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What is Expected Value

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If you can begin to understand “Expected Value” and how it effects the entire casino industry, then you are well on your way to understand how you can take the advantage away from casinos and have a long lasting card counting career.

Video Transcription

This next concept is going to completely change the way that you look at casinos. In fact if you come to understand this next concept you will never be able to walk into a casino again and see it the same way. Because the concept of EV or ‘Expected Value’ is what runs the entire casino industry. And in fact will run the entire way that we operate as card counters or professional blackjack players.

So let’s get into what EV is. EV stands for ‘Expected Value.’ Now, Expected Value is the amount that you expect to make over a given time period. It’s based upon mathematical variables and equations that are not expected to change.

In order to understand this we have to kind of look at what EV is not. Now what EV is not is the amount that you actually win or lose. Which this is a huge difference between how most gamblers view their playing blackjack or gambling as how investors or card counters do. A card counter needs to base all of their decisions on the mathematical expectation of what you expect to make. Very similar to how a casino operates. When a customer walks into a casino and wins $100, the casino’s not concerned. In fact usually they are excited because they know that in the long run they expected to make money off of that player. And even in the short run they did. So the outcome or the variables that are always changing have very little to do with how a casino bases their performance.

So let’s get into an example. Now if we have a coin and we flip it the chance of it landing on heads in 50% or one half. Now it’s really important to distinguish that it’s not actually going to land half on heads and half on tails. It’s going to land on one or the other but the EV is one half or 50%. So Similarly in blackjack we could walk into a casino and expect to make $200. Now, almost never are we actually going to make exactly $200 in one hour. Chances are we will walk up plus $400 or plus $1,000 or minus $10 or minus $30, but in the long run we’ll expect to make $200 an hour.

The bottom line is EV is always going to be different from what happens in real life, but the mathematical concepts behind EV are really important to understand. Because the longer you play blackjack the closer you will come to EV. So EV is a pretty complicated concept and we’ll get into more about how it affects your blackjack play later. Because the more you understand it the more successful blackjack player you’re gonna be.


19 Responses to “What is Expected Value”

  1. Grant says:

    Hi Ben/Colin,

    I know you and companies sell software that calculates the EV, but how do I calculate it manually? Do I just say I want to make R100 / hour (I’m South African) or is there a set method?

    Many Thanks

  2. admin says:

    EV is calculated off of simulations that run Billions of hands of blackjack using the specified bet spread. The more you use the software, the easier it is to ballpark EV in your head, but that is really just based from experience using the simulator. So to answer your question directly, EV is most accurately calculated using computer simulations. There really is no effective way to calculate EV manually.

  3. Shomy says:

    Hah… I get it… With the coin example… If you toss it 10 times theoretically it should land 50% tails 50% heads, but it won’t…. But if we toss it long enough then we will have that relation (50:50)….

  4. Joel says:

    Just to add to Shomy’s comment: using knowledge from Calculus 1, EV seems to follow the properties of limits. As the number of coin tosses approaches infinity, you get the 50:50 split for heads and tails. Taking this concept to blackjack, it would mean that you simply have to play more to guess watch your EV is….

    According to the admin, EV can only be measured exactly on a simulator, because it will have all of the parameters defined. Since blackjack is in the real world, all the variables involved are not fixed, let alone known. Still, I find it difficult for one to estimate EV if there aren’t any parameters to work with…

  5. Big Bart Sanger says:

    Refreshing Videos! I’m an oooollldd Guy and have dabbled at playing Blackjack for years with only modest ‘success’. I’ve read many books on the subject, tried many ‘systems’ and ‘count Patterns’, both at home with pencil/paper/calcs AND atvarous small & big Casinos (mostly here in Las Vegas).
    YET several of your Videos a startled me with practical advice whic I have somehow ‘overlooked’! Most of all, your video on the difference between ‘Gambling’ versus ‘Investing’ attitudes has freed me of the whispering ‘Guilt’ felt all these years that I’ve been ‘dabbling’ (cautiously; i.e. never played past a loss of more than $100 or a Win of more than $200).
    Now I have ‘invented’ some Real Card/Flash Card Decks which are designed to refresh my Basics of Strategy more naturally.
    SO what? Well thanks for your website (amongst the many).

  6. Big Bart Sanger says:

    P.S. I forgot to say I’m interested in BJ ‘Team’ play but fear my modest experience & more modest Soc Sec Income Limitations may prevent such a pastime. Any suggestions?

