Jump to Positive vs. Negative EV - Negative Expected Value It is of essential importance for a blackjack player to be able to figure out what expected valueΒ ...

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Regardless if you play poker, blackjack or on horses you will always have an expected value for the outcome of your play.

The meaning of EV and that is it good for?

The basic meaning of EV or expected value is the potential long-term equity in a specific situation.

It can be applied on all sorts of things, but are often used in context of gambling.

In poker, on the other hand, the situation is more dynamic.

All decisions you make will affect your results in some way.

Opposite to lottery, in poker you can actually achieve a positive expected value.

Not being aware of what your expectations are in a particular situation is a serious risk factor article source your total result.

Positive EV means that you can expect a positive long term result in a given situation and negative EV is the opposite.

As a consequence, you want to bet as much as possible how to calculate expected value blackjack you have a positive expectation and as little as possible when you have a negative expectation.

Your guidance to this cause how to calculate expected value blackjack the how to calculate expected value blackjack />Within every situation in poker there are odds of the possible outcomes.

The more you know about the odds, the more how to calculate expected value blackjack can you get an advantage, or, as gamblers put it: getting the best of it.

Here we can see that you have a positive expected value and you will earn money in the long run on this bet.

In poker things will not be as simple as in this example.

But through knowledge and experience you can make estimations that serve your calculations.

You will for a certain win in the long run in situations with positive EV in poker, and by short terms you will maybe win.

The variance is, however, big from a short perspective and can be.

To always follow an approach that yields good winning chances is continue reading to formulate in words, but much more difficult to make a practice of in reality.

This is because poker not only consist of mathematics and strategical elements, but also lots of psychology.

The EV perspective is click right way to approach gambling, including poker.

Try to always think: "Do I have a positive EV or not?

This can be applied to everything from table selection to a single call decision.

In abstract terms, EV is everything in poker.

Risk aversion The risk aversion differ between people.

Whereas some doesn't like the idea to gamble that much, others willingly do just that provided that the odds are favorable.

People with high risk aversion are simply not suitable for a game such as poker in which you must risk something to get something.

Even if the gamble have a positive outcome in the long run some, not everyone likes the idea of a possible short run loss, especially if lots of money is on stake.

Any advantage player, a gambler looking for a mathematical edge to exploit before wagering on something, will accept taking big risks as long the outcome seems to be positive in the long run and that his bankroll can tolerate a loss.

By only gamble in situations with minor risks, the potential how to calculate expected value blackjack prospect decrease.

He wants to win immediately.

Sure, sometimes it's correct to protect the hand, but it's better to do that with calculated value bets than over bets.

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Follow our guide to fully understand blackjack insurance.. Insurance bets in all forms have a negative expected value (EV).. much actual math, you can roughly calculate whether or not buying insurance is a smart move in a given situation.

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Good Blackjack and Spanish 21 games have house edges below 0.5%. Example #1:. Therefore, the expected value may be calculted as follows: ExpectedΒ ...

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With just simple math you can calculate your expected bonus value.. Let's pretend you play Blackjack with a 3% house edge, and you wager 100β¬ in total, you.

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can look for in the game of Blackjack that will increase my expected value?.. examples of Independent games, one role of the dice or spin of the roulette wheel.

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Does anyone know where to find a good, dependable EV Calculator? Thanks.

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The measure of the difference from the mean is called standard deviation, which is the square root of variance.

Please see this link: Computing variance for blackjack using combinatorial analysis In combinatorial analysis how to calculate expected value blackjack is known that the sum of the probabilities of all possibilities must equal 1.

In other words every possible outcome is accounted for.

In blackjack there are 2 basic types of outcomes to consider relative to variance: simple and compound.

A simple how to calculate expected value blackjack means that the amount won or lost on the round is a single value, such as player hands played with a strategy of stand, double, or hit.

There is also a chance of a tie on these hands.

A compound outcome results from pair splitting or playing multiple hands simultaneously.

Depending upon rules the outcome of a round where 3 splits are allowed can result in a gain or loss of 8 times original bet or anything in between.

A tie means that an equal amount is won and lost.

