mcallister3200
Joined: Dec 29, 2013
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April 17th, 2017 at 11:09:01 AM permalink
Quote: Romes

My interpretation of the long run has always been the point at which it's mathematically impossible for you to be "down". In the mathematics of blackjack this has often been referred to as NO.

That is not what NO is, I've seen you state it several times without correcting it but have to at some point, it is a measure of the "long run", however. I think you are referring to 3x-4x NO as being NO. At 1 NO, you have I believe an 84% chance of being ahead, 2x NO about a 95% chance of being ahead; and 3x NO you will be ahead all but 3 times out of 1,000. That assumes perfect play as you simmed and NL mid shoe backoffs etc combination of which is impossible so may as well bump the numbers for long run up some.QFIT or EJ can correct that if it is wrong.

Number of rounds to NO will vary widely by the game very good DD or SD game played aggressively may be as low as 6,000 for 1 NO, marginal 6d 75% h17 DS is going to be about 30k NO with a 1-32 or so spread, not counting rounds below -1.
LostWages
Joined: May 6, 2013
• Posts: 353
April 17th, 2017 at 11:51:35 AM permalink
Quote: QFIT

A coupla points:

1. SD is going to be substantially higher than 1.1 * AvgBet if you are not flat betting.
2. There is no number of hands where it is “mathematically impossible” to be down.
3. N0 is defined as 1SD, not 3SD. The exact definition is: “the number of rounds that must be played, with a fixed betting spread, such that the accumulated expectation equals the accumulated standard deviation. As such, it is a measure of how many rounds must be played to overcome a negative fluctuation of one standard deviation with such a fixed spread.”
4. At N0, the probability of being down is about 16%.
5. Incidentally, the theoretic chance that you are ahead at N0 hands by 50% of your EV or better is about 69%, and the chance you are ahead by double your EV or better is about 16%. Many players consider this the “long run”.

QFIT - appreciate your additional comments. I am unable to argue any issues, as the level of math conversation here is a bit over my head, but thanks anyway!
Eat real food . . . and you won't need medicine (or a lot less!)
QFIT
Joined: Feb 12, 2010
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April 17th, 2017 at 2:44:26 PM permalink
Quote: mcallister3200

That is not what NO is, I've seen you state it several times without correcting it but have to at some point, it is a measure of the "long run", however. I think you are referring to 3x-4x NO as being NO. At 1 NO, you have I believe an 84% chance of being ahead, 2x NO about a 95% chance of being ahead; and 3x NO you will be ahead all but 3 times out of 1,000. That assumes perfect play as you simmed and NL mid shoe backoffs etc combination of which is impossible so may as well bump the numbers for long run up some.QFIT or EJ can correct that if it is wrong.

Number of rounds to NO will vary widely by the game very good DD or SD game played aggressively may be as low as 6,000 for 1 NO, marginal 6d 75% h17 DS is going to be about 30k NO with a 1-32 or so spread, not counting rounds below -1.

You’re on the right track. 84% (100-16) is correct. 2SD would be 97.5% (midway between 95% and 100%) and 3SD would be 1.5 times out of 1,000, again halfway. This is because the SDs straddle the standard normal curve (bell curve). Half ahead, half behind. But, 2SD would be 4xN0 and 3SD would be 9xN0 as this is squared, not linear. Takes rather a lot of hands to get down to that tiny a difference.

(Just came back from a meeting which involved fermented grapes; so EJ or the Wiz are welcome to correct. “Alcohol may be man's worst enemy, but the bible says love your enemy.”)
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
mamat
Joined: Jul 13, 2015
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April 17th, 2017 at 3:43:10 PM permalink
Quote: QFIT

You’re on the right track. 84% (100-16) is correct. 2SD would be 97.5% (midway between 95% and 100%) and 3SD would be 1.5 times out of 1,000, again halfway. This is because the SDs straddle the standard normal curve (bell curve).

N0 and SD only behave this way for univariate normal distributions (68-97-99.5% rule).

For distributions and games which have "long tails", you can still compute 2SD and 3SD, but the probabilities of being >2 SD and >3 SD will be much higher.

