Results 1 to 4 of 4

Thread: VerdugoJohn: Frequency Distribution of Results?

  1. #1
    VerdugoJohn
    Guest

    VerdugoJohn: Frequency Distribution of Results?

    How does bet spreading and counting effect the range of outcomes for playing a typical shoe game?
    I would expect counting with bet ramping to alter the distribution of results from a normal distribution attained from a flat bet basic strategy approach to something different.

    I've read often quoted statistics about blackjack, the average expected win rate and standard deviation, which is approximately 11 times the win rate for a skilled counter. These statistics are the summarization/averages of tens of millions of hands played.

    Those stats are fine, but they really don't help me appreciate fully what is likely to happen to me in the short run--that is while I am playing 10 hours of more over a weekend or two. Ultimately, this all ties into risk a player takes on. But, you folks have addressed so many questions in your years, I think perhaps you might have the answer for this one, and posted it somewhere.

    I wonder if there is any statistics available in a frequency distribution form that would describe range of wins/losses in units for all hands played in shuffle? That is, if I were to play all hands for a million shuffles given a set of criteria, and chart those results on a graph, what would the graph look like? I suspect counting and bet variation alters results from the normal distribution, or bell curve.

    Such a graph would have units loss/won as the X, or horizontal, axis, and number of occurances for that result as the Y, or vertical, axis.

    From what I know about blackjack and statistics, I can make a few predictions for one set of playing rules, conditions and strategies, but I would prefer to see the actual results for only flat betting and basic strategy...what would the graphic or curve look like under other scenarios?

    If I were to play a game with 6 decks, S17, DAS, LS and RSA, play all and flat bet with basic strategy, I would expect the frequency graphic to result in a perfect bell curve (or normal distribution) with the mean (average), median (half-way mark on X axis) and mode (most frequent result or highest point of curve on Y axis) at -.26% units.

    But, if in the same game I use Hi-Lo with I18 and spread to 1-12 as the betting ramps used in Chpt 10 of Blackjack Attack, the mean would shift towards my expected value of 1.26% (which I got from bjstats.com), but where would the median and mode wind up, and how would the shape of the frequency graphic change? Would it still look like a bell curve, or would it become skewed to one side? Would the altitude of the mode change?

    And then of course, how would the graphic change if one played the same game White Rabbit style with a 1-8 spread?

    I guess my feeling when playing blackjack are somewhat like a batter in baseball. When I get a hit (average win) I am happy, when I hit a homer (win big!) I am overflowing, and when I don't reach base (lose) I am discouraged. And most times I will not win and I must count on big wins to offset the more frequent small losses. Thus, seeing some analysis like the above described could help one to cope with the grind of playing and the grief of a losing hand.

    Anyone know of where I could find a table with the above data, or a graphic showing it? (Will this be in BJA3?)

    Thanks

  2. #2
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Frequency Distribution of Results?

    > How does bet spreading and counting effect
    > the range of outcomes for playing a typical
    > shoe game?
    > I would expect counting with bet ramping to
    > alter the distribution of results from a
    > normal distribution attained from a flat bet
    > basic strategy approach to something
    > different.

    No, the results are quite normal -- simply with a positive mean. The third and fourth moments, skew and kurtosis, are virtually nonexistent for blackjack outcomes. In the end, only mean and variance matter, whether you're counting or playing BS.

    > I've read often quoted statistics about
    > blackjack, the average expected win rate and
    > standard deviation, which is approximately
    > 11 times the win rate for a skilled counter.
    > These statistics are the
    > summarization/averages of tens of millions
    > of hands played.

    Eleven (hourly number, not per hand) is for a flat-betting BS player. The ratio can be considerably higher for a counter.

    > Those stats are fine, but they really don't
    > help me appreciate fully what is likely to
    > happen to me in the short run--that is while
    > I am playing 10 hours of more over a weekend
    > or two. Ultimately, this all ties into risk
    > a player takes on. But, you folks have
    > addressed so many questions in your years, I
    > think perhaps you might have the answer for
    > this one, and posted it somewhere.

    We answer it all the time.