So, as with most problems in computing for blackjack, pair splitting is the big problem in computing variance.

The case where doubling on any number of cards is a compound outcome but for a non-split hand it doesn't present the problems that pair splitting does in order to compute variance.

Variance related to expected value Consider these 2 games and probabilities of outcomes: 1.

However, they have differing variances.

Obviously in game 1 there is no chance of ever being behind so the wager can be as large as possible without fear of losing.

In game 2 there is the possibility of being behind and even maybe losing everything at some point.

It turns click here that simple variance is a function of the probability of a tie if EV is known for a single blackjack hand.

Betting the farm on game 2 means leaving farmless 49.

So is game 1 a better choice than game 2 or vice versa?

They both have the same expected value but are distinguished by differing variances.

In my opinion it could boil down to what you have to start with and what you are hoping to accomplish.

Game 1 is a 100% risk free proposition but you may have to wait a long time before realizing any profit.

If you don't have much to wager to begin with you could be waiting a long time for a small profit.

Game 2 is much more of a gamble.

In game 2 you have more of a chance of luckily realizing a pretty good profit fairly quickly article source also have more of a chance of unluckily losing everything.

In reality trying to profit from positive expected value is far removed from game 1 and much more like game 2.

Since I have no training in statistics I have tried to stick with observations that are basic.

If there was an ongoing discussion by persons having more than just very basic knowledge of statistics, I would not have too much to contribute.

It is much slower than the original version due mainly to the way pair splitting is handled in order to compute variance.

This version was updated 08-11-2012 to include output of standard deviation for overall calculations as well as individual player hands.

Below is output for an overall calculation for a single deck.

This variance version can be downloaded from the software page.

Computing variance for blackjack using combinatorial analysis. it doesn't present the problems that pair splitting does in order to compute variance.. The prerequisite to expect to win in the long run is a positive expected value and bothΒ ...

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The measure of the difference from the mean is called standard deviation, which is the square root of variance.

Please see this https://microrcracing.com/blackjack/surrendering-in-blackjack.html Computing variance for blackjack using combinatorial analysis In combinatorial analysis it is known that the sum of the probabilities of all possibilities must equal 1.

In other words every possible outcome is accounted for.

In blackjack there are 2 basic how to calculate expected value blackjack of outcomes to consider relative to variance: simple and compound.

A simple outcome means that the amount won or lost on the round is a single how to calculate expected value blackjack, such as player remarkable, timex blackjack watch review phrase played with a strategy of stand, double, or hit.

There is also a chance of a tie on these hands.

A compound outcome results from pair splitting or playing multiple hands simultaneously.

Depending upon rules the outcome of a round where 3 splits are allowed can result in a gain or loss of 8 times original bet or anything in between.

A tie means that an equal amount is won and lost.

So, as with most problems in computing for blackjack, pair splitting is the big problem in computing variance.

The case where doubling on any number of cards is a compound outcome but for a non-split hand it doesn't present the problems that pair splitting does in order to compute variance.

Variance related to expected value Consider these 2 games and probabilities of outcomes: 1.

However, how to calculate expected value blackjack have differing variances.

Obviously in game 1 there is no chance of ever being behind so the wager can be as large as possible without fear of losing.

In game 2 there is the possibility of being behind and even maybe losing everything at some point.

It turns out that simple variance is a function of the probability of a tie if EV is known for a how to calculate expected value blackjack blackjack hand.

Betting the farm on game 2 means leaving farmless 49.

So is game 1 https://microrcracing.com/blackjack/youdagames-blackjack.html better choice than game 2 or vice versa?

They both have the same expected value but are distinguished by differing variances.

In my opinion it could boil down to what you have to start with and what you are hoping to accomplish.

Game 1 is a 100% risk free proposition but you may have to wait a long time before realizing any profit.

If you phrase blackjack never split tens apologise have much to wager to begin with you could be waiting a long time for a small profit.

Game 2 is much more of a gamble.

In game 2 you have more of a chance of luckily realizing a pretty good profit fairly quickly but also have more of a chance of unluckily losing everything.

