standard deviation q
  • coudl anyone explain how standard deviation is derived from expected percentages. example: a coin toss being 50/50 proposition, over 100 flips it is unlikely to be exactly 50/50. how is the deviation determined? what would it be in the coin toss case? a blackjack shoe where im expecting to win 43% of the time? any help is appreciated as i am mathmatically inept.
  • Drew- SD or luck is not predictable in the usual sense. However, you can
    predict the probability of being able to tolerate the swings for a certain
    bet size and for x time period. These calculations are related to the win
    rate of 50/50, 43/47 or whatever. The greater your bankroll the greater
    your chances of staying within the SD for a given timeframe.

    Post # 50 by SAGE gives a good overview of how this relates to blackjack
    and the calculations to determine probability.

    Ray
  • You need to know your bet size for standard deviation. Ray makes a good point, standard deviation is different from win rate or expected percentages and is determined by bet size for a given time period.

    Example for flat betting 100 coin tosses at $10

    1. (Square each bet size) x (number of hands played at that bet size)
    ($10 x $10) x 100 = 10,000

    2. Take the square root of that number and multiply by 1.1
    square root of 10,000 = 100 x 1.1 = 110

    3. Divide this number by the square root of total hands played
    110 / (square root of 100) = 110 / 10 = 11

    11 is your standard deviation per hand

    4. multiply standard deviation per hand times the square root of the number of hands
    11 x (square root of 100) = 11 x 10 = $110

    In this example one standard deviation is $110 or 11 units. Two standard deviations is $220 or 22 units.

    Example for 100 hands of blackjack
    (50 hands at $10, 25 hands at $20, 25 hands at $30)

    1. (10 x 10 x 50) + (20 x 20 x 25) + (30 x 30 x 25) = 5000 + 10000 + 25000 = 40,000
    2. square root of 40,000 = 200 x 1.1 = 220
    3. 220 / (square root of 100) = 220 / 10 = 22
    4. 22 x (square root of 100) = 22 x 10 = 220

    One standard deviation is $220, two deviations is $440.

    You can use SD to determine how much to bring to the casino for a session. For flat betting its easy to figure out. A counter can use expected frequency distributions to determine bet size and SD. For progressions its more difficult because you can't predict what kind of streaks you'll have what your average bet size will be, although you could make an educated guess and be close enough.
  • If I were a progression player of 10-20-30-40-50, I think I'd use the method above with an average bet size of 25. Why 25? You most
    likely will be spending over 90% of your time at the 1,2,3 levels, but
    mostly at the 1,2 level. The extra five bucks allows for the occasional
    3rd level. How about the 4th and 5th levels you say? Well, those are
    few and far between.
  • ah thank you. very very helpful. you guys are total eggheads (and i mean that in the best possible sense).
  • I seem to remember a simple rule for figuring sigma... 2/3 of all the data points lie within 1/3 total variance (+ - 1/6) is this about right? What would be the correct %. Seems like it must be close to 70%

    N&B
  • If you want to apply standard deviation more precisely to your blackjack game then you'll need to know the EV of the game your playing.

    Lets say you flat bet $10 playing with a -.5% EV. If you played 100 hands (using perfect basic strategy) you'd expect to lose $5.

    So using SD from first example above then one standard deviation would be a range of (-$5 - $110) = -$115 to (-$5 + $110) = $105.
  • There are many hands in blackjack where a large bankroll is required to justify the correct basic strategy play. My classis example would be Ace-2 vs. 5.

    DOUBLE has an expectation of +13.635987% and Variance = 3.8026169
    HIT has an expectation of +13.633091% and Variance = 0.9305211

    Notice that while doubling is a "better" play, it isn't the best approach, but causes a huge variance. The player should hit, not double. Another example would be when you get 88 vs. 9/T/A, you split and resplit up to four hands. The process caries a huge variance within. The player should surrender rather then splitting.
    .

    There are several factors that effect your standard deviation or variance for that matter. I suggest that you make your insurance play very accurately when you have a potentially winning hand like A8, A9, TT, BJ, 11 (56,74,92) or 10 (55,64,73,82) If you win at least half of your bet every time you get a 19, 20 or a full bet when getting a BJ vs. the dealer's ACE you will offset the balance on your side.
    Do not ever over bet your bankroll. Do NOT make strategy plays that require marginal splits or double downs. Seek out games that offer Surrender.
  • Notice that while doubling is a "better" play, it isn't the best approach, but causes a huge variance. The player should hit, not double. Another example would be when you get 88 vs. 9/T/A, you split and resplit up to four hands. The process caries a huge variance within. The player should surrender rather then splitting.

