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Thread: Standard Deviation Calculation

  1. #14
    Random number herder Norm's Avatar
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    Was busy doing my taxes. Some more explanation:

    CVData calculates variance by round (not by hand) by TC. Independently, it calculates variance by round for all counts. These calculations are separate. Since calculations are by round, no co-variance correction is required. Any skew, kurtosis, change in actual penetration, or any other aberration would be included in these calcs.

    CVCX is a single-hand simulator. The two-hand estimates are rather complex as they allow for changing from one to two hands at a specified count, which significantly alters TC frequencies. These calcs are based on a set of tables that were created running many billions of hands. It must also hold the data to recalc results instantly when switching the penetration card by card, or rules, decks, etc. But, the results are estimates for two hands as stated in the manual.

    If you want to see accurate multi-hand results in CVCX, you would need to run a CVData sim with two to seven hands, and then click Call CVCX. The data will be transferred to CVCX and allow modification of the bets there. In this case, results should be accurate.
    Last edited by Norm; 01-30-2019 at 11:55 AM.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  2. #15


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    Quote Originally Posted by ericfarmer View Post
    Sorry, I did gloss over the reference to Griffin's formula, which is indeed correct-- at least in form. That is, the 0.50 covariance seems to be dragged along as a "constant" into current calculations, when it isn't clear to me that this is justified (and from your follow-on comment about Wong's data, it probably isn't).
    Right. It wasn't unknown to me or Peter that both the per-hand variances AND covariances change a bit from line to line. To be more precise, one should use the values that are appropriate for each true count in question. Clearly, that is not what was done on page 20, nor for Griffin's one-size-fits-all formula. But, to do so would have greatly complicated both demonstrations, and, apparently, neither of us deemed it necessary to do so.

    Quote Originally Posted by ericfarmer View Post
    This is a good point; the difference depends on how the variance is being used. As we've discussed in past email exchange, if it's being used, for example, to compute SCOREs, win rates, etc., then it's definitely of practical importance, causing a difference of roughly 6-7% errors in win rate for the 6D study from a couple of years ago.
    I'm not getting this part. The overall variance shouldn't cause an error in win rates or SCOREs, because, as you mentioned earlier, the line-by-line individual variances are correct. And again, there are minor differences in the covariances, as true count varies, but I don't think that's what your point is. So, the line-by-line optimal bets are correct (if the edges and individual variances are). Therefore, the win rates should be right, as they are simply the aggregate of the line-by-line results. SCORE is the hourly win rate for an optimal bettor with a $10,000 bankroll, so how is SCORE affected by your change in overall variance?

    Don

  3. #16


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    Quote Originally Posted by DSchles View Post
    I'm not getting this part. The overall variance shouldn't cause an error in win rates or SCOREs, because, as you mentioned earlier, the line-by-line individual variances are correct. And again, there are minor differences in the covariances, as true count varies, but I don't think that's what your point is. So, the line-by-line optimal bets are correct (if the edges and individual variances are). Therefore, the win rates should be right, as they are simply the aggregate of the line-by-line results. SCORE is the hourly win rate for an optimal bettor with a $10,000 bankroll, so how is SCORE affected by your change in overall variance?

    Don
    You are absolutely right, I misspoke. The root problem is really in computing RoR, and thus only indirectly on *optimal* (risk-constrained) win rate. That is, suppose that we have fixed our playing strategy, and want to select a betting ramp to maximize win rate, subject to a pre-specified risk of ruin. If we are computing (as we have done in recent studies) the ordered pair (RoR, win rate) for each of a collection of possible betting ramps, and are getting that RoR calculation wrong (due to incorrectly computing per-round variance), then as a result we select the wrong "best" win rate as well. How much the incorrect variance matters depends on the "slope" of feasible win rate vs. RoR... in the recent study this made about a 6-7% difference.

  4. #17


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    Quote Originally Posted by Norm View Post
    Was busy doing my taxes. Some more explanation:

    CVData calculates variance by round (not by hand) by TC. Independently, it calculates variance by round for all counts. These calculations are separate. Since calculations are by round, no co-variance correction is required. Any skew, kurtosis, change in actual penetration, or any other aberration would be included in these calcs.
    Ok, interesting. If I understand this correctly, then this suggests that CVData per-TC variances should agree with, say, Table 2.1 (for the same setup), but the corresponding CVData *per-round* variance should *disagree* with the corresponding overall variance in Table 2.1 (since the latter is computed from the per-TC variances with the missing cross terms). (Note that this is all independent of number of hands per round.)