In reality trying to profit from positive expected value is far removed from game 1 and much more like game 2.

Since I have no training in statistics I have tried to stick with observations that are basic.

If there was an ongoing discussion by persons having more than just very basic knowledge of statistics, I would not https://microrcracing.com/blackjack/count-cards-on-online-blackjack.html too much to contribute.

It is much slower than the original version due mainly to the way pair splitting is handled in order to compute variance.

This version was updated 08-11-2012 to include output of standard deviation for overall calculations as well as individual player hands.

Below is output for an overall calculation for a single deck.

This variance version can be downloaded from the how to calculate expected value blackjack page.

All tables of expected values given below were calculated using the public domain software package available in the Blackjack project onΒ ...

Enjoy!

The measure of the difference from the mean is how to calculate expected value blackjack standard deviation, which is the square root of variance.

Please see this link: Computing variance for blackjack using combinatorial analysis In combinatorial analysis it is known that the sum of the probabilities of all possibilities must equal 1.

In other words every possible outcome is accounted for.

In blackjack there are 2 basic types of outcomes to consider relative to variance: simple and compound.

A simple outcome means that the amount won or lost on the round is a how to calculate expected value blackjack value, such as player hands played with a strategy of stand, double, or hit.

There is also a chance of a tie on these hands.

A compound outcome results from pair splitting or playing multiple hands simultaneously.

Depending upon rules the outcome of a round where 3 splits are allowed can result in a gain or loss of 8 times original bet or anything in between.

A tie means that an equal amount is won and lost.

So, as with how to calculate expected value blackjack problems in computing for blackjack, pair splitting is the big problem in computing how to calculate expected value blackjack />The case where doubling on any number of cards is a compound outcome but for a non-split hand it doesn't present the problems that pair splitting article source in order to compute variance.

Variance related to expected value Consider these 2 games and probabilities of outcomes: 1.

However, they have differing variances.

Obviously in game 1 there is no chance of ever being behind so the wager can be as large as possible without fear of losing.

In game 2 there is the possibility of being behind and even maybe losing everything at some point.

It turns out that simple variance is a function of the probability of a tie if EV is known for a single blackjack hand.

Betting the farm on game 2 means leaving farmless 49.

So is game 1 a better choice than game 2 or vice versa?

They both have the same expected value but are distinguished by differing variances.

Game 1 is a 100% risk free proposition but you may have to wait a long time before realizing any profit.

If you don't have much to wager to begin with you could be waiting a long time for a small profit.

Game 2 is much more of a gamble.

In game 2 https://microrcracing.com/blackjack/jugar-blackjack-21-casino.html have more of a chance of luckily realizing a pretty good profit fairly quickly but also have more of a chance of unluckily losing everything.

In reality trying to profit from positive expected value is far removed from game 1 and much more like game 2.

Since I have no training in statistics I have tried to stick with observations that are basic.

If there was an ongoing discussion by persons having more than just very basic knowledge of statistics, I would not have too much to contribute.

It is much slower than the original version due mainly to the how to calculate expected value blackjack pair splitting is handled in order to compute variance.

This version was updated 08-11-2012 to include output of standard deviation for overall calculations as well as individual player hands.

Below is output for an overall calculation for a single deck.

This variance version can be downloaded from the software page.

Casino game expected return and variance calculator with hours of play estimate.. These table values are used, if you select a player speed of "Maximum.

Enjoy!

expected value calculation help. I posted this over in the card counting section too, but thought I might get a quicker answer here. I bet $100Β ...

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Otherwise, all the data scientists out there would be sitting on piles of cash and the casinos would shut us out!

But, in this article we will this web page how to evaluate if a game in Casino is biased or fair.

We will understand the biases working in a casino and create strategies to become profitable.

We will also learn how can we control the probability of going bankrupt in Casinos.

To make the article interactive, I have added few puzzles in the end to use these strategies.

If you can crack them there is no strategy that can make you hedge against loosing in a Casino.

If your answer for second question is more than half of question one, then you fall in same basket as most of the players going to a Casino and you make them profitable!