    .

    If that is true, why does the basic strategy chart at blackjackinfo.com indicate double down A2 v dealer 5 and 6, and ALWAYS split 8"s even when dealer shows 9/10/A?
  • AlexD30,
    I have read that you should NOT insure a TT since you have already removed from the deck two cards which could help the dealer make her BJ, thus reducing her percentages. It has been said that TT is the absolute worst hand to insure. I see it happening all the time when I play. Are you talking about advantage plays as a counter as opposed to basic strategy for a non-counter? Would there be a difference, anyway, in how you play those hands mentioned above?
  • Hi PJ,

    Well, The mathematics of Basic Strategy doesn’t take into account the bankroll. It doesn’t take into account the VARIANCE or for that matter the Standard Deviation. It only take into account which method of play loses less or wins more over the long run when the player is flat betting.

    Now, in the case of A2 vs. 5 up card and for that matter for other plays the difference in profit between doubling down vs. hitting is minuscule while the standard deviation is HUGE during doubling.

    For example for every $100,000 action, for you to win an extra $2.89, you will have to double down instead of just hitting. But when you double the math says you have to be prepared to absorb $3,802 variance. Are you willing to put at risk $3,802 for $2,89 extra profit :?:

    For the case of Insurance when you have TT vs. A, this play is kind of more delicate. Obviously if you do not count and only flat bet the game and do not have any idea of the value of remaining cards to be played you probably should not insure. On the other hand, if you bet by the count and have a max bet out you obviously will insure because the count is very elevated. That’s why you have the max out :!: - Right :?:

    Now, if you play some kind of progression and got lucky to reach a high betting level , I would definitely insure a TT vs. Ace, to make sure that if the dealer has a BJ, I push, or I win unless he’s got a 9 in the hole where in that case I lose half the bet. So, I’m risking half bet to make sure I will have at least half bet profit. Matter of fact this play is better then splitting 8,8 vs. T in most circumstances when one is risking two bets without any hope against the T up card.
  • Alex – You are throwing numbers around like there is no tomorrow, so I really don’t know where to start…….It appears you are using these figures as “stand alone” numbers and not relating them to “real play”, which of course doesn’t prove anything.

    Let me try to explain with your statement about A-2 vs 5…….you said:

    “Notice that while doubling is a "better" play, it isn't the best approach, but causes a huge variance.”

    The key word here is your use of “huge”. In “real play”, you will get A-2 vs 5 about 1 time every 1,000 hands (once every ten hours)………Now let’s say your average bet is $10 (let’s make it easy). You play the 1,000 hands, get the A-2 vs 5 once and don’t double, so your “turn” is $10,000……..Keeping everything else the same, you play the same hands, except this time you double that hand……so your “turn” is now $10,010.

    With all due respect, I do not see how anyone can call a difference of $10 over a total bet of $10,000 a “huge variance”.

    Regards……Grifter

    p.s. to all: Do not deviate from basic strategy (unless for reasons of a count)......Size your bankroll to include the SD of your method.
  • Touche.. grif... you just don't get that hand often enough for it to make much difference unless you're simming 100 lifetimes of 9-5 Mon-Fri 50 weeks a year for 50 years at 100 hands per hour. If you play 100,000 hands in your lifetime, the hundred bets on A2v5 is a swing of what... 3 units?

    N&B
  • I think most long term players use SD as an initial guide in determining
    their bankroll requirements, but over a period of time, adjust those
    requirements based on individual experience. A typical 4 hr. session
    for a moderate green player with an average bet of $50 at 60 hands
    an hour is a good example. One SD = 800, so at two SD we need 1600
    which is about right, but not all players play the same strategy and they
    don't play the same game and one rule don't fit all. Grifter said it best;
    know what's what for the game your playing and further, know your own
    "EXPERIENCE".

    One question for the board: Do you think it makes any sense at all to
    develop your own variations to basic stratey, when the best possible way
    to play the game was detemined 30 years ago and remains true today?
  • Ray said:
    I think most long term players use SD as an initial guide in determining
    their bankroll requirements, but over a period of time, adjust those
    requirements based on individual experience. A typical 4 hr. session
    for a moderate green player with an average bet of $50 at 60 hands
    an hour is a good example. One SD = 800, so at two SD we need 1600
    which is about right, but not all players play the same strategy and they
    don't play the same game and one rule don't fit all. Grifter said it best;
    know what's what for the game your playing and further, know your own
    "EXPERIENCE".

