April 16th, 2017 at 1:06:56 PM
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This is a 14-page thread from 2014 discussing "What is the long run?"

http://wizardofvegas.com/forum/questions-and-answers/gambling/18140-what-is-the-long-run/#post357678

Here we are 3 years later. I read the entire thread once, and could not find an answer I could understand. I read the thread a 2nd time, and either got lost in tangential discussions, or the math went way over my head.

There did not appear to be a finite answer, even from the Wiz.

I am just hoping there might be some new opinions from the WoV forum mathletes? Please express in non-technical terms, if possible, or add explanations to terms used.

My question is "what is generally considered as the long run in Blackjack?"

75,000 hands? More? Less? Do you run a simulation calculating the number of hands after which you will experience getting positive returns? How do you account for betting, and different house rules?

I don't believe I'll be able to play "the long run". I have quite a ways to go, since I've only made 2 trips to Las Vegas to play BJ, totaling maybe 6 hours.

I just wanted to enjoy reading a clearer explanation to the "long run" compared to the 2014 post.

http://wizardofvegas.com/forum/questions-and-answers/gambling/18140-what-is-the-long-run/#post357678

Here we are 3 years later. I read the entire thread once, and could not find an answer I could understand. I read the thread a 2nd time, and either got lost in tangential discussions, or the math went way over my head.

There did not appear to be a finite answer, even from the Wiz.

I am just hoping there might be some new opinions from the WoV forum mathletes? Please express in non-technical terms, if possible, or add explanations to terms used.

My question is "what is generally considered as the long run in Blackjack?"

75,000 hands? More? Less? Do you run a simulation calculating the number of hands after which you will experience getting positive returns? How do you account for betting, and different house rules?

I don't believe I'll be able to play "the long run". I have quite a ways to go, since I've only made 2 trips to Las Vegas to play BJ, totaling maybe 6 hours.

I just wanted to enjoy reading a clearer explanation to the "long run" compared to the 2014 post.

Eat real food . . . and you won't need medicine (or a lot less!)

April 16th, 2017 at 1:44:48 PM
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The long run is different for every one. It's when nothing surprises you, anymore, at which point you've seen enough, or just grown old. Same goes for the universe.Quote:LostWagesI just wanted to enjoy reading a clearer explanation to the "long run" compared to the 2014 post.

EDIT: In other words, not a lot to look forward to.

Believers are the ones who keep at it long after they've been told it can't be done. On the other hand, the real experts shouldn't care about the crackpots. But, if the wrong answer begs the question, then the wrong question begs the answer.

April 16th, 2017 at 2:50:39 PM
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Thanks for your insights! While I've seen and experienced many things in only 67 years, I am not yet satisfied that I've "seen enough". Here's to another 10-20 years walking on reasonably steady feet! :-)Quote:InTimeForSpace1The long run is different for every one. It's when nothing surprises you, anymore, at which point you've seen enough, or just grown old. Same goes for the universe.

EDIT: In other words, not a lot to look forward to.

Eat real food . . . and you won't need medicine (or a lot less!)

April 16th, 2017 at 3:10:17 PM
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It's different for different games. Some will be the same or similar just by mere coincidence.

Some say the long run is when EV = actual. Of course, you can't calculate a number of rounds to play such that both will be exactly the same since variance exists. Instead, you need to determine how "off" your results can be from EV, and use that figure, as well as how likely you are to be within that range.

Say your Blackjack game is worth $100/hour and a 1% advantage. You can calculate how many rounds you'll need such that you'll have a 99.95% (or whatever degree of certainty you want) chance to be within 2% of your EV (0.98% to 1.02% edge).

Some say the long run is when EV = actual. Of course, you can't calculate a number of rounds to play such that both will be exactly the same since variance exists. Instead, you need to determine how "off" your results can be from EV, and use that figure, as well as how likely you are to be within that range.

Say your Blackjack game is worth $100/hour and a 1% advantage. You can calculate how many rounds you'll need such that you'll have a 99.95% (or whatever degree of certainty you want) chance to be within 2% of your EV (0.98% to 1.02% edge).

"What would Brian Boitano do?"

April 16th, 2017 at 4:00:38 PM
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RS - thanks for a MUCH clearer explanation than what I've been able to gather so far. I am math-challenged and not ready to ask more in equations or formula.Quote:RSIt's different for different games. Some will be the same or similar just by mere coincidence.

Some say the long run is when EV = actual. Of course, you can't calculate a number of rounds to play such that both will be exactly the same since variance exists. Instead, you need to determine how "off" your results can be from EV, and use that figure, as well as how likely you are to be within that range.

Say your Blackjack game is worth $100/hour and a 1% advantage. You can calculate how many rounds you'll need such that you'll have a 99.95% (or whatever degree of certainty you want) chance to be within 2% of your EV (0.98% to 1.02% edge).

My understanding of your explanation is that while there may not be a FINITE answer to the "long run", I should be better off determining my comfort level and acceptability RANGE of how "off" my results can be from EV. That is, how much variance can my bankroll support.

If I still didn't get it right, that's ok, I'll be patient and read some more. Thanks again, though! Appreciate your input.

Eat real food . . . and you won't need medicine (or a lot less!)