Hence, the expected losses of a trade in Casino is almost equal to zero.

Why do our chances of gaining 100% or more are less than 50% but our chances of losing 100% is a lot more than 50%.

My recent experience with BlackJack Last week, I went to Atlantic City β the casino hub of US east coast.

BlackJack has always been my favorite game because of a lot of misconceptions.

For the starters, let me take you through how BlackJack is played.

There are few important things to note about BlackJack.

Player tries to maximize his score without being burst.

There are a few more complicated concepts like insurance and split, which is beyond the scope of blackjack video poker strategy article.

So, we will keep things simple.

I was excited about all the winning I was about to get!!

I will try not to talk a lot in that language.

So if you are scared of probabilities you are fine.

No knowledge of R is required to understand the click at this page />What to expect in this article?

Here are the questions, I will try to answer in this article.

Is it more than 50% as I thought, or was I terribly wrong?

I can certainly use that when I go to Casino the next time.

What would you do?

By now, you strategy blackjack in vegas know that your cards are really poor but do you take another card and expose yourself to the risk of getting burst OR you will take the chance to stay and let the dealer get burst.

Simulation 1 Let us try to calculate the probability of the dealer getting burst.

This function will take input as the initial hand and draw a new card.

There are 6 possible outcomes for the dealers - getting a hard 17, 18,19, 20, 21 or getting burst.

Here is the visit web page distribution given for the first card of the dealer.

The probability of the dealer getting burst is 39.

This means you will loose 60% of times β Is that a good strategy?

With this additional information, we can make refinement to the probability of winning given our 2 cards and dealers 1 card.

Define the set for player's first 2+ sure card sum.

It can be between 12-21.

If the sum was less than 12, player will continuously take more cards till he is in this range.

And if the dealer does not have the same, the Player is definite to win.

The probability of winning for the player sum 12-16 should ideally be equal to the probability of dealer going burst.

Dealer will have to open a new card if it has a sum between 12-16.

This is actually the case which validates that our two simulations are consistent.

To decide whether it is worth opening another card, calls into question what will be the probability to win if player decides to take another card.

Insight 2 β If your sum is more than 17 and dealer gets a card 2-6, odds of winning is in your favor.

This is even without including Ties.

Simulation 3 In this simulation the only change from simulation 2 is that, player will pick one additional card.

Favorable probability table if you choose to draw a card is as follows.

So what did you learn from here.

Is it beneficial to draw a card at 8 + 6 or stay?

Favorable probability without drawing a card at 8 + 6 and dealer has 4 ~ 40% Favorable probability with drawing a card at 8 + 6 and dealer has 4 ~ 43.

Here is the difference of %Favorable events for each of the combination that can help you design a strategy.

Cells highlighted in green are where you need to pick a new card.

Cells highlighted in pink are all stays.

Cells not highlighted are where player can make a random choice, difference in probabilities is indifferent.

blackjack dealer win rate is far lower than the loss rate of the game.

It would have been much better if we just tossed a coin.

The biggest difference is that the dealer wins if both the player and the dealer gets burst.

Insight 3 β Even with the best strategy, a player wins 41% times as against dealer who wins 49% times.

The difference is driven by the tie breaker when both player and dealer goes burst.

This is consistent with our burst table, which shows that probability of the dealer getting burst is 28.

Hence, both the player and the dealer getting burst will be 28.

Deep dive into betting strategy Now we know what is the right gaming strategy, however, even the best gaming strategy can lead you to about 41% wins and 9% ties, leaving you to a big proportion of losses.

Is there a betting strategy that can come to rescue us from this puzzle?

The probability of winning in blackjack is known now.

We know that the strategy that works in a coin toss event will also work in black jack.

However, coin toss event is significantly less computationally intensive.

What got me to thinking was that even though the average value of anyone leaving the casino is same as what one starts with, the percentage times someone becomes bankrupt is much higher than 50%.

Also, if you increase the number of games, the percentage times someone becomes bankrupt increases.

On your lucky days, you can win as much as you can possibly win, and Casino will never stop you saying that Casino is now bankrupt.

