See the top rated post in this thread. Click here

Results 1 to 13 of 24

Thread: What is the fastest way to get to the long run in Blackjack?

Hybrid View

Previous Post Previous Post   Next Post Next Post
  1. #1


    Did you find this post helpful? Yes | No
    Brh

    Help me here
    Is N0 a measure of the long run?

    Does N0 refer to a 13.53% fixed ror?
    Or
    Does it refer to Kelly resizing?

    Doesn't N0 or the long run go up about 4 times
    Fixed betting vs Kelly resizing?

    The more frequently one resizes the longer their time horizon, so doesn't that mean a small fraction of Kelly has a shorter time horizon?

    Thanks for your time
    Last edited by blackjack avenger; 10-25-2012 at 09:18 AM.

  2. #2
    Senior Member brh's Avatar
    Join Date
    Oct 2012
    Location
    Melbourne, Australia
    Posts
    284
    Blog Entries
    5


    1 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    Quote Originally Posted by blackjack avenger View Post
    Brh

    Help me here
    Is N0 a measure of the long run?

    Does N0 refer to a 13.53% fixed ror?
    Or
    Does it refer to Kelly resizing?

    Doesn't N0 or the long run go up about 4 times
    Fixed betting vs Kelly resizing?

    Thanks for your time
    BA,

    Yes NO is a measure of the long run, but (see my response above) it technically refers to an individual game,
    with a particular count, a fixed (1 - M) UNIT spread (that is for example 1, 2, 3, 4, 5 per count value for a 1-5
    spread - it's usually more complicated than that for an Optimal spread such as 3.34 etc by stay with me),
    and a Wonging strategy such as "leave at all counts less than -1". NO is minimised when the exact
    1-M spread is found for these conditions is found. As I alluded to above, the intermediate bets will
    be fractional, such as 3.34 etc. the minimum bet will still be 1, the maximum bet will still be 5 in the above
    example, it will tell you when you should bet the maxim, such as TC=+6, and when you are Wonging
    your bet is 0.

    At this stage, there is no money involved.

    The same game as described above generates another parameter called "ekb" or Equivalent Kelly Bankroll.

    Together (N0,ekb) characterise the optimal spread for this "game".

    N0 has no effect on the ROR, what it does tell you is how many rounds it will tel you to have an ev = ekb.

    It is ekb which is critical for ROR - it tells you how to calculate you monetary unit bet $B, which will be
    your minimum bet in the real world should be in the real world for a given ROR.

    Just say for some six deck game, we have a 1-10 spread, leave at Hilo TC=-1.
    Typically for a game like this, N0 will be 40000 rounds and ekb will be 500 units.

    Say you have a $10000 bankroll:

    If we divide $10000 by N0 and multiply by 100 we get SCORE = 10000/40000 x 100 = $25.

    If divide $10000 by ekb we get $B = $10000/500 = $20.

    That is your betting scheme will be $20 - $200.

    Now let's go in reverse and multiply ekb by $B: $B x ekb = $20 x 500 = $10000. This is called the EKB - your
    actual Equivalent Kelly Bankroll.

    If your actual bankroll was $10000, and you spread $20 -$200 your ROR would be 13.53%,
    That's why we call $10000 the EKB. Notice that the ROR does not depend on N0.

    Once you know the EKB you can calculate your Kelly fraction.

    In this case, for a real bankroll of $20000 your Kelly fraction would be k = EKB/$20000 = 0.5 and your ROR = 5%.

    I can understand this is quite difficult and you really need a simulator to work it all out.

    Luckily we have the "veritable" Norm, so with a laptop and CVCX it will do it all for you.

    As Tthree says, you can play with the CVCX tool on this site.

    Cheers,
    Brett.

  3. #3


    Did you find this post helpful? Yes | No
    I haven't looked at this area of BJ in a while si I might not give the most intelligent answer . But in mind, N0 is the number of rounds after which the accumulated expectation is equal to the accumulated standard deviation. I personally prefer N0 because in order to calculate it all you need is the expectation value and standard deviation (in fact i was so fascinated with standard deviation, that I wrote a CA that calculates both the expectation value and standard deviation). N0 is the measure of overall intrinsic advantage of the game you are playing, which includes number of decks, casino rules, penetration, playing strategy, betting strategy. Kelly fraction, ROR etc... has nothing to do with the "juiciness" of the game you are playing. The only relationship is that the juicier is the game (i.e the lower the N0) you will make more money for the same risk.
    Chance favors the prepared mind

  4. #4
    Senior Member Anton Chigurh's Avatar
    Join Date
    Dec 2011
    Location
    Eagle Pass, TX
    Posts
    190


    Did you find this post helpful? Yes | No
    Quote Originally Posted by blackjack avenger View Post
    The more frequently one resizes the longer their time horizon, so doesn't that mean a small fraction of Kelly has a shorter time horizon?
    N0 is the number of hands at which your EV for that number of hands equals one standard deviation for that number of hands.

    For any number of hands, both EV and standard deviation are directly proportional to bet level, assuming all bets in your ramp are multiplied by the same constant. So if you spread 10-200 on odd-numbered days and spread 25-500 on even-numbered days, except for the 29th of each month, when you spread 100-2000, your N0 will not change, even though your EV and standard deviation will, and your chances of achieving negative bankroll will be higher or lower accordingly.

    Multiplying all bets by 1/2 cuts EV by 1/2 and standard deviation by 1/2, and hence has no effect on N0.

Similar Threads

  1. playing too long at a place you have ploppy history
    By Goatlife in forum General Blackjack Forum
    Replies: 4
    Last Post: 06-12-2012, 01:45 PM
  2. No Heat - how long would you play
    By Some Action in forum General Blackjack Forum
    Replies: 3
    Last Post: 05-13-2012, 02:03 PM
  3. It seems like a long shot, but....
    By blackjackomaha in forum General Blackjack Forum
    Replies: 17
    Last Post: 01-26-2012, 05:03 PM

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  

About Blackjack: The Forum

BJTF is an advantage player site based on the principles of comity. That is, civil and considerate behavior for the mutual benefit of all involved. The goal of advantage play is the legal extraction of funds from gaming establishments by gaining a mathematic advantage and developing the skills required to use that advantage. To maximize our success, it is important to understand that we are all on the same side. Personal conflicts simply get in the way of our goals.