Modified N0 Metric

[SteinMeister]

So the other day my wife asked me a simple question: “How long before you’re profitable playing BlackJack?”

Of course I explained that it could vary depending on variance, but then I realized that I could work out the N0 value to hours and, using an average # of hours of play per week, I could give her a statistical estimate. She went to bed while I pulled up CVCX and started calculating.

I then realized that N0 gives the low end expected value with only 1 sigma from the mean, which is only a 84% (CORRECTED 8/17) probability (at or above the low end). I wanted greater accuracy. Therefore using CVCX I set one of the 3 input probabilities to 95% (under expected results) (which equates to 97.7% probability at or above low range (ADDED 8/17) ), and graphed the low end expected value for different inputted hours of play. Note that this was based on my current parameters AND assumed future method of heads up playing and playing 2 hands (I currently don’t do this, but I had to get the hours of play down to make it palatable for my wife). Then, when the CVCX’s low end reached zero, that would be the “statistical” # of hours of play to become profitable with a 97.7% (CORRECTED) probability level.

The result was as follows (with corrections):
N0 (traditional): 84.4% probability that after 322 hrs of play (I had to convert rounds per hour to hours of play) I should “statistically” be profitable.
N0(modified): 97.7% probability that after 1242 hrs of play I should “statistically” be profitable.
Wow, almost 4 times longer to get from 84.4% to 97.7% confidence level. Of course, I gave her the traditional N0 value of 322 hrs.

(I NOW RECANT THE FOLLOWING...)But statistically speaking, I feel the modified N0 with 95% confidence level makes more sense as a metric to use for this type of analysis.

(see chart below) (NOTE: the chart references incorrect probabilities; see above)

Modified N0 Metric-2.jpg

[Freightman]

So the other day my wife asked me a simple question: “How long before you’re profitable playing BlackJack?”

Of course I explained that it could vary depending on variance, but then I realized that I could work out the N0 value to hours and, using an average # of hours of play per week, I could give her a statistical estimate. She went to bed while I pulled up CVCX and started calculating.

I then realized that N0 gives the low end expected value with only 1 sigma from the mean, which is only a 66% probability. I wanted greater accuracy. Therefore using CVCX I set one of the 3 input probabilities to 95% (under expected results), and graphed the low end expected value for different inputted hours of play. Note that this was based on my current parameters AND assumed future method of heads up playing and playing 2 hands (I currently don’t do this, but I had to get the hours of play down to make it palatable for my wife). Then, when the CVCX’s low end reached zero, that would be the “statistical” # of hours of play to become profitable with a 95% probability level.

The result was as follows:
N0 (traditional): 66% probability that after 322 hrs of play (I had to convert rounds per hour to hours of play) I should “statistically” be profitable.
N0(modified): 95% probability that after 1242 hrs of play I should “statistically” be profitable.
Wow, almost 4 times longer to get from 66% to 95% confidence level. Of course, I gave her the traditional N0 value of 322 hrs.

But statistically speaking, I feel the modified N0 with 95% confidence level makes more sense as a metric to use for this type of analysis.

(see chart below)

Modified N0 Metric-2.jpg

Looks lik3 halfers with th3 wife now, and only when you win.

[Three]

Wow, almost 4 times longer to get from 66% to 95% confidence level. Of course, I gave her the traditional N0 value of 322 hrs.

Mathematically it should be 4 times n0 for EV equals 2SD (2^2) and 9 times n0 for EV equals 3SD (3^2). And for EV equals X*SD, X^2 times n0.

[SteinMeister]

Mathematically it should be 4 times n0 for EV equals 2SD (2^2) and 9 times n0 for EV equals 3SD (3^2). And for EV equals X*SD, X^2 times n0.

Having difficulty following you there Three. Can you please clarify. What is the "it" in your statement?

[lij45o6]

Having difficulty following you there Three. Can you please clarify. What is the "it" in your statement?

The N_0.

For every standard deviation from 0, you should square the SD, multiply it by the N_0 to get the N_1, N_2, and N_3, for 2, 3, and 4 SD's.

-dogman

[SteinMeister]

The N_0.

For every standard deviation from 0, you should square the SD, multiply it by the N_0 to get the N_1, N_2, and N_3, for 2, 3, and 4 SD's.

-dogman

Thanks dogman for the clarification. I will go back to my data and verify that my data matches this (it should, since it came from CVCX). I was concentrating on # hours, not # rounds.

[DSchles]

N0 (one standard deviation) is NOT two-sided; it's one-sided. After playing the requisite number of hands, you don't have a 66% probability of being ahead, as you state; rather you have an 84% probability of being ahead. And for 2 N0, the value is 97.7%, not 95%. Do you understand why?

Don

[lij45o6]

N0 (one standard deviation) is NOT two-sided; it's one-sided. After playing the requisite number of hands, you don't have a 66% probability of being ahead, as you state; rather you have an 84% probability of being ahead. And for 2 N0, the value is 97.7%, not 95%. Do you understand why?

Don

I'm gunna guess it has to do with the fact that we are playing with +EV? or the fact that, as you mentioned, we are only looking at this one sided, so we are working with only partial of the population?

Other than that, can't really guess any other way. Maybe it is a simple explanation that I am missing.

[SteinMeister]

N0 (one standard deviation) is NOT two-sided; it's one-sided. After playing the requisite number of hands, you don't have a 66% probability of being ahead, as you state; rather you have an 84% probability of being ahead. And for 2 N0, the value is 97.7%, not 95%. Do you understand why?

Don

Yes, I understand. This is why....
Modified N0 Metric--Response to Don.jpg



However, here is how I understand the Expected Results and Probability within CVCX...




Modified N0 Metric--Response to Don--2.jpg

[Three]

Having difficulty following you there Three. Can you please clarify. What is the "it" in your statement?

EV grows linearly and SD grows by the square root as rounds accumulate. So for rounds to double the ratio of SD to EV you need four times as many rounds because that is two squared. And to triple the ratio of SD to EV you need 9 times as many rounds since nine is three squared.

[SteinMeister]

N0 (one standard deviation) is NOT two-sided; it's one-sided. After playing the requisite number of hands, you don't have a 66% probability of being ahead, as you state; rather you have an 84% probability of being ahead. And for 2 N0, the value is 97.7%, not 95%. Do you understand why?

Don

Don, I understand what you were referencing now. And (of course) you're correct in that my analysis for 1 sigma (low end) was not with a 66% probability, but instead was 84% because I needed to add ALL percentages above that point. Likewise, the 2 sigma should have referenced 97.7% like you said.

Thank you for the correction.

I have now corrected my original post.

[Stealth]

But statistically speaking, I feel the modified N0 with 95% confidence level makes more sense as a metric to use for this type of analysis.

This is not new news.

Have long considered N0 at 2SD to be a more meaningful indication of the long term and accumulate sessions experience to contrast to the metric.

IMHO, concept is valid especially for the professional AP and especially for teams.

[DSchles]

Don, I understand what you were referencing now. And (of course) you're correct in that my analysis for 1 sigma (low end) was not with a 66% probability, but instead was 84% because I needed to add ALL percentages above that point. Likewise, the 2 sigma should have referenced 97.7% like you said.

Thank you for the correction.

I have now corrected my original post.

No problem. The stats from CVCX show a different metric. They show one-, two-, and three-SD "bandwidths" around the mean result. As such, they are useful for making statements such as, "About two-thirds of the time, my result will fall between x and y." But that is a different notion from the N0 metric, which, in essence, states the number of hands necessary to overcome one standard deviation of "bad luck" and still not be losing any money.

Don