Conversely, some non-normal distributions will have "skinnier tails".
QFIT
Joined: Feb 12, 2010
• Posts: 260
April 17th, 2017 at 3:45:33 PM permalink
And skewed. And, I suppose, with a measure of kurtosis in progressive jackpots. But, I'm not a statistician.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
Romes
Joined: Jul 22, 2014
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April 18th, 2017 at 8:37:50 AM permalink
Quote: mcallister3200

I think you are referring to 3x-4x NO as being NO.

Quite right and I apologize for my ambiguity. Similar to SD when I say "SD" for something I generally refer to 2SD or 3SD because 68% confidence is a lousy assumption in my opinion and 1SD means practically nothing =P.

Quote: QFIT

2. There is no number of hands where it is “mathematically impossible” to be down.
3. N0 is defined as 1SD, not 3SD. The exact definition is: “the number of rounds that must be played, with a fixed betting spread, such that the accumulated expectation equals the accumulated standard deviation. As such, it is a measure of how many rounds must be played to overcome a negative fluctuation of one standard deviation with such a fixed spread.”

I think your #2 and #3 disagree with each other if you think of 3x-4x N0 similar to 3SD.

If your EV for a set number of hands is \$1,000,000 and your 3SD is +/- \$400,000... yes, I consider that a mathematical certainty to "not be down" at that point. The only way you would be down is if you're playing incorrectly or being cheated.
Playing it correctly means you've already won.
QFIT
Joined: Feb 12, 2010
• Posts: 260
April 18th, 2017 at 8:58:09 AM permalink
Quote: Romes

I think your #2 and #3 disagree with each other if you think of 3x-4x N0 similar to 3SD.

If your EV for a set number of hands is \$1,000,000 and your 3SD is +/- \$400,000... yes, I consider that a mathematical certainty to "not be down" at that point. The only way you would be down is if you're playing incorrectly or being cheated.

At N0, it is not that unlikely to be down. 3SD equates to 9xN0. That can be a great deal of hands. In any case, I believe that precision in language is a must when discussing mathematics as whatever is stated may be used as a part of a further proof. Certainly at 9xN0 the odds of being behind are tiny, assuming perfect play/betting and no forced variations (table closings or limit changes, backoffs, chip confiscations, cover play, cover betting, low funds on hand with a hi count, wongers entering and eating cards at hi counts, etc.). But, there is no number of hands where it is “mathematically impossible” to be down.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
FleaStiff
Joined: Oct 19, 2009
• Posts: 10889
April 18th, 2017 at 9:20:39 AM permalink
I think long run is an illusory concept that we resort to when we've lost our money making decisions and tell ourselves that 'hit' and 'stand' were the correct decisions just made at the wrong time. If we had had a sufficient bankroll to attain this illusory 'long run' that is constantly over the horizon we would be leaving the table flush.
RS

Joined: Feb 11, 2014
• Posts: 5222
April 18th, 2017 at 9:24:37 AM permalink
Quote: FleaStiff

I think long run is an illusory concept that we resort to when we've lost our money making decisions and tell ourselves that 'hit' and 'stand' were the correct decisions just made at the wrong time. If we had had a sufficient bankroll to attain this illusory 'long run' that is constantly over the horizon we would be leaving the table flush.

What?
"should of played 'Go Fish' today ya peasant" -typoontrav
Romes
Joined: Jul 22, 2014
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April 18th, 2017 at 9:45:48 AM permalink
Quote: QFIT

At N0, it is not that unlikely to be down. 3SD equates to 9xN0. That can be a great deal of hands. In any case, I believe that precision in language is a must when discussing mathematics as whatever is stated may be used as a part of a further proof.

Quite correct - but (genuine complement) you're so advanced in them that you often seem to forget your audience on different topics. A good teacher must curve their verbiage to the understanding of their pupils. Less you can be technically correct all day and no one would ever know it.

Quote: QFIT

But, there is no number of hands where it is “mathematically impossible” to be down.

Depends on what you determine "mathematically impossible" to be. Many in the math community agree after 4 decimal places (for most calculations, certainly not molecular/atom level for physics calculations) the rest of the decimals are erroneous. Thus, if after 1,000,000 hands I have a .00001 chance of being down, I take that as a mathematical certainty that I won't be. I definitely believe there is a "mathematical certainty" with which each counter (counting/playing correctly and not getting bar'd over the world) will not be down anymore.
Playing it correctly means you've already won.