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Thread: Quantifying Long Run for Counters

  1. #1

    Default Quantifying Long Run for Counters

    Originally posted by 'Sonny' at Ken Smith's BJINFO HERE

    How long is the "long run"?

    That’s a great question.
    Most players know that they are playing for the “long run” but they have no idea how long it takes to get there (or, at least, reasonably close).
    While the outcome of a few hours of play is fairly uncertain (within the limits of Standard Deviation). In fact, the results after several hundred hours of play are still subject to variance. So how long will we have to play before we have a reasonable chance of reaching our EV? Well, there are two different ways to look at it.

    N0 (N-zero)

    As you know, variance will sometimes be positive and other times be negative. In the long run we expect the “lucky” and “unlucky” times to cancel each other out so that we are left with our EV. The N0 formula will tell us how many hands (or hours) we will have to play in order to overcome the variance. A simplified version of the formula is:

    N0 = SD^2/EV^2

    So if your hourly EV is 1.5 units and your hourly SD is 28 units you will get:
    N0 = 28^2/1.5^2 = 784/2.25 = 348.44

    You would have to play for 348 hours (at 100 hands per hour) to overcome one SD (about 68% of the variance). You can expand this to two SDs (about 93%) by multiplying by 4 (the same as 2^2).

    That would give you about 1,394 hours of play to have a very good chance of reaching your EV. That’s a lot of playing! If you played for 10 hours every week it would take you over 2.5 years to get close to the long run. That’s pretty discouraging for recreational players, but fear not – there are ways to improve the situation.
    N0 is basically a comparison of EV to SD. If you can raise your EV, relative to your SD, then you can save yourself some time. By playing more aggressively (Wonging out, backcounting, using a more optimal bet spread, spreading to multiple hands, etc.) you can either increase your EV, reduce your SD, or both! Look what happens when we make a small change to our playing style”

    N0 = 676/3.24 = 209
    4N0 = 835

    Our 4N0 is only 835 hours instead of 1,394. We’ve saved ourselves 559 hours of our lives! That’s over a year that we can spend away from the dark, smoky casinos. Early retirement anyone?
    But that’s still over 1.5 years of play. That’s still pretty discouraging, especially if we don’t play that often. Isn’t there a formula for people who only play a few times a year?


    Most recreational players do not rely on their BJ winnings for their livelihood. They just want to win a little money on the side. Sure, it can feel disheartening to look back on a year’s worth of play and only see a $100 profit, but it sure beats losing!

    For players like this there is a formula for calculating the probability that you will be ahead (by any amount) after a given number of hours of play. This number is often much more encouraging because the probability of being richer, even if only by $1, is much higher than reaching your precise EV.

    The formula for this is a bit more complicated. The formula is HERE

    In this case, with an EV of 1.8 units and a SD of 26 units your probability of being ahead is roughly:


    Now that’s a lot better, right? You have about a 60% chance of winning any given month. After 1 year of play (10 hours per week, 520 hours per year) you won’t get all the way to the long run, but you will overcome most of the variance and have over a 94% chance of being ahead. It ain’t perfect, but that’s about as much security as you’re going to get in the gambling world.

    This is another reason why it is crucial to understand optimal betting strategies. Sometimes a little change in your bet spread or playing style can add up to a huge improvement in your N0. After all, what good is a healthy EV if you never have a chance to get it?

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  2. #2


    It would take a lot of time to commit to playing 10 hours a week under my circumstances because of the constant traveling, but 10 hours a week really isn't a lot of time at all. If a person has the time and the bankroll to commit to playing 20-40 hours a week, that seems reasonable to getting to the long run faster as long as the player hasn't lost all their money. With the use of a team, it could be done even faster with more players involved.

  3. #3
    Join Date
    Sep 2017


    Two classic examples. Most people won't have time to play alot of blackjack until they retire.

    I nevet liked the term "long run." Perhaps because so many use it az an excuse for failure.

    I have a buddy that is 77 years old. He is a stud. We played ball togethet back in the early 80s. At that time, he was in his 40s and the rest of us were in our 20s. He still plays in a 75 and over league today. Except the travel demands are too difficult.

    Suppose you play 20 sessions a week at 100 hands per session. At 50 weeks annually, it will take 10 years to get to a million hands. Now, when you run a sim, SCORE will bounce all over the place until you get to around 40 million hands. So the Sims are going to give you the best comparisons of tag value.

    From here, you have to define "your" game. THIS the most crucial piece of the puzzle. The better job done in defining your game makes the long run a secondary consideration.

  4. #4
    Join Date
    Sep 2017

    Default Short sessions

    I was going to say there is both a memory bias if no records were kept and a response bias as gamblers, which include APs, tend to tell you about and exaggerate wins while being mum about losses.

    T3 writes ^:

    Moses replies:

    Good point T3. Especially on BJTF. For me it's just the opposite. I wish I could forget the losses. Especially, in sports bets. Quite often being so close to a win and then suffering defeat is like a double whammy.

    Another Zee trap starts today about Short Sessions. The over/under on this thread should be 65. But Sonny's post here already provides the best answer.

    One of the things I like most about the Zen Zone is finding resolution without 100 posts. Then it's like WTF did I just read?

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