  5. #18
    Random number herder Norm's Avatar
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    Actually, I don't think I've seen a difference. But, I haven't looked at this in years. Realize that CVCX is designed to show practical RoR and SCORE; not theoretical. I do not use the work created by several seriously sharp folks to calculate optimal betting in CVCX. The first version used this stuff and I thank them for their work, and it was great as far as it went. Problem was when I started adding real life constraints. Like we need to make rational bets. You can't bet $43.12. So, CVCX now starts with their calcs, and then uses a repetitive method to home in on the best SCORE based on the constraints set by the user. Like optimizing the SCORE and user set RoR with user set simplicity settings -- like reducing the number of chips required to make a bet.
    Last edited by Norm; 01-30-2019 at 02:39 PM.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  6. #19


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    Quote Originally Posted by ericfarmer View Post
    You are absolutely right, I misspoke. The root problem is really in computing RoR, and thus only indirectly on *optimal* (risk-constrained) win rate. That is, suppose that we have fixed our playing strategy, and want to select a betting ramp to maximize win rate, subject to a pre-specified risk of ruin. If we are computing (as we have done in recent studies) the ordered pair (RoR, win rate) for each of a collection of possible betting ramps, and are getting that RoR calculation wrong (due to incorrectly computing per-round variance), then as a result we select the wrong "best" win rate as well. How much the incorrect variance matters depends on the "slope" of feasible win rate vs. RoR... in the recent study this made about a 6-7% difference.
    OK, understood. But, as you state, this is a somewhat different consideration.

    My main interest now would be knowing, for any calculation that follows the page 20 methodology, what the lack of using the cross terms contributes to the ultimate calculation of overall variance. My sense is that the discrepancy ought to be minor or negligible. But, I'm getting that you think otherwise, and so I'd like to determine the magnitude of any error.

    Obviously, I understand that this will vary with different scenarios. Note, as well, that this doesn't affect the Chapter 10 studies, as they don't involve playing two hands.

    Don

  7. #20
    Random number herder Norm's Avatar
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    I don’t have time at the moment to deeply discuss. But, there’s something I call the “tyranny of exactness” in simulations. You run a billion hands with a set of rules. But, you assume that other players all play perfectly in a certain method. We like to say that other players don’t affect your results. That’s sorta, kinda true. But, not purely true. And dealers don’t always deal the exact same penetration. And players leave and enter during a shoe. That’s why I have added various types of reality into CVData. I think this, and other realistic constraints have more of an effect on realistic results.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  8. #21


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    Quote Originally Posted by Norm View Post
    I don’t have time at the moment to deeply discuss. But, there’s something I call the “tyranny of exactness” in simulations. You run a billion hands with a set of rules. But, you assume that other players all play perfectly in a certain method. We like to say that other players don’t affect your results. That’s sorta, kinda true. But, not purely true. And dealers don’t always deal the exact same penetration. And players leave and enter during a shoe. That’s why I have added various types of reality into CVData. I think this, and other realistic constraints have more of an effect on realistic results.
    Well, of course, they do, and software should have this kind of flexibility, but when you're doing research, you need to have norms (no pun intended!), because, if you're ever going to be able to compare results and have someone else validate your work, you can't be doing a study with A doing it one way while B does it differently. So, we need to begin by agreeing on the plain-vanilla variety before we start fooling around with the cherries on top.

    That's why, although I understand the significance, I'm not a fan of quoting BS edge with the CCE. It requires every writer or researcher, trying to enunciate a precise BS edge, to stipulate an exact level of penetration for every game considered, whereas that variable isn't at all necessary if everyone agrees to quote off-the-top edges, whether they conform to the real-world playing of the game or not.

    Don
    Last edited by DSchles; 01-30-2019 at 05:46 PM.

  9. #22


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    Quote Originally Posted by DSchles View Post
    OK, understood. But, as you state, this is a somewhat different consideration.

    My main interest now would be knowing, for any calculation that follows the page 20 methodology, what the lack of using the cross terms contributes to the ultimate calculation of overall variance. My sense is that the discrepancy ought to be minor or negligible. But, I'm getting that you think otherwise, and so I'd like to determine the magnitude of any error.

    Obviously, I understand that this will vary with different scenarios. Note, as well, that this doesn't affect the Chapter 10 studies, as they don't involve playing two hands.

    Don
    My memory hasn't been very good-- as I work through these calculations again, I find that I need to correct myself yet again: this *does* affect SCORE (since we're talking about computing variance). Note that this implies that it *would* affect Chapter 10 results as well, at least assuming that variance is computed in the weighted-sum manner indicated in Table 2.1-- this is about partitioning the space of outcomes by true count, not how many hands are played within the round.

    Having said that, the magnitude of the error is small, typically only affecting the decimal places of SCORE. I have a single anecdote from a past study where this error came up, where the SCORE of 31.1135 was corrected to 31.1018.

    E

  10. #23


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    Quote Originally Posted by ericfarmer View Post
    My memory hasn't been very good-- as I work through these calculations again, I find that I need to correct myself yet again: this *does* affect SCORE (since we're talking about computing variance). Note that this implies that it *would* affect Chapter 10 results as well, at least assuming that variance is computed in the weighted-sum manner indicated in Table 2.1-- this is about partitioning the space of outcomes by true count, not how many hands are played within the round.

    Having said that, the magnitude of the error is small, typically only affecting the decimal places of SCORE. I have a single anecdote from a past study where this error came up, where the SCORE of 31.1135 was corrected to 31.1018.

    E
    As I said, Eric, I appreciate the drive for accuracy, but I'm not going to lose any sleep over this. :-)

    Don

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