    > I wonder if there is any statistics
    > available in a frequency distribution form
    > that would describe range of wins/losses in
    > units for all hands played in shuffle? That
    > is, if I were to play all hands for a
    > million shuffles given a set of criteria,
    > and chart those results on a graph, what
    > would the graph look like? I suspect
    > counting and bet variation alters results
    > from the normal distribution, or bell curve.

    See above. The curve will be quite normal. The Chapter 10 charts of BJA3 give e.v.s (means) and s.d.s (standard deviations) for hundreds upon hundreds of scenarios. They are all you need to construct the distributions you're looking for.

    > Such a graph would have units loss/won as
    > the X, or horizontal, axis, and number of
    > occurances for that result as the Y, or
    > vertical, axis.

    Right.

    > From what I know about blackjack and
    > statistics, I can make a few predictions for
    > one set of playing rules, conditions and
    > strategies, but I would prefer to see the
    > actual results for only flat betting and
    > basic strategy...what would the graphic or
    > curve look like under other scenarios?

    Typical e.v. for BS has mean of anywhere from 0 to -0.75%. Typical per-hand s.d. is 1.12-1.16. The rest is easy, no?

    > If I were to play a game with 6 decks, S17,
    > DAS, LS and RSA, play all and flat bet with
    > basic strategy, I would expect the frequency
    > graphic to result in a perfect bell curve
    > (or normal distribution) with the mean
    > (average), median (half-way mark on X axis)
    > and mode (most frequent result or highest
    > point of curve on Y axis) at -.26% units.

    OK.

    > But, if in the same game I use Hi-Lo with
    > I18 and spread to 1-12 as the betting ramps
    > used in Chpt 10 of Blackjack Attack, the
    > mean would shift towards my expected value
    > of 1.26% (which I got from bjstats.com), but
    > where would the median and mode wind up, and
    > how would the shape of the frequency graphic
    > change? Would it still look like a bell
    > curve, or would it become skewed to one
    > side? Would the altitude of the mode change?

    Bell curve.

    > And then of course, how would the graphic
    > change if one played the same game White
    > Rabbit style with a 1-8 spread?

    Better mean for the bell curve! :-)

    > I guess my feeling when playing blackjack
    > are somewhat like a batter in baseball. When
    > I get a hit (average win) I am happy, when I
    > hit a homer (win big!) I am overflowing, and
    > when I don't reach base (lose) I am
    > discouraged. And most times I will not win
    > and I must count on big wins to offset the
    > more frequent small losses. Thus, seeing
    > some analysis like the above described could
    > help one to cope with the grind of playing
    > and the grief of a losing hand.

    Why "most times I will not win"? If you count, you will win more often than you lose, even if by "times," we mean just a single hour's worth of play (see BJA3, p. 21, Table 2.2).

    > Anyone know of where I could find a table
    > with the above data, or a graphic showing
    > it? (Will this be in BJA3?)

    Norm's CVCX can probably produce such graphs, but all the math needed can be found in BJA3.

    Don

  3. #3
    VerdugoJohn
    Guest

    VerdugoJohn: Re: Frequency Distribution of Results?

    Thanks for your reply, I am honored you took the time to answer.

    Re: lose most of the time, I should have been more precise in meaning...sorry. I meant, lose most hands, and while playing a shoe. As I play I see my stake ground down as I wait for a favorable opportunity. It takes a fair degree of patience.

    Anyway, I guess my concern is knowing how risky playing a shoe game is. I believe it is possible that a bell curve and an inverted bell curve could have the same the statistical measures of mean and standard deviation, although the span along the X axis of each would not be different. And I would think that if an inverted curve described a blackjack player's experiences, it would be riskier game to a player, more emotionally stressful due greater swings of fortune, and a larger bankroll would required.

    Again, thanks for your answer.

  4. #4
    VerdugoJohn
    Guest

    VerdugoJohn: Ooops! Correction if anyone cares...

    > Anyway, I guess my concern is knowing how
    > risky playing a shoe game is. I believe it
    > is possible that a bell curve and an
    > inverted bell curve could have the same the
    > statistical measures of mean and standard
    > deviation, although the span along the X
    > axis of each would not be different.

    Correction...would BE different. sorry


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.