    One question for the board: Do you think it makes any sense at all to
    develop your own variations to basic stratey, when the best possible way
    to play the game was detemined 30 years ago and remains true today?


    The only thing I can say is that my betting and playing system will extract more money over and over in short sessions then any other card counting system ever devised. Obviously my sort runs will add up to the long run. I am into the 25 years long run and still making money steadily.

    Moreover, in 1982 I challenged Kenny Uston to play his APC (advanced point count system) against mine for one hour in Caesars Las Vegas. The deal was that one would play for an hour and record the hands then we would go over the hands and play them both ways. We agree that the player that makes more money during that hour will get from the other one $100,000. He initially agreed, once he and his business associate studied my betting system, he agreed that I will win more in that short run than his system, backed out of the deal and admitted my system would beat his betting system based on card counting.
  • Ray: I think it does when you bet more than 1 unit INITIALLY. As I've posted previous, my thoughts are that the phrases 'Basic Strategy' and 'varying the bet' are mutually exclusive terms. When you vary the bet playing Basic, you are exposed to greater risk than Basic presumes, and MUST manage financial variance.

    Having said that, when one DOES wager 1 unit, and plays Basic, the strategy presented for the conditions are the best plays to make.

    N&B
  • DOUBLE has an expectation of +13.635987% and Variance = 3.8026169
    HIT has an expectation of +13.633091% and Variance = 0.9305211


    Grif, with all due respect, as you can see the variance goes from 0.9305211 when you hit to 3.8026169 when doubling down. It gets 4.087 times higher. I must state again, If you put in action 100K when you have A2 vs. 5 over the long run, you in fact bet at risk $3,800 to make $2.89

    Just look at the expectations and figure out how much “better” are you if you double and compare with the rate of how great the variance become. Would you risk in a Martingale system on any game a total action of $3,800 just to make an extra $2.89 :?:

    Would you bet Martingale starting from $3 for the next 10 rounds when you lose every hand while the total action gets to $3,072 when you finally win that last hand and make a profit of $3 :?:
  • Alex – Did you totally ignore my post above about the A2 vs 5 in “real play”? I honestly think you are still looking at the ‘tree’ instead of the ‘forest’; or the ‘big picture’ of real play.

    As I posted yesterday, no matter how you slice it the deviation in your total turn for that particular play is going to be one average bet per 1,000 hands.......If that still bothers you, then by all means don’t make the play; it is extremely marginal anyway….but it is not the correct way to play.
    …………………………………………

    Sure, we can look at your $100,000 action for this play if you want, but let’s also look at it in “real play” instead of a “stand alone” number. And let’s make it really “real” for this forum……Let’s make our player a member of this group. My SWAG for the average player on this board would be an average bet of $10 and he is lucky if he averages 50 hours per year in a casino.
    1. The bet per hand is $10, therefore ……….
    2. It will take 10,000 bets to get a turn of $100,000, and we know…...
    3. He/she will get the hand 1 time in every 1,000 hands; therefore….
    4. It will take 10,000,000 hands to get a total turn of $100,000, and we know….
    5. We will average 100 hands per hour; therefore……
    6. It will take 100,000 hours to play those hands, and we know…..
    7. Our player is going to play 50 hours per year, therefore………
    8. He/she will have your $100,000 total turn in 2,000 years of play.

    Kinda’ makes that “huge” variance rather insignificant, doesn’t it?

    …………………………………….

    And finally, and this is my last post on the A2 vs 5…..

    AlexD30 said:
    Would you bet Martingale starting from $3 for the next 10 rounds when you lose every hand while the total action gets to $3,072 when you finally win that last hand and make a profit of $3 :?:


    Assuming your example is static and re-occurring………

    Absolutely I would make that bet :!: ………………….Why wouldn’t you :?:

    Your “Win Rate” would be $30/hour with a $3 base unit. That is fantastic!. And our average player above who uses a $10 unit would probably do this……

    Play 6 hours a day, 5 days a week, for 50 weeks a year……….and make:

    $150,000.00 per year!!................Where can I find that game? 8)

    Regards.....Grifter

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