The Long Run??
- Thread starter Anthony
- Start date
Not a pro...
I don't think being a pro has much to do with the question.
In practice, your results at the table mean very little over spans under 100,000 hands (approx 1000 hours). But that is not what "The Long Run" means. It is simply a statement that the "variance in blackjack is large".
To understand the law of large numbers, you really need a decent Statistics course.
5000 to 10000 hands is totally meaningless for blackjack.
I don't think being a pro has much to do with the question.
In practice, your results at the table mean very little over spans under 100,000 hands (approx 1000 hours). But that is not what "The Long Run" means. It is simply a statement that the "variance in blackjack is large".
To understand the law of large numbers, you really need a decent Statistics course.
5000 to 10000 hands is totally meaningless for blackjack.
zengrifter
Banned
2000 hours starts to approximate it.
Sonny
Well-Known Member
Even less of a pro's opinion
> What in your research makes up the long run? Is it 5,000 hands, 10,000 hands,
> or am I really off?
Yes, unfortunately you are very far off. We all wish that we could reach the long run after 10,00 hands. I could reach it every weekend!
The distance of the "long run" depends on several factors such as win rate, variance, speed, and game selection.
The higher your win rate, the sooner you will approach the long run (notice that I said APPROACH the long run - not arrive!). Someone with a 15% advantage will realize their goal much sooner than someone with a 5% advantage. Since they are playing "more correctly" they should expect to see their results sooner.
They will also experience somewhat smaller fluctuations along the way. Obviously variance will play a large role in how far away the long run can be. The larger the swings are, the more likely you are to drift very far away from your expectation. The less you drift, the more you approach the long run (or, at least, the closer you stay to it).
However, 15% and 5% advantages are very unreasonable for most blackjack players. A player who only counts cards should not expect to exceed an overall 2% advantage which is why, as the Mayor rightfully pointed out, "the variance in blackjack is large." With only a 1% advantage you will experience huge fluctuations and have very little chance of nearing the long run. That is why bankrolls of 1000-2000 units are not uncommon among serious players.
Another factor is your speed. Someone playing alone at 200 hands per hour will begin to approach the long run in fewer hours than someone playing 75 hands per hour at a crowded table.
Okay, enough about the factors - lets get to the answers! I was taught to use Brett Harris' N0 formula to find the length of the long run (or, more correctly, the time it would take to reach your expectation with a given degree of certainty). Here's how it works:
Simply square your SD and divide it by your hourly win rate, then divide this by your per-hand win rate. Sounds easy, huh? Lets look at an example:
Your win rate is 2 units per hour with a 30 unit SD and you are able to play 100 hands per hour. The formula is:
(SD^2/Hourly EV)/(Hourly EV/Hands per Hour)
You would end up with:
(30^2/2)/(2/100) = (900/2)/(.02) = 22,500 hands
That's quite a bit more than you thought, huh? And it only gets worse. The formula tells you that you will have to play around 22,500 hands in order to overcome ONE standard deviation. This will encompass roughly 68% of the bell curve. To expand this to two standard deviations, and roughly 95% of the bell curve, you would multiply this number by four. So now you are playing 90,000 hands in order to have a 95% chance of reaching your expectation. Using the above numbers you would have to play for 900 hours to achieve that. Of course, you might win that much money after 600 hours and consider an early retirement. You might also play for 800 hours and still be in the red. You simply never know.
Now, playing a better game with a 2 unit win rate but only a 25 unit SD would reduce the number of hands from 22,5000 (and 90,000) to 15,625 (and 62,500). You have just saved yourself almost 69 hours (or 275 hours for the 95% certainty level). If you can also speed up your play to 150 hands per hour (and thus raise your hourly EV to 3 units) you can further reduce it to around 10,417 (and 41,667). Those two steps have reduced your initial N0 number from 225 hours to only 104 hours. This is why playing in good games can be so crucial to success.
As the Mayor indicated, the "long run" is simply a expression used to define a indefinite interval of time. The long run is not a goal but rather a journey. Expanding the original example above to three standard deviation would bring the grand total up to 3,600 hours with only 97% certainty. There is still roughly a 3% chance that you will not realize your expectation after 3,600 hours of play.
Still want to play blackjack?
-Sonny-
> What in your research makes up the long run? Is it 5,000 hands, 10,000 hands,
> or am I really off?
Yes, unfortunately you are very far off. We all wish that we could reach the long run after 10,00 hands. I could reach it every weekend!
The distance of the "long run" depends on several factors such as win rate, variance, speed, and game selection.
The higher your win rate, the sooner you will approach the long run (notice that I said APPROACH the long run - not arrive!). Someone with a 15% advantage will realize their goal much sooner than someone with a 5% advantage. Since they are playing "more correctly" they should expect to see their results sooner.
