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

#### JohnCrover

##### Banned
Let's say someone's N0 is 10k. It will take 10k hands to be 66.7% certain of being in the black. 40K hands to be 84% certain of being ahead and 90k hands to have a 97.72% certainty of being in the black.
Correct?

#### DSchles

##### Well-Known Member
JohnCrover said:
Let's say someone's N0 is 10k. It will take 10k hands to be 66.7% certain of being in the black. 40K hands to be 84% certain of being ahead and 90k hands to have a 97.72% certainty of being in the black.
Correct?
Nope. You need the one-sided tail numbers, not the two-sided values. Numbers you're looking for are: 84.1%, 97.7%, and 99.87% respectively.

Don

#### LC Larry

##### Well-Known Member
gronbog said:
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.
But what if the coin flipper is a "beast?"

#### gronbog

##### Well-Known Member
Ha! That's why I was careful to say "fair coin"