December 10, 2023

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There are many fine먹튀검증 먹튀폴리스 players who have, at best, only a basic understanding of math. Some of these players are able to intuitively “know” the approximate odds and act accordingly and others don’t even care what the odds are and just play by other factors. There was even a time when David Sklansky and math geniuses like him were thought to be geeks not worth the time to read. With the publication of Dan Harrington’s series of books there has been a resurgence in interest in the math of poker. Nowadays most any random online player can quote you an “M” value. But this is only part of the poker math picture.
In this article I will attempt to explain the broader concept of probability in a way that is accessible to everyone. Once you understand probability you will have another piece of information at your disposal to use at the poker table. Or, at the very least, you will be able to help an eighth grader with his homework.
Gamblers make their living by trying to determine which of many possible outcomes will happen. Had you been smart enough to figure out that the NY Giants would win the super bowl this year you could have made some money. Bet on the right horse to win the next race and you get paid.
Let’s look at one of the simplest cases – flipping a coin. When you flip a coin to gamble you choose either heads or tails and then the coin is tossed and depending what comes up you either win or lose. There are exactly two possibilities that can come up and you want one of them. To find the probability that you will win you always take the number of things you want and divide by the number of things that can possibly happen. In this case that would be one divided by two or one half. So there is a one out of two chance, or fifty percent, that you will win.
To continue with another example, this time we roll one die. The game this time is for you to pick one out of the six possible numbers that could come up and you win. To find the probability that you will win you once again divide the number of things you want, which is still one, by the total number of possible outcomes, which is now six and you get one sixth. Now there is a one out of six chance, or about seventeen percent, that you will win.
Now let’s move into using a deck of cards. As we all know, in a deck of cards there are fifty two cards made up of thirteen ranks in each of four suits. This time the object of our game is to pick a card and get a heart in order to win. Now, instead of only thing that can win us our game we have thirteen things (hearts) out of a possible fifty two things that can come up, so we divide fifty two by thirteen and get a one out of four chance, or twenty five percent to win.
Hopefully by now you are feeling pretty good about figuring out basic probability. So it’s time to ask what makes cards different from tossing a coin or rolling dice. The answer is that nothing about any previous flip of a coin or roll of a dice affects the next flip or roll. The fact that you got heads on the last flip is completely irrelevant to the current flip and does not influence the probability one way or the other. The fact that you rolled a six last time does not make rolling a six this time either more or less likely. The only thing that may be influenced is human perception. If a coin comes up heads six times in a row, people may believe that “tails are due” and want to bet more on tails. But this simply isn’t the case. On that seventh roll, heads and tails are still both 50%. Each event is separate and does not depend on the previous event so they are called independent.
With cards however, there is a new factor to consider with every successive drawn card. In most card games, once a card is drawn or played it is not then placed back in the deck and cannot be drawn again. Let’s start with a simple game where you have to draw a spade from the deck, so on your first draw you have thirteen out of fifty two chances, or 25%. Let’s say you draw the ace of spades and you win. Now what happens to your chances on the next draw?
Probabilities do change now. For one thing the chances of your drawing the ace of spades on your next draw are now zero out of fifty one remaining cards, or 0%. The chances of your drawing any spade have also decreased, though not as dramatically. Out of the fifty one remaining cards there are twelve spades left so the probability is now twelve out of fifty one or 23.5%. If you get lucky and draw the deuce of spades this time, on your next draw your probability goes down again. You now have only eleven spades left out of fifty remaining cards and you are down to 22%. In the case of the cards here the first event influences the second event and so on down the line, so they are called dependent.
Many times those who are not true math people get confused about what is dependent and what is independent. The casinos use this fact to their advantage when they have huge boards posted above the roulette wheel showing the last ten winning numbers. If there are mostly red numbers up on the board the suckers will usually bet a lot more black thinking that “it is due”, when the truth is that all spins are completely independent. Also, with cards, it is easy to forget that the cards that are out change the probabilities of all the remaining draws until the cards are shuffled again.
If you want to delve deeper into gambling math, there are only about a zillion (not a real number ;o) books that you can read. Or, if you like, post in the “ask seal” forum with a request and I’ll be happy to expand this in a future article.