April 16th, 2017 at 4:03:24 PM
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That's right -- you got it.

"What would Brian Boitano do?"

April 16th, 2017 at 4:50:26 PM
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It must be how well you described your insight about "long run". OK, I'm now on my looooooooong journey. Have a great week ahead!Quote:RSThat's right -- you got it.

Eat real food . . . and you won't need medicine (or a lot less!)

April 17th, 2017 at 9:26:50 AM
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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 "N0".

Say you have the following:

AvgBet = $100

AvgAdv = 1%

OriginalSD = 1.1 * AvgBet = $110

EV(50,000 hands) = (50,000 * 100) * (.01) = $50,000

SD(50,000 hands) = Sqrt(50,000) * 110 = ~$24,600... 2SD = ~$49,000... 3SD = ~$73,800 ...so you could still be down!

EV(100,000 hands) = (100,000 * 100) * (.01) = $100,000

SD(100,000 hands) = Sqrt(100,000) * 110 = ~$34,800... 2SD = ~$69,600... 3SD = ~$104,000

Thus, to me 100,000 hands would basically be your N0, because with 3SD of confidence it's impossible for you to mathematically be down. The reason it's different for everyone as it refers to blackjack (in my opinion) is because everyone has different bankrolls, spreads (.5xkelly vs 1x kelly vs 1.5xkelly), average bets, and skill level / Average Advantage. An average counter might have a 1% AvgAdv, but a great counter with lots of deviations also selecting good situations could have a 2% AvgAdv. Then again if he wonged a ton more then perhaps he would have a 2% AvgAdv but it would take him twice as long to get the same amount of hands as the first guy. It's all relative to the choices you want to make with your game... which often times aren't even our choices but our available options around us. If someone only has 1 casino within 5 hours of them (and it's 5 min away) but it's a H17 8D game, well then they're going to have to play a crappy game AND a camp out strategy if they want to play and get hours/hands. However, if someone lived near 10 casinos and 3-4 of them had good rules, then this person could afford to make more picky choices/decisions to play only the better games.

Thus, it's different for everyone because we all live in different areas and have different situations as it comes to not only casinos/games, but also to our personal finances/bankrolls and the risk tolerance we want to play with our spreads/etc.

Say you have the following:

AvgBet = $100

AvgAdv = 1%

OriginalSD = 1.1 * AvgBet = $110

EV(50,000 hands) = (50,000 * 100) * (.01) = $50,000

SD(50,000 hands) = Sqrt(50,000) * 110 = ~$24,600... 2SD = ~$49,000... 3SD = ~$73,800 ...so you could still be down!

EV(100,000 hands) = (100,000 * 100) * (.01) = $100,000

SD(100,000 hands) = Sqrt(100,000) * 110 = ~$34,800... 2SD = ~$69,600... 3SD = ~$104,000

Thus, to me 100,000 hands would basically be your N0, because with 3SD of confidence it's impossible for you to mathematically be down. The reason it's different for everyone as it refers to blackjack (in my opinion) is because everyone has different bankrolls, spreads (.5xkelly vs 1x kelly vs 1.5xkelly), average bets, and skill level / Average Advantage. An average counter might have a 1% AvgAdv, but a great counter with lots of deviations also selecting good situations could have a 2% AvgAdv. Then again if he wonged a ton more then perhaps he would have a 2% AvgAdv but it would take him twice as long to get the same amount of hands as the first guy. It's all relative to the choices you want to make with your game... which often times aren't even our choices but our available options around us. If someone only has 1 casino within 5 hours of them (and it's 5 min away) but it's a H17 8D game, well then they're going to have to play a crappy game AND a camp out strategy if they want to play and get hours/hands. However, if someone lived near 10 casinos and 3-4 of them had good rules, then this person could afford to make more picky choices/decisions to play only the better games.

Thus, it's different for everyone because we all live in different areas and have different situations as it comes to not only casinos/games, but also to our personal finances/bankrolls and the risk tolerance we want to play with our spreads/etc.

Playing it correctly means you've already won.

April 17th, 2017 at 10:23:56 AM
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Thanks for a very eloquent and easy-to-follow (not necessarily grasp and understand!) mathematical description. At last, I now know what N0 means! It's been bothering me. I understand a little bit about SD and the bell curve for normal distributions.Quote:RomesThus, it's different for everyone because we all live in different areas and have different situations as it comes to not only casinos/games, but also to our personal finances/bankrolls and the risk tolerance we want to play with our spreads/etc.

I understand now why in other posts you mentioned that the long run would at least be 50,000 hands; then in another post, it was 75,000 hands. I forgot to take into consideration the situations you were describing, and they were both different - the bankrolls, the spreads, the betting strategy, and the types of games. I don't think I'll do much ABOUT the long run, but I just wanted to know the animal a little better and respect it for what it is.

Thanks to you & RS for the math-spirin!

Eat real food . . . and you won't need medicine (or a lot less!)

April 17th, 2017 at 10:48:22 AM
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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%, not 0%.

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”.

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%, not 0%.

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”.

Last edited by: QFIT on Apr 17, 2017

"It is impossible to begin to learn that which one thinks one already knows." -Epictetus