Most people think that poker is a game that relies on luck. This idea is very common. Perhaps when you search for this question, you also tend to think that poker is a game of luck.
But the facts are completely contrary to people’s impressions. You may be fooled by your own feelings! Most players who play poker seriously know that skill is more important than luck.
Poker is 100% a game of skill in the long run. Luck in a single hand of poker does affect the outcome of the game to a certain extent. But players who are proficient in the same situation are more likely to win. In the long-term game, the influence of luck will be greatly weakened. In contrast, the importance of skill in poker will be greatly enhanced. So, poker is actually a game of skill rather than a game of luck as people think.
In this article, I will discuss the role of luck and skill in different kinds of poker games. I will also explain from several aspects why poker is a game of skill in the long run.
Poker is a game of mathematics
One of the big reasons why people think poker is a game of luck is the uncertainty of poker. You never know what the next card will be. It seems to depend entirely on luck. ( Unless you use poker cheating devices. But I will not discuss this in this article. If you are interested, you can read this article: How to cheat in poker )
Yes, what cards you can get really depends on your luck. But this is a typical probability event. There is a fixed probability of what card you get. The more you play, the closer the cards you get to the ratio given by the probability.
Next, I will explain the basic mathematical principles involved in poker.
We all know that playing cards have many uses. There are countless kinds of poker games all over the world. We roughly divide poker games into two categories: luck games and strategy games.
First, let’s talk about why people believe in luck.
Although I used the word luck here, I will explain the mathematical principles in detail. This type of game is mostly used for fast betting. These games have some common characteristics: simple gameplay and clear results. For example, blackjack. There are also simpler poker games that play like craps.
I think you must have been exposed to a lot of these games. So what kind of mathematical principles are involved in games that seem to rely entirely on luck?
In order to avoid my explanation becoming very complicated, let us first set simple gameplay. We just use 2 to 10 and an A, and there is only 1 card for each point. A total of 10 cards, of which A is the largest. Suppose 2 people play this game. The players are just me and you. After the shuffle, you and I each get a card.
If the card I get is 2, then I will lose 100%. Since there are 10 cards in total, the probability of me getting a 2 is 10%. For the situations that will arise, I have listed Table 1 to show the probability of winning in various situations.
|Win by the card||0%||11.1%||22.2%||33.3%||44.4%||55.6%||66.7%||77.8%||88.9%||100%|
|Get the card and win||0%||2.22%||4.44%||6.66%||8.88%||11.12%||13.34%||15.56%||17.78%||20%|
“Win by the card” means you have already got the card, the probability of winning the game by the card.
“Get the card and win” means the probability of you getting the card and win the game.
If the rules of the game allow you to bet after you know your own card, you can decide how to bet based on the probability of winning. For example, if you get a 7, 8, 9, 10, or A, you will win more than you lose. If you get the A, you can all in. Because you can win 100% with the A.
Of course, if your opponent also follows the probability of the game completely, then it will be difficult to win. But your opponent will not always be a math proficient player. In other words, people who are better at math will benefit more easily than people who are not good at math.
But there are also many games that are played without you knowing what card you get. This kind of completely random blinds is the luck side of poker. Everyone played the game without obtaining any information.
If the rules of the game are completely fair, then in each round you have a 50% chance of winning and the other 50% chance of losing. A single hand depends entirely on luck. But the more you play, your total profit and loss in the game will tend to be the same.
This is determined by mathematics. If you need to pay a certain fee to the casino for each hand, then this fee will become your main loss.
If you understand my previous example, then I will further elaborate on the use of mathematics in poker.
The example I give this time will be a little more complicated. First of all, I am playing with you. Only use 5 cards from 2 to 6. First, give everyone a card. Then you can look at the card you got and place bets. After that, a card is dealt to everyone and bet again. Finally, the total points of the two cards are compared, and the person with the higher points wins.
Then we analyze what might happen next:
Regardless of the order in which the cards are dealt, the probability of my first card being a 2 is 20%. Some people may not understand, so I will explain in detail.
Probability in this poker game
If I get the card first, then there is no doubt that the probability of getting a 2 is 20%.
If you get the card first, then the probability that you won’t get a 2 is 80%, and the probability that I get a 2 in the remaining cards is 25%. So the probability of this situation is 80%*25%=20%.
Okay, now you should understand how probability works. Next, I will conduct a follow-up analysis.
What is the probability that I get a 2 on the first card and a 3 on the second card? You can calculate this. In order not to make this article too long, I will give the answer directly. The probability of this happening is 5%. In this case, I will undoubtedly lose the game.
If you calculate the probability, you will find that the probability of each situation is the same. So we only discuss the probability of winning. I list the probabilities in Table 2:
|First Card||Second Card||Win||Draw||Lose||Expectation|
So if the first card is 2, what is the probability of my winning? 0%*25%+0%*25%+0%*25%+33.3%*25%=8.325%
If the first card is 3, the winning probability is 25%.
If the first card is 4, the winning probability is 41.675%.
If the first card is 5, the winning probability is 50%.
If the first card is 6, the winning probability is 75%.
So knowing the winning percentage of the first card, you can know how to bet.
Expectation in this poker game
In order to further explain how to use mathematical strategies specifically, I use a parameter in statistics: Expectation.
For the first card, I make Table 3 to list the expectation.
|The first card||2||3||4||5||6|
It can be seen from Table 3 that if the first card is 2 or 3, I will lose money in the long run.
According to Table 2, if the first card is a 2, I should fold it immediately. Because no matter what the second card is, the expectation is not greater than zero. It means I can’t win money in the long run.
The first card is 3, I can make a basic bet. If the second card is 2, 4, or 5, I will fold. But if the second card is 6, I will bet as big as possible.
When the first card is 6, I will make a big bet. Unless the second card is 2, I will continue to maintain a big bet.
The interesting thing is that if we add up all the expectations, we will get a total expectation: zero. It means that if all bets are the same, then, in the long run, we will neither lose nor win.
Although the card you get is completely determined by luck, you can guess the result through mathematics. Minimize losses when you are more likely to lose the game. Conversely, increase revenue when you are more likely to win the game. So you can win in the long run.
So when you adopt the correct poker strategy, the poker game is no longer a pure luck game.
Of course, these are just poker games from a purely mathematical perspective. The actual situation will be much more complicated.