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Thread: Help me understand EV

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    Senior Member Mr2Project's Avatar
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    Help me understand EV

    Math has not been my strong suit, so i have a little difficulty wraping my head around the concept of EV. When it comes to blackjack is where it gets confusing to me. I understand EV for a coin flip game is .5 for both heads or tails. When it comes in terms of bj game where is the EV either negative or positive coming from? Is it a constantly changing variable due to the hands that are dealt or can it be static based on the rules of the game? Is there a book that is recommended that will help me understand this more?

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    Senior Member bigplayer's Avatar
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    If you're keeping track of the cards as they are played EV is dynamic, it changes from round to round. If you aren't keeping track of the cards EV is static based on the rules of the game and number of decks in play. Pick up a copy of Stanford Wong's Professional Blackjack.

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    Mathematicians would use the term "expectation" instead of "expected value." Expectation is nothing more or less than the AVERAGE value of a random variable that has a known distribution. If you place a bet at blackjack, the result of that bet (your win or loss) can be represented by a random variable. This is a variable that can take any of a number of values. You won't know what the value will be until the hand is over. However, the factors that will determine that value are known--the random selection of cards that will make up your hand and the dealer's hand, and the strategy that you will follow. Therefore, if you specify the composition of the deck and your strategy--for example, correct basic strategy--up front, the distribution of results--that is to say, all of the values that your result can take, and the frequency of each of those values--is determinable.

    In the case of a fair coin flip, it's very easy to wrap your mind around the physical process that determines the distribution of results. It's easy to realize that the probability of the coin landing with heads up is 50%, and that the probability of it landing with tails up is 50%. From that, you can easily calculate the expectation of a bet on, say, heads.

    In the case of blackjack, the physical processes that determine the distribution of results are vastly more complex. It's no small task to do a direct calculation of the distribution of results, assuming that you are starting with a full deck and will play basic strategy. However, computer simulations using sample sizes of millions of hands can give us a very close approximation of that distribution. Once the distribution is known, calculating the expectation is straightforward.

    If you are varying your bet size, and are changing your strategy, from hand to hand as the composition of the deck changes, once again the task becomes more complex. But once again, simulations come to the rescue. Simulations can take into account that the player will increase bets according to a specified ramp when the count is high, and will decrease them when it is low, and the player will vary play strategy according to the count. Once again, the aggregate output of a large simulation will be a very close approximation of the true distribution of results, given these parameters. Once again, the expectation for those parameters is just the average of that distribution.
    Last edited by WRX; 11-10-2012 at 11:39 PM.

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    WRX is on the money, but if you are still having trouble with your original question, consider this:

    When you flip a coin, the probability of heads is 0.5, and the same for tails. However, it doesn't really make sense to ask what the 'expected value' of the coin flip is. What you CAN say is "the expected value of the NUMBER of heads I will see in this coin flip is 0.5". That's basically saying if you flipped the coin a bunch of times, you'd see about 0.5 heads per flip (and the same for tails). The more times you flip, the more likely it is that you will get results which are similar to that number.

    In Blackjack, the expectation of a bet is the expected amount of money you'll win or lose if you make that bet. Another way of saying that is "the average amount of money you'll win or lose per bet if you make the bet a really large number of times (approximately)."

    So, if you're playing just using basic strategy, your expectation every time you make a bet is something like -0.004 units, where 1 unit is the amount you're betting. It varies depending on the rules, but that's about how much money the casino makes on average from every hand played using basic strategy. If you count cards, you gain extra information about hands where you're likely to win more money, so with that new information you can say that those hands have a different expectation (maybe +0.01, maybe even more). That's just saying "if I could play a large number of hands at exactly this count, this is the average amount of money I'd make per hand".

    As the above post points out, expectation can be calculated using the laws of probability - and when that gets complicated, computer simulations give good estimates.

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    Actually the probability of a coin-flip is rarely 50%.

    It is usually closer to 51% for TAILS, as most coins are heavier weighted on the HEADS side.

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    Quote Originally Posted by Mr2Project View Post
    Math has not been my strong suit, so i have a little difficulty wraping my head around the concept of EV. When it comes to blackjack is where it gets confusing to me. I understand EV for a coin flip game is .5 for both heads or tails. When it comes in terms of bj game where is the EV either negative or positive coming from? Is it a constantly changing variable due to the hands that are dealt or can it be static based on the rules of the game? Is there a book that is recommended that will help me understand this more?
    An example may make it easier to understand.
    if you receive a hand of 20 at the beginning of a shoe, it has very little value because it wasn't predictable.
    If you receive the same hand, at or near the end of the shoe, and the count is high, the hand is of a higher value, because it was more predictable, and encourages you to bet a higher amount from your bankroll. Thus Expected Value.

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    Senior Member Mr2Project's Avatar
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    So where would the positive and negative expectations come from?

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    Quote Originally Posted by ZenMaster_Flash View Post
    Actually the probability of a coin-flip is rarely 50%.

    It is usually closer to 51% for TAILS, as most coins are heavier weighted on the HEADS side.
    Yep, The coin flip is a unfair proposition...Always choose tails...

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    Quote Originally Posted by Bushido View Post
    Yep, The coin flip is a unfair proposition...Always choose tails...
    Quote Originally Posted by Mr2Project View Post
    So where would the positive and negative expectations come from?
    According to counters, every card removed from the deck or decks, will increase or decrease your chances of getting a winning hand. A high count means the remaining cards are tipped in your favor, you are less likely to get a stiff hand. A positive expectation.
    A minus count means you are more likely to get a stiff hand. A negative expectation.

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