation theory that will always lead to the most logical and best decision. There are so many variations that it is simply physically impossible to count them all.
If you don't use the apps and are playing multi-table In poker, you have dozens, if not hundreds, of calculations and decisions to make in your head every minute. Therefore, you have to realise that you simply will not be able to make all the decisions mathematically, and in some cases you will just have to go on a hunch and hope that the decision you make is the right one.
If you try to count anyway, you won't have enough time, because in poker, the time allotted for a turn is limited. As a result, all top players try to gather as much information as possible to minimize reliance on AKLA have a hunch and feel for decisions based on probabilities and information gathered about other players.
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Secondly, there is often also mathematics behind hunches
There is an unofficial opinion that jazz musicians are the best improvisers in the world. Because their music almost never has any written notes or set rhythms (it's constantly changing), most jazz musicians improvise and play what comes to mind. So to speak, they follow their hunches. But there is a popular saying among jazz musicians themselves - "There is no better improvisation than rehearsed improvisation". So even the greatest improvisers rehearse, learn, improve and prepare, and read the situation, look for solutions to it, and don't just do what they think is right at the time.
In this respect, there are similarities between two very different things, poker and jazz. It is convenient and easy for players to rely on their hunches. In addition, intuition solutions that have proven to work can create the most beautiful and Hollywood's most popular moments of the game, but in the long term, when playing many rounds, you need to rely on maths, otherwise you will often fall into the trap of bluffing and overestimating your ability to read situations. Mathematics is particularly important preflop in situations where the foundations are being laid for the rest of the game. Afterwards, we have to guess and calculate the chances of only a few (but at least not all) opponents.
How do you get the most out of real games?
If the greatest mathematician and the greatest oracle were to play at a poker table, it is very possible that the oracle could win a match or two. But the more and the longer they play, the more matches the mathematician wins. As much as we want to win, trusting our instincts does not overcome probability theories and math-based calculations. Minimising losses will help you stay at the poker table longer than going all-in every other hand.
According to poker players, intuition at the table is only useful when the player has knowledge and experience. In general, hunches and gut feelings are not worth using if the player is a beginner or less experienced. After all, intuition is born when we draw conclusions about our surroundings. Therefore, intuition is more accurate when those conclusions are more accurate, and the accuracy of the conclusions is directly related to our discernment. This is why looking at professional players can give the false impression that they are just guessing what is going on. After all, there is so much talk around the table that it is hard to understand that there is a lot of calculation and reflection behind it all.
All experienced poker players will agree that it is essential to have at least a basic understanding of the mathematics of poker probability in order to maximise your success at the real game table. Otherwise, the chances of making unnecessary and avoidable mistakes simply increase. There is more than one area and formula that can be applied in real game conditions to increase the probability of success.
Best game (for the inexperienced)
Inexperienced players should rely on intuition no more often than 5% hands. Why? Because by doing it more often, they will simply increase the chances of losing, because their instincts are simply not sharp enough to know at what stage a player will bluff and which player will constantly bluff bully manoeuvres and will try to collect small wins easily.
The best thing you can do when playing remotely is to play from very low stakes and hone your skills using poker apps. This way, you will slowly develop an intuition for the game situations, and you will understand your mistakes and see which ones you make most often. By being more calculating and taking your time, you will reduce the number of mistakes, so you won't miss much, which should be the main goal of every beginner player.
Optimal game (for experienced players)
Experienced players can already think about earnings or results. Everyone wants to win, but everyone also has a unique and distinctive strategy to achieve it. We have players who are quiet and calculating, and we have players who are a bit irrational and take a lot of risks. But both types of players can be successful, it all depends on how one plays to one's strengths and how one masks one's weaknesses. You don't have to think too much about masking if you use a poker program. It then calculates all the risks itself, identifies the mistakes and helps you to take advantage of your opponents' mistakes, guaranteeing you the maximum benefit in the game.
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Experienced players rely on intuition more than mathematics up to 25% times, but it is not advisable to take risks based on intuition alone more than 10-15% hands. In some cases, mathematical formulas call for you to withdraw from the game (fold). But even experienced players should not wait for their intuition to reach inside them. It's only when the cards are drawn and seen a premonition awakens and, according to statistics, ~75-95% of the time she is right. But it is precisely because of the 5 extra percent that is missing from the full hundred that dry math still wins in the long run, because Probability theory is the strongest weapon and most powerful knowledge a poker player can have in his arsenal. It's a good thing that now you don't have to learn them from A to Z if you have a poker software that does all the calculations for you.
Examples from real game situations
Whatever the situation, mathematical probabilities are most applicable when a player is trying to get a certain hand but doesn't have it yet, or when he suspects that his opponents are doing the same. Thus, the most common way to calculate probabilities is when a player is aiming for a flush or straight combinations.
Remember that it is enough to know the basics. Pot odds, EV (expected value) and equity are the three formulas that make up approximately 90% of all the math in poker.
EV (expected value)
You can find a lot of information about each of these formulas on the internet. For the sake of maximum usefulness, let's look at one of the most important mathematical functions - the bluff probability. Suppose you are left with two opponents who bluff 1 time in 5 when they have the best hand after river. He does not bluff four times.
This means that we have a 20% probability (1 in 5) of holding a better hand. That is the probability that he is bluffing. Therefore, parallel to the above calculation, there is about an 80% probability (4 out of 5) that we do not have the best hand. Therefore, we win once for every four losses. Let's say that if we have the best hand, we win €25, but if we lose the call, we lose €6. This means that after 5 times we win €25 but lose €24. Therefore, according to the general theory, we will have a profit of €1 for each bet after five hands. So, although the benefits are small, it means that we it pays answer the bet.
The textual description may be difficult to understand. Then watch this YouTube video, which will clearly show you the most important information about pot odds.
Based on real-life situations and statistics, we can say that relying on intuition alone is advisable no more than 10% times. All other times, intuition is the result of rational inferences that we can generate using simple mathematical formulas such as pot odds. Therefore, it is better to rely on boring statistics in poker and only when you have enough experience to improvise when your gut feeling tells you it is the best solution.