Backcounting and N0

[Bodarc]

Hi RoadWarrior

I will explain it as I see it which may help you a little.

""N0 (hands)" (N-zero) is a term coined by the blackjack researcher and system developer Brett Harris. It is the number of hands one must play so that expectation is equal to one-standard-deviation result: that is, e.v. - s.d. = 0." From BJA 3rd edition pg 213

I am looking at a game set up on CVCX. The N0 of this game if I play every hand (100%) is 30,284 using my bet spread. If I backcount and only play hands with a true count of +1 or higher (omitting all of the negative ev hands), I will only play 34.6% of the hands dealt and N0 drops to 12,626. To get that N0, I can only play hands with a true count of +1 or higher, so while I am at the table observing 100% of the hands (back counting), I am only playing 34.6% of them ie, I am sticking to the game plan to obtain my reduced N0.

Now, N0 is quoted in "rounds", not hands played, so after 12,626 rounds have passed (35% I will play and 65% I will bet zero ...actually skip) I should have reached N0.

That is how I see it, if I am wrong, I look forward to begin corrected.

As far as the math is concerned, buy cvcx and enter your game, rules etc and the math will be done automatically for you. It is based on math and not just theory.

Don, I hope it is ok to quote from your book, if not I will delete it.

[DSchles]

Everything you wrote is exactly correct, and I am happy to have you quote the book.

Don

[RoadWarrior]

Hi RoadWarrior

I will explain it as I see it which may help you a little.

""N0 (hands)" (N-zero) is a term coined by the blackjack researcher and system developer Brett Harris. It is the number of hands one must play so that expectation is equal to one-standard-deviation result: that is, e.v. - s.d. = 0." From BJA 3rd edition pg 213

I am looking at a game set up on CVCX. The N0 of this game if I play every hand (100%) is 30,284 using my bet spread. If I backcount and only play hands with a true count of +1 or higher (omitting all of the negative ev hands), I will only play 34.6% of the hands dealt and N0 drops to 12,626. To get that N0, I can only play hands with a true count of +1 or higher, so while I am at the table observing 100% of the hands (back counting), I am only playing 34.6% of them ie, I am sticking to the game plan to obtain my reduced N0.

Now, N0 is quoted in "rounds", not hands played, so after 12,626 rounds have passed (35% I will play and 65% I will bet zero ...actually skip) I should have reached N0.

That is how I see it, if I am wrong, I look forward to begin corrected.

As far as the math is concerned, buy cvcx and enter your game, rules etc and the math will be done automatically for you. It is based on math and not just theory.

Don, I hope it is ok to quote from your book, if not I will delete it.

So using example 12,626 rounds, 35% ill play them and 65% im betting 0, but is N0 still decreasing when i betting 0 on 65% of the time? You dont exactly explain correctly? Let me explain. If i stand watching the table the for lets say 30 rounds, is my N0 now 12,596?

[Bodarc]

The 12,626 is obtained if you observe that many hands dealt and backcount 65% of them (whether sitting at the table, standing behind someone or hanging from the ceiling as long as you skip all of of the -EV hands and play all hands at +1 or better.
As long as you are doing that, N0 is remaining the same. If you change anything, N0 will change because your EV and SD will then change.

The formula for N0 is: N0 = SD^2/EV^2 (Standard Deviation Squared divided by Expected Value Squared)

So, if you want to decrease N0, you must decrease the numerator (SD) or increase your denominator (EV).

I hope this helps

[Three]

Your N0 stays the same but the rounds observed count toward hitting that N0. The expectation is 35%/65% but it could be anything from 0%/100% or 100%/0% for hands observed and hands played. The N0 doesn't care what the ratio is.

[Nyne]

N0 is a mathematical constant based on the specific game parameters. It doesn't change as you play more hands. Your expected results after observing and/or playing any given number of rounds can be described as winning (EV_for_total_play) with a standard deviation of (SD_for_total_play). That's true after 100 rounds or 1 billion rounds. The EV_for_total_play goes up proportional to the number of hands played or observed, so if your game is worth $20/hr and you decide to go play 3 hours, you accumulate $60 in EV, even if it turns out you never place a bet. That is compensated by the times you place many more bets than usual. The SD_for_total_play goes up proportional to the square root of the number of hands played. For a small amount of play, your EV will be swamped by variance, so for a short period of play, we don't have much certainty about whether we will win or lose or by how much. As your amount of play increases, your odds of being ahead improve because the EV_for_total_play will increase at a steady rate while SD_for_total_play will increase at a diminishing rate. The point where being down money would be a -1 standard deviation event is N0, where EV = SD. These parameters don't change as you play, but as you play your accumulated performance is more and more likely to be positive. You never "reach" the infamous long run, you only approach it. No matter how many hands you've played, the next 1,000 or 10,000, or 100,000 hands have the same EV and SD as the first, if you are using the same betting and playing strategy.

I think the question you are asking is do the observed hands where you don't place a bet contribute to getting you to that point of greater certainty of being ahead. If that's the question, the answer is yes, but looking forward, from whatever point you are at, you haven't done anything to change your future probabilities of winning or losing, so if N0 is 12000 and you play 6000 hands, you can't use your current result to predict anything about the next 6000 hands. The math for the second 6000 hands is the same as the first 6000, and the same distribution of possible outcomes applies.

[ohbehave]

So using example 12,626 rounds, 35% ill play them and 65% im betting 0, but is N0 still decreasing when i betting 0 on 65% of the time? You dont exactly explain correctly? Let me explain. If i stand watching the table the for lets say 30 rounds, is my N0 now 12,596?

Lets say you simulate a game and the strategy for your simulation is to play only positive TC rounds and the simulation reports a N0 of 10,000 rounds.

In order to play that game when you go to the casino you must sit out all rounds that aren't positive, if instead you play some negative rounds you are playing a different game with a longer N0 because now you must play additional positive TC rounds to make up for the lost EV from the negative rounds.

But lets say you do actually sit out all negative rounds and after 1,000 rounds there were 300 rounds where you placed bets and 700 rounds that were sat out. Although you've only played 300 rounds you now have 9,000 rounds remaining to reach N0.

[RoadWarrior]

Lets say you simulate a game and the strategy for your simulation is to play only positive TC rounds and the simulation reports a N0 of 10,000 rounds.

In order to play that game when you go to the casino you must sit out all rounds that aren't positive, if instead you play some negative rounds you are playing a different game with a longer N0 because now you must play additional positive TC rounds to make up for the lost EV from the negative rounds.

But lets say you do actually sit out all negative rounds and after 1,000 rounds there were 300 rounds where you placed bets and 700 rounds that were sat out. Although you've only played 300 rounds you now have 9,000 rounds remaining to reach N0.

Thank you, that cleared it up now!