  7. colin says:

    Welcome to the site, Big Bart!

  8. colin says:

    Start with step 1… mastering basic strategy. Then counting, then playing BS while counting, then deviations and betting. When you’ve established yourself as a successful counter, then think about starting or getting involved with a team. But first things first.


  9. Josh says:

    Hello Awesome Blackjack people!

    I am still very much at the beginning here. (Still working on Basic Strategy). But, something came to mind about using variance to your advantage. Maybe this is obvious (or wrong) but I just wanted to check. It seems that if you happen (through short term variance) to be “up” move than your EV for the given amount of time you want to play, you should stop. For example, if I was a rock star like Colin or Ben and my EV was $500 an hour and I wanted to play 3 hours…It would seem that if I ever happen to be up OVER $1500 it would be a good time to stop since my EV for that same amount of time is $1500. Again, just beginning here and this might be talked about more in the forums but I am still bring to get my basic strategy perfected. Also, I saw Colin had suggested in number 8 to practice counting before memorizing the deviations. Is that always recommended? Thanks again!

  10. colin says:


    We do have a video on this, but it’s probably in the member’s section.

    So first off, there are no bad questions, but yeah, this is bad logic. (; You have to treat your entire career like one never-ending session. If you’re above EV after an hour, the next shoe is still worth the same amount of EV as it would be worth if you were down $1500. Each hand and each shoe has a value, and you need to start thinking that way. How much you win or lose in an hour needs to stay divorced from the task of “Generating EV”. So If you’re up $100,000 when you’ve only generated $1500 of EV, that’s not a good reason to stop. It might be a good time to stop for other reasons (you’re tired, losing of focus, you want to avoid heat from the casino by winning too much at one time). But “tricking the cards” by stopping when you’re ahead is not a good reason to stop.

    Hope that helps.

    Oh yeah, and follow my advice about the order of training… basic strategy, basic while counting, then start adding deviations and betting.

  11. Josh says:

    Colin -

    Thanks so much. I have not taken probability since 8th Grade! I totally forgot that. This is why you are the Money Maker! By the way, have I told you that you are my new favorite person in the world? If you are ever in Chicago I would be honored to buy you a beer. Gotta get back to Basic Strategy Practice! Running about 97% but I still have to stop and think about some of the soft totals and some of the splits. Damn You A,6 and 6,6!!!

  12. Tom Andre Nilsen says:

    I am so lost now! Ok is + bad or good? Is – bad or good?

    Lets say I have +17. Is this good or bad?

    The higher +19 or good? I should hit?
    or – is good? I have – 3 I should hit?

    I understand the hi-lo rule but I dont understand what is good and what is bad! + or – ?

    I just took a look at the basic

    but + and – confuses me! Someone please explain. Admin please send a mail to my mail.

  13. Colin says:

    A positive count is good. A negative count is bad. This tells you when the advantage shifts from casino to player.

  14. Shane says:

    Sorry I have made mistake in my quiere. If the dealer takes 11 cards out of the pay in the begining and only plays half of the cards in the shoue how can we have an accurate count. Since you have said only a 100% accurate card counter can bead the game and not a 99%. Please explain

  15. Colin says:


    If the dealer cuts off more than 2 decks from a 6 or 8 deck shoe, then the game isn’t worth playing. If they cut off 2 decks or less, then it’s beatable (assuming the rules are decent).

    That being the case, YOUR skills must be 100%. If you get off on the running count, then you can’t beat the game. That’s what we mean by a 100% accurate card counter. A 100% accurate card counter can beat a blackjack game with acceptable rules and where they deal out at least 4 of 6 decks or 6 of 8 decks.

    Hope that helps clarify what we mean.

    Best regards,

  16. Shane says:

    Dear Colin,

    over here in Sri Lanka they cut off the game in appoximatly 3 deacks. And the dealer draws 11 cards when he starts. So its impposible to have an accurate count or to beat the game. Can you name some cities who go on playing untill at leat 4 to 5 deacks.


  17. Colin says:


    I’ve never played in Sri Lanka. Sorry man.

  18. Jay says:

    I just sent you an e-mail via “info@blackjackapprenticeship.com” regarding interest in attending your boot camp and some questions. If you have the time, it would mean the world to me if you could respond to the e-mail. Thanks and God bless!

  19. Colin says:

    We’re trying to take the weekend off, but one of us will get to our email on Monday!