They will also experience somewhat smaller fluctuations along the way. Obviously variance will play a large role in how far away the long run can be. The larger the swings are, the more likely you are to drift very far away from your expectation. The less you drift, the more you approach the long run (or, at least, the closer you stay to it).
However, 15% and 5% advantages are very unreasonable for most blackjack players. A player who only counts cards should not expect to exceed an overall 2% advantage which is why, as the Mayor rightfully pointed out, "the variance in blackjack is large." With only a 1% advantage you will experience huge fluctuations and have very little chance of nearing the long run. That is why bankrolls of 1000-2000 units are not uncommon among serious players.
Another factor is your speed. Someone playing alone at 200 hands per hour will begin to approach the long run in fewer hours than someone playing 75 hands per hour at a crowded table.
Okay, enough about the factors - lets get to the answers! I was taught to use Brett Harris' N0 formula to find the length of the long run (or, more correctly, the time it would take to reach your expectation with a given degree of certainty). Here's how it works:
Simply square your SD and divide it by your hourly win rate, then divide this by your per-hand win rate. Sounds easy, huh? Lets look at an example:
Your win rate is 2 units per hour with a 30 unit SD and you are able to play 100 hands per hour. The formula is:
(SD^2/Hourly EV)/(Hourly EV/Hands per Hour)
You would end up with:
(30^2/2)/(2/100) = (900/2)/(.02) = 22,500 hands
That's quite a bit more than you thought, huh? And it only gets worse. The formula tells you that you will have to play around 22,500 hands in order to overcome ONE standard deviation. This will encompass roughly 68% of the bell curve. To expand this to two standard deviations, and roughly 95% of the bell curve, you would multiply this number by four. So now you are playing 90,000 hands in order to have a 95% chance of reaching your expectation. Using the above numbers you would have to play for 900 hours to achieve that. Of course, you might win that much money after 600 hours and consider an early retirement. You might also play for 800 hours and still be in the red. You simply never know.
Now, playing a better game with a 2 unit win rate but only a 25 unit SD would reduce the number of hands from 22,5000 (and 90,000) to 15,625 (and 62,500). You have just saved yourself almost 69 hours (or 275 hours for the 95% certainty level). If you can also speed up your play to 150 hands per hour (and thus raise your hourly EV to 3 units) you can further reduce it to around 10,417 (and 41,667). Those two steps have reduced your initial N0 number from 225 hours to only 104 hours. This is why playing in good games can be so crucial to success.
As the Mayor indicated, the "long run" is simply a expression used to define a indefinite interval of time. The long run is not a goal but rather a journey. Expanding the original example above to three standard deviation would bring the grand total up to 3,600 hours with only 97% certainty. There is still roughly a 3% chance that you will not realize your expectation after 3,600 hours of play.
Still want to play blackjack?
-Sonny-
one quick comment
>Someone with a 15% advantage will realize their goal much sooner than someone with a 5% advantage. Since they are playing "more correctly" they should expect to see their results sooner.
Unfortunately, edge alone has nothing to do with the rate at which you approach the long run. Suppose you paid $1 for a 1billion-1 shot that paid 2billion dollars. That has a 100% edge, but the variance is so huge it would not be worth it.
>Someone with a 15% advantage will realize their goal much sooner than someone with a 5% advantage. Since they are playing "more correctly" they should expect to see their results sooner.
Unfortunately, edge alone has nothing to do with the rate at which you approach the long run. Suppose you paid $1 for a 1billion-1 shot that paid 2billion dollars. That has a 100% edge, but the variance is so huge it would not be worth it.
Sonny
Well-Known Member
I stand corrected
> Suppose you paid $1 for a 1billion-1 shot that paid 2billion dollars. That
> has a 100% edge, but the variance is so huge it would not be worth it.
Well, that's really a matter of certainty equivalence. Many people would be willing to risk a buck for the chance to win $2 billion. Why else would state lotteries and progressive slot machines be so popular?
Regardless of my nit picking, you are right. In my example I did not indicate that the odds were constant for both advantages. Your example above clearly illustrates why advantage alone is not an indication of the rate at which a player will approach the long run. After all, how many state lottery players will reach the long run in their lifetime?
-Sonny-
> Suppose you paid $1 for a 1billion-1 shot that paid 2billion dollars. That
> has a 100% edge, but the variance is so huge it would not be worth it.
Well, that's really a matter of certainty equivalence. Many people would be willing to risk a buck for the chance to win $2 billion. Why else would state lotteries and progressive slot machines be so popular?
Regardless of my nit picking, you are right. In my example I did not indicate that the odds were constant for both advantages. Your example above clearly illustrates why advantage alone is not an indication of the rate at which a player will approach the long run. After all, how many state lottery players will reach the long run in their lifetime?
-Sonny-