Blackjack Probability, Statistics, and Getting a Competitive Advantage in the Casino

The probability of blackjack is the same as any other probability in a casino. It is a way to measure the probability of certain events. You will often see probabilities expressed as percentages, but they can also be expressed as fractions or odds.

Blackjack statistics are a way to measure your actual results and compare them with your predicted results. In the long run, your actual results will begin to resemble your predicted results. But in the short term, chance will ensure that anything is possible.

This is why some players have huge losing streaks, while others have big win streaks. The casino doesn't care because they have set up the games and  payouts to ensure long term profits. It's a matter of expected value. 토토사이트

Some definitions related to probability and expected value

In fact, that's probably the best way to introduce this blog post: with some definitions of some terms related to blackjack odds in general. This way, you can dig  into the main points of the article below.

Let's start with the term "probability". This word has 2 meanings. The first is  probability which is the branch of mathematics that deals with the probability of an event occurring. The second way is more useful: probability also refers to the probability of an event.

Probability is measured numerically, and the probability of an event is always a number between 0 and 1. An event with  probability zero will never happen. An event with  probability  1 will always happen.

An event with a 50% probability  will happen on average half the time. 50% is one of the most common ways to express this probability, but you could also say that the event has a probability of 1/2 and that's true. Another useful way to express probability is in the form of odds. This is when you compare the number of ways something can't happen with the number of ways it can happen. With  50% probability, an event has “even odds” or 1 to 1 odds.

Expressing probabilities as odds can be useful when trying to decide if you have an edge. In most casinos, the games  have an inbuilt advantage, but blackjack is a special case in this respect. I will come back to this a bit later in this article. Another important concept  to understand when it comes to gambling probabilities is the concept of “expected value”. This is the “value” bet. The expected value of the bet can be positive or negative, but if you are a casino player that value is almost always negative. The formula for calculating the expected value is also simple:

You multiply the probability of winning by the amount you have to win. You also multiply the probability of losing by the amount you can lose. You subtract one from the other and you get the expected value of the bet.

For example, if you have a 50% chance of winning $1 and you also have a 50% chance of losing $1, your expected value is 0. This bet is a balance bet; Over time, you won't gain or lose anything.

But let's say you have a 45% chance of winning $1 and  a 55% chance of losing $1. Now your expected value is very different: 

+0.45$ – 0.55$ =​​-$0.10

This means that over time you will lose 10 cents on each of these bets.

Almost all bets on casino games have  negative expected value. Either you will lose more often than you win, or you will win too little by breaking even, or a combination of these factors. This is how casinos continue to do business.

This is also the reason why players leave with wins. In the scenario described above, you cannot lose 10 cents on a single bet or even on a sequence of 2 or 3 bets. You will win or lose $1 per hand.

Expected value is the average value expected in the long run.

And in the long run it's longer than most people think.

This is why casinos can afford to pay out winners over time while still making huge net profits. The "house edge" is another way of assessing the expected value of a bet, but it is only used to describe bets where the casino has an advantage over the player.

How Casinos Win Regularly at Blackjack

You would think that the casino would have no advantage in a game like blackjack. In the end, the dealer will receive the same cards as the player. He has the same probability of getting blackjack or going bankrupt as a player.

The amazing thing about  house advantage in casino games is that it is often just a  byproduct of the rules that casinos use to gamble. For example, in roulette, the dealer gains an advantage by returning all  bets as if the numbers 0 and  00 were not on the wheel.

In blackjack, the dealer gains an advantage by forcing players to decide their actions and bets  before the dealer acts. In other words, you must make all of your gaming decisions before the dealer takes action. This means that if you lose (22 or more total) you automatically lose your bet, even if the house loses too. Since you act first and the dealer settles your bankruptcy before you have to play, the house has the advantage.

This is a huge advantage, made even more important by the fact that some players do not play their cards mathematically optimally. In many cases, the best way to play is to stand on a hand with no chance of winning unless the dealer goes bankrupt. A lot of players struggle with that.

