Probability: what happens when it doesn't match?

Poker is a game with much more involved than just chips and cards.

“The bird lands on a very thin branch and stays there peacefully, because its trust is not in the branch, but in the strength of its wings.”

We all know that poker is a game of strategy, and that it involves a multifactorial analysis. We are all saturated with knowledge about it. However, some factors are worth understanding so that we don't get frustrated with unexpected results in a hand. For example, the fact that you lost a hand in which you were the favorite cannot influence your decisions from that moment on. Take a look at this series of probabilities of a hand of yours being dominated, against the possible range of players (pairs and non-pairs):

Click here to see the tables

These tables were created by randomized simulation. Each cell of the pairs table was based on 7.8 million hands, and 21.7 million non-pairs.

Note in the first table that AA will obviously never be dominated, because it is the highest possible pair pre-flop. Now the question arises: Why did you lose with AA against an opponent who entered with J8o, when you made the standard pre-flop raise, as the rulebook dictates?

The answer is simple, although AA is the clear pre-flop favorite and unbeatable at this point, the cards that are coming can change the course of the hand completely, giving the victory to the weaker pre-flop player. Now this is no reason for you to stop believing in mathematical probabilities, what you have to keep in mind is that the probability does not confirm that it will happen, but that it is likely that it will.

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Knowing that AA loses its strength when playing against more than one opponent, paying attention to the game's mathematics can help in the long run.

AccessOnce, while talking to some friends after a live, we asked a friend why he called a raise that cost him the tournament, understanding that the probability of him getting it right was 1 in 8, the “partner’s” response was that the same thing happened 7 other times and that the next time it would work out. What I wrote may seem like a joke, but that’s what happened in a tournament here in my city.

We have to keep in mind that even though something we expected to happen by probability didn't happen, it doesn't mean that it will happen next time, because the cards have no memory. In the next round, the statistics are reset, the cards are shuffled and everything starts from square one.

In the book Poker for Dummies – Harrock and Krieger, they show an experiment that was carried out on the issue of probability on a computer that simulated 60,000 hands in hold'em, aiming to verify when the long term would be.

They entered information from players with equal skills. They expected an exact balance, that is, a draw, in the end. After 60,000 hands, 4 players lost and 5 won, with different ROIs. The experiment showed that in 1 year, with a regular daily playload, the expected long-term return was not achieved.

In another experiment, they asked the computer to simulate 3 million hands, with an average of 30 hands per hour, 2,000 hours per year. That's about 50 years or so. Still, equilibrium was not observed, with both winning and losing players.

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But here comes the big question: probability does not guarantee equilibrium in the long run, but rather what can happen. If we take a coin with heads and tails, and toss it 100, 1,000, 10,000 times, we will not reach the perfect equilibrium of times that one side or the other comes up.

To finish the experiment, they replaced two players at the table who all had the same skill and put in two others who were slightly weaker in terms of poker skills. The results: both of them lost significant amounts, while the other 7 were profitable in the long run.

So the most important thing for a poker player, especially a beginner, is to believe that his difference is not or will not be in the cards, but rather in his multifactorial analysis skills that poker demands.

Article written by: prof_anselmo

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