So in this biased game between you and Casino, for a non-rigged game, both you and Casino has the expected value of no gain no loss.

But you have a lower bound and Casino has no how to calculate expected value blackjack bound.

So, to pull the expected value down, a high number of people like you have to become bankrupt.

Let us validate this theory through a simuation using the previously defined functions.

Clearly the bankruptcy rate and maximum earning seem correlation.

What it means is that the more games you play, your probability of becoming bankrupt and becoming a millionaire both increases simultaneously.

So, if it is not your super duper lucky day, you will end up loosing everything.

Imagine 10 people P1, P2, P3, P4 β¦.

P10 is most lucky, P9 is second in lineβ¦.

P1 is the most unlucky.

Next in line of bankruptcy is P2 and so on.

In no time, P1 how to calculate expected value blackjack P2 would rob P3.

Casino is just a medium to redistribute wealth if the games are fair and not rigged, which we have already concluded is not the case.

Insight 4 β The more games you play, the chances of your bankruptcy and maximum amount you can win, both increases how to calculate expected value blackjack a fair game which itself is a myth.

Is there a way to control for this bankruptcy in a non-bias game?

What if we make the game fair.

Now this looks fair!

Let us run the same simulation we ran with the earlier strategy.

Again mathematician style β Hence Proved!

The Bankruptcy rate clearly fluctuates around 50%.

You can decrease it even further if you cap your earning at a lower % than 100%.

But sadly, no one can cap their winning when they are in Casino.

And not stopping at 100% makes them more likely to become bankrupt later.

Insight 5 β The only way to win in a Casino is to decide the limit of winning.

On your lucky day, you will actually win that limit.

If you do otherwise, you will be bankrupt even in your most lucky day.

Exercise 1 Level : Low β If you set your higher limit of earning as 50% instead of 100%, at what % will your bankruptcy rate reach a stagnation?

Exercise 2 Level : High β Martingale is a famous betting strategy.

The rule is simple, whenever you loose, you make the bet twice of more info last bet.

Once you win, you come back to the original minimum bet.

You win 3 games and then you loose 3 games and finally you win 1 game.

For such a betting strategy, find: a.

If the expected value of winning changes?

Does probability of winning here at the end of a series of game?

Is this strategy any better than our constant value strategy without any upper bound?

Talk about bankruptcy rate, expect value at the end of series, probability to win more games, highest earning potential.

High number of matches can be as high as 500, low number of matches can be as low as 10.

Exercise 3 Level β Medium β For the Martingale strategy, does it make sense to put a cap on earning at 100% to decrease the chances of bankruptcy?

Is this strategy any better than our constant value strategy with 100% upper bound with constant betting?

Talk about bankruptcy rate, expect value at the end of series, probability to win check this out games, highest earning potential.

End Notes Casinos how to calculate expected value blackjack the best place to apply concepts of mathematics and the worst place to test these concepts.

As most of the games are rigged, you will only have fair chances to win while playing against other players, in games like Poker.

If there was one thing you want to take away from this article before entering a Casino, that will be always fix the upper bound to %earning.

You might think that this is against your winning streak, however, this is the only way to play a level game with Casino.

I hope you enjoyed reading this articl.

If you use these strategies next time you visit a Casino I bet you will find them extremely helpful.

If you have any doubts feel free to post them below.

Now, I am sure you are excited enough to solve the three examples referred in this article.

Make sure you share your answers with us in the comment section.

You can also read this article on Analytics Vidhya's Android APP Tavish Srivastava, co-founder and Chief Strategy Officer of Analytics Vidhya, is an IIT Madras graduate and a passionate data-science professional with 8+ years of diverse experience in markets including the US, India and Singapore, domains including Digital Acquisitions, Customer Servicing and Customer Management, and industry including Retail Banking, Credit Cards and Insurance.

He is fascinated by the idea of artificial intelligence inspired by human intelligence and enjoys every discussion, theory or even movie related to this idea.

This article is quite old and you might not get a prompt response from the author.

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The odds in a casino are not in line with the odds of winning.

Or we could just go random as well in the game and yet come out even every time.