This advantage is so important to the casino that it can even afford to offer very high payouts on certain hands. In most casinos, a 2-card hand with a total of 21 ("blackjack" or "natural") pays odds of 3 to 2. This means if you bet $100 and get  blackjack, you win $150.  The casino can cover this bonus while maintaining a beneficial mathematical advantage over the player. This 3 to 2 win is one of the reasons that smart players can have an edge over the casino and I will talk more  about that later in this article. 카지노사이트

Since there is a finite number of hands in the game of blackjack, it is possible to mathematically calculate the  best way to play in each situation. This is called the “basic strategy”. Computer programs analyze the potential outcome of every possible decision in every possible scenario. The move with the highest expected value is the correct decision of the game. The average blackjack player loses an average of 5% per bet on the blackjack table. The average blackjack player plays with "common sense", "hunch" or simply stupid instinct.

However, the smart blackjack player will remember and use the basic strategy in every situation. This reduces the house edge to less than 1%. Depending on variations in the rules  at a particular blackjack table, the house edge can be significantly less than 0.5%.

But it doesn't matter how low the house edge is. If the dealer has an advantage over the player, if the player plays long enough, he will eventually lose all his money. This is how  casinos continue to do business.

However, Blackjack is different from most other casino games. This is a game where  smart players with the right strategy can take advantage of the casino. This is beyond the capacity of most players and even many players  THINK that they are playing with an advantage over the casino is wrong.

I will explain why and how this happens in the next section.  How is probability in Blackjack different from probability in other casino games

The reason that a strategic player can gain an advantage in blackjack is that with each card  dealt, the entire texture of the game changes. In any random shuffle of a 52-card deck, the cards can fall into any  pattern. But sometimes higher value cards and lower value cards are scattered unevenly in the deck.

When I say "higher value cards", I'm talking about 10s and Aces. Since these are the only cards that can produce blackjack (and the payouts are 3 to 2), it's best for players to leave a relatively large number of these cards  in the deck. Conversely, "lower value cards" will increase your chances of going bankrupt when  hit. They also make it harder to win 3-2 in blackjack. If a deck contains a relatively high percentage of lower value cards then the casino has a bigger advantage than usual.

This may seem obvious but think of it this way if it's still not clear:

You are playing blackjack and in the first two hands there are 4 aces.

What is the probability to get a natural then? Since you need a 10 AND an ace to get a wild, your probability of getting a wild drops to 0.

Here's another way to think about it:

When  playing roulette or craps, the odds for each outcome are the same. This is because the number of possible outcomes on the roulette wheel does not change. You always have 38 numbers of equal probability.

When you play dice, these 2 dice have the same number of faces (6) each time you roll them.  You do not discard the roulette number once the ball has landed in that box. You start over on the next turn.

You don't discard a number from the sides of the dice just because it appeared on the previous roll of the dice.

But when a card is dealt in blackjack, it disappears from play until the deck is shuffled again.

This changes the odds of each side. 

How  to use this information to gain an advantage over the casino in blackjack

If you can bet more when the game has  higher odds of 10 and Ace and bet less when it is not, you can have an edge over the casino. You will invest more money in stocks when you are more likely to get a payout of 3 to 2.

And  it turns out that's exactly what you CAN do.

You've probably heard the term "card counting".

Unless you've heard of this topic before, you might think it's beyond  most people's reach. Maybe you saw Rain Man as a teenager and thought you needed to be able to memorize each card as you played to be successful at card counting. But the truth is that anyone who knows how to add and subtract 1 can count cards. Maintaining the level of focus needed to count correctly without looking like you're counting is the real trick.

You don't keep track of specific cards when  counting cards in blackjack. You just need to follow the ratio of high hand and low hand. For example, you specify a value from -1 to 10 and an ace. Then you assign the value +1 to 2, 3, 4, 5, and 6. Each number 7, 8 and 9 has a value of 0.

When the  count is positive, you bet more. The higher the number, the more you bet.

When the number of runs is 0, you bet less. This way you get a mathematical advantage over the casino.

