# What exactly does 'lowering/minimizing N0" mean?

#### Titan

##### Member
I feel like my interpretation of N0 is getting a bit fudged. Could someone please clarify what N0 is and why it's "good" to have a really low N0?

#### gronbog

##### Well-Known Member
Specifically N0 is the number of rounds you need to play for your expected value to equal one standard deviation.

It is used as a measure of reaching the long run. Because your EV equals one standard deviation at N0 rounds played, we can say that you have approximately an 84% chance of being in the black at that point. Some prefer to use 4xN0 as their threshold, because at that point your EV equals 2 standard deviations and you have approximately a 99% 97.72% chance of being in the black.

As for why it's good for N0 to be low, it's because it means that you reach the long run more quickly.

Last edited:

#### DSchles

##### Well-Known Member
"Some prefer to use 4xN0 as their threshold, because at that point your EV equals 2 standard deviations and you have approximately a 99% chance of being in the black."

Make it 97.72%.

Don

#### Titan

##### Member
gronbog said:
Specifically N0 is the number of rounds you need to play for your expected value to equal one standard deviation.

It is used as a measure of reaching the long run. Because your EV equals one standard deviation at N0 rounds played, we can say that you have approximately an 84% chance of being in the black at that point. Some prefer to use 4xN0 as their threshold, because at that point your EV equals 2 standard deviations and you have approximately a 99% chance of being in the black.

As for why it's good for N0 to be low, it's because it means that you reach the long run more quickly.
Oh ok I see. How exactly does one lower their N0? What does in the black mean?

#### 21forme

##### Well-Known Member
Titan said:
Oh ok I see. How exactly does one lower their N0?
By playing better games (rules, penetration, etc.) It's inversely proportional to SCORE.

#### BJgenius007

##### Well-Known Member
DSchles said:
"Some prefer to use 4xN0 as their threshold, because at that point your EV equals 2 standard deviations and you have approximately a 99% chance of being in the black."

Make it 97.72%.

Don
Wow. A clash of the titans.

#### gronbog

##### Well-Known Member
DSchles said:
"Some prefer to use 4xN0 as their threshold, because at that point your EV equals 2 standard deviations and you have approximately a 99% chance of being in the black."

Make it 97.72%.

Don
Thanks -- I incorrectly split the upper part of the distribution beyond 2 standard deviations.

#### JohnCrover

##### Banned
You mathematicians can play with your silly numbers all you like but your numbers will never have the answer to the soul.

#### Titan

##### Member
JohnCrover said:
You mathematicians can play with your silly numbers all you like but your numbers will never have the answer to the soul.
Simple answer to my soul. Money

#### Dopple

##### Well-Known Member
Dons book speaks about the poor soul at the sad tail of the bell curve that is still behind after 500 hours of play. While trying to not think like a gambler; he must be "due" something in the form of positive variance in order to be at his ev after a large number of NO completions, yes? I know we should not think that something is due or owed in the world of math but how else does one get back to their actual EV after a long run of bad variance?

#### DSchles

##### Well-Known Member
"I know we should not think that something is due or owed in the world of math but how else does one get back to their actual EV after a long run of bad variance?"

This is a really bad way to think. What's done is done. The past has absolutely no effect whatsoever on the future, insofar as playing blackjack is concerned. Do you think the cards remember what happened to you?

Don

#### BoSox

##### Well-Known Member
Dopple said:
I know we should not think that something is due or owed in the world of math but how else does one get back to their actual EV after a long run of bad variance?
Self-evaluation and honesty must also come into play. Is the individual actually playing with a positive EV expectation? If not, go back to square one and learn how to eliminate any and all of the weak areas.

#### Dopple

##### Well-Known Member
I submit for your analysis myself and my doppelgänger, an exact twin of myself. We have each sat at identical tables playing the same game for 20 years nonstop. I have had bad variance and find myself and the very pinnacle of neg. var. Could never be worse in any universe. My twin is at the opposite side of the spectrum. Who is more likely to experience a change in the next twenty years and in which direction? Bad thoughts but they are thoughts and I just can't stop em.

#### gronbog

##### Well-Known Member
Dopple said:
Dons book speaks about the poor soul at the sad tail of the bell curve that is still behind after 500 hours of play. While trying to not think like a gambler; he must be "due" something in the form of positive variance in order to be at his ev after a large number of NO completions, yes? I know we should not think that something is due or owed in the world of math but how else does one get back to their actual EV after a long run of bad variance?
Good question on a topic which is one of the most misunderstood in gaming math.

Yes, with enough play, your EV will once again approach what is expected after a run of bad variance. But it does not happen due to some offsetting run of good variance. It happens because the run of short term bad variance eventually becomes insignificant.

Consider someone who flips a fair coin 1,000 times and ends up flipping 600 heads and 400 tails. We all know that the expected number of each is 500. The EV is 50%. The actual result for tails is 40%. What is expected after this point is not that he will hit a run on tails (although that might happen). It is expected that additional flips still have an EV of 50%. Let's see what happens to his overall EV if this occurs. Let's say he flips an additional 1,000 times and actually does flip 500 heads and 500 tails. His overall EV on tails will now be (400 + 500) / 2000 = 45%.

What has happened here? He is still 100 tails short of expected, but his actual result has crept 5% closer to the expected 50% although there has been no "correction" whatsoever. The reason is that the 100 flip differential is now out of 2000 flips rather than out of 1000. It has become less significant.

And for those who still think that some sort of bias on tails is "due", consider the case where he goes on to flip another 1,000 times and gets 510 heads and 490 tails (i.e. betting on tails loses even more over this span). His overall result on tails is now (400 + 500 + 490) / 3000 = 46.33%. Despite continuing to lose on betting tails, his overall result has crept even closer to the expected 50%

The bottom line is that nothing is ever "due". We can only know what is expected.

#### Titan

##### Member
DSchles said:
"Some prefer to use 4xN0 as their threshold, because at that point your EV equals 2 standard deviations and you have approximately a 99% chance of being in the black."

Make it 97.72%.

Don
Could either of you please explain what 4xN0 means in practical terms? as in does it mean you need to play more and more hands in a shorter amount of time or something like that? Or is it simply a point in time where once reached you'll most certainly be in profit? Those are what I'm taking from it correct me if i'm wrong

#### Dopple

##### Well-Known Member
Gronbog thanks for the help. I echo Dons sentiments. Knowing does matter to me so that makes the thanks genuine. I will take a stab at helping Titan.................... After playing a certain number of hands at a certain EV you should have won enough money that you have a 97.72% chance that you will still be a state of positive money, a net winner if even a penny. The money you are expected to have is greater than any random series of misfortunes on the table that will occur on average only 100%- 97.72%= 3.28% of the time and deplete you bankroll to the point you are in the red. Not sure if I helped. The sages will correct this if I am proliferating falsities. Nothing brings me closer to my comrades than the exchange of thought. We should all meet for coffee sometime.

#### gronbog

##### Well-Known Member
You have the idea, except that 100%- 97.72%= 2.28%

#### gronbog

##### Well-Known Member
Titan said:
Could either of you please explain what 4xN0 means in practical terms? as in does it mean you need to play more and more hands in a shorter amount of time or something like that? Or is it simply a point in time where once reached you'll most certainly be in profit? Those are what I'm taking from it correct me if i'm wrong
N0 is a number of rounds that you need to play. It may take you a month, a year, or longer depending on how much you play. 4xN0 is simply four times that number of rounds. It takes you four times as many rounds to reach the 97.72% certainty level as it does to reach the ~84% certainty level.