You can also use statistics to make your basic strategic decisions. The basic strategy assumes a full deck of 52 cards, but as the card ratio changes as the deck is depleted, the game decision with the highest expected value may change.

This can increase your house edge  even further.

However, you do not gain a great advantage over the casino through card counting. You usually get an advantage over the casino that is roughly equal to the  casino advantage over  basic strategy players.

This means  you can play with a 0.5% or 1% advantage over the casino.

That's not a big advantage.

But it's big enough.

Expect hourly win rate, loss rate and capital requirement

How much does an average blackjack player lose per hour?

The formula is very simple:

This is the number of bets per hour, multiplied by the average size of those bets, multiplied by the house edge.

With an average blackjack player, you might see 80 hands per hour. Let's say you bet an average of $5 per hand and you're not using a basic strategy, you're looking at activity of $400  per hour and you lose 5% of that or $20/hour.

Conversely, a basic strategy player can reduce the house edge by 0.5%. This reduces his hourly loss rate to just $2/hour.

However, the card counter can work with  the number 1 in the house. With the bet we're talking about, he makes $4/hour.

But consider this:

He increases his bet based on the number, so his average bet  won't be $5. It will probably be closer to $20. We are currently looking at a salary of 16 USD/hour. That's not a great life, by the way. In fact, you can earn the same amount working at  In N Out Burger.

But as your bankroll increases, so does your average bet. Real money card counting winners can invest an average of  $100 per hand. That's $8,000 an hour, or $80 an hour income.

$80/hour is  real money.

But there is one thing that card counters need to think about is something called “Risk of Destruction”.

Remember how I talked about divergence in the short term  and how can't you  expect long term expectations to be correct in the short term?

Just because you have an edge in card counting  doesn't mean you will show your winnings every hour. You will have some crazy luck. This first age is the average over thousands of hands.

You need a large enough capital to handle fluctuations in assets without going bankrupt.

The larger your margin, the less likely you are to go bankrupt before gaining an advantage, and in the long run it will work.

This probability is called the “risk of destruction”.

The most conservative approach is to have 1,000 units to bet. If you bet  $100 on average, you need  $100,000 to play. If you have such a budget, your risk of bankruptcy is only 1%.

On the other hand, if your risk tolerance  is better than that, you can get away with a much smaller margin, maybe 200 units. You still need $20,000, but you can play at that level. However, your risk of ruin increases dramatically: up to 40%.

I suggest to Texas holdem players that they know they are good enough to level up  when they can increase their bankroll to the appropriate amount for that new level. I think this recommendation also applies to blackjack players.

If you have $2,000, you should play with an average of $10/hand. If you succeed at this level you will end up with an initial capital of $4,000 and you can grow to $20/hand and so on.

How conservative or aggressive you are depends on you and your temperament.

Conclusion

Blackjack probability is a fascinating topic with loads of subtopics to discuss. I could just as easily write about bankruptcy probability  with certain tables as  with the approach I took. I just thought it would be more useful to approach the topic of blackjack statistics from an aerial perspective.

Honestly, most people have no interest in card counting. This seems easier in theory than  in practice. Blackjack at most casinos is fast and confusing, especially if you are new to the game. It's hard to keep track of those numbers in your head without seemingly paying too much attention.

And don't forget this part:

Casinos monitor gambling counters. To say that they do not accept card counting  is an understatement. Casinos run the risk of kicking out players they can profit from if they suspect they are counting cards.  In fact, I think most casinos would do better  if they lightened up the gambling counters. I know a lot of people who want to be card counters who make such consistent mistakes that they just think they are playing with an advantage over the casino.

I assume the number of  card stands with potential long-term profitability is between 5% and 10% of the total number of card stands in the company.

Either way, knowing something about the odds behind the game will make the game more enjoyable, even if you're not interested in being an edge player.

And if you're not an edge player,  it's fun that matters. Comparing the cost of that fun with the amount of fun you get from playing is what smart entertainment is all about. 토지노사이트