what is "the long run"
Your math skills are amazing . I'm not good at math.
I've played blackjack 67 times in the last 2 years at $5, $10, and $25 tables averaging 5 hours per trip broken into 2 to 3 sessions / trip at 2 deck, 6 deck, and CSM's at 3/2 and 6/5 tables. I follow your recommended basic strategy for H,S, Sp, DD with the exception I don't ever hit 16 nor split 88 against dealer A or 10.
I've made a profit of $1850 during this time and made $10,000 profit in the previous 10 years.
I keep records of all my wins and losses.
Life is short.
What is considered the "the Long run" when commenting that blackjack cannot be beaten in the " long run"?
Best Regards!
that is only 335 hours of playing. There are people on this board who have done that amount of play in 2014 alone.
Quote: GWAEI bet Bob is foaming at the mouth wanting to jump in on this thread.
that is only 335 hours of playing. There are people on this board who have done that amount of play in 2014 alone.
The long run is a thin edge play that you have to grind on forever to suck a low wage out of. To hell with that.
Quote: treetopbuddyApparently everybody loses in the long run. So, if your losing, you are in the long run. If you are winning, you are in the short run.
lmao, thanks for making me laugh at work. Now people know that I am not working.
Quote: treetopbuddyApparently everybody loses in the long run. So, if your losing, you are in the long run. If you are winning, you are in the short run.
I agree. Anyone who gambles against me loses in the long run. But every once in a while they experiece some short term luck.
Quote: cwwbjrWhat is considered the "the Long run" when commenting that blackjack cannot be beaten in the " long run"?
This is one of the most frequent questions I get. You truly arrive at the long run after an infinite number of hands. However, for practical purposes, you can get very close with a big finite number. "How big is big?" you might ask. There is no simple answer. It is like asking how many grains of sand do you need to form a pile of sand. It can be said that the more you play the closer to the "long run" you will get, but you will never fully arrive there. As with many things in life, there is not an absolute answer. It is a matter of the shade of the grey.
In general the "long run" is measured as a probability of the casino being ahead of you after a given number of hands. Obviously, as the number of hands goes to infinity, this probability goes to 1. But that's meaningless information. Hence, N_0.
this is easily extended to include the z-scoreQuote: teliot(SD/EV)^2
(Z*SD/EV)^2
This concept in math = Standard Score
"The number of standard deviations from the mean is also called the "Standard Score", "sigma" or "z-score"."
http://www.mathsisfun.com/data/standard-normal-distribution.html
your example is Z=1 (or could be -1)
I think my table is correct for a few z-scores and probabilities
-1 0.841344746
-2 0.977249868
-3 0.998650102
-4 0.999968329
-5 0.999999713
(one needs to do the math for the number of trials)
-1 13,225.0
-2 52,900.0
-3 119,025.0
-4 211,600.0
-5 330,625.0
and with a .005 edge (instead of the example of .01) I show
-1 52,900.0
-2 211,600.0
-3 476,100.0
-4 846,400.0
-5 1,322,500.0
looks like it keeps taking more trials to have a larger confidence of being further into the long run
Sally
Z*(SD/EV)^2 (typo? - I think this is what you meant).Quote: mustangsallythis is easily extended to include the z-score (Z*SD/EV)^2
Thanks for filling in the gaps in my post 8-) The values of N_0 are extraordinary for the basic strategy blackjack player. That's why players can think they have the edge for a long time. These values are similar to baccarat rolling chip programs, which is why baccarat players are similarly deceived. But by far, the largest values of N_0 are for pass line craps players taking full odds. Hence endless pointless arguments about DI.
No typoQuote: teliotZ*(SD/EV)^2 (typo? - I think this is what you meant).
The number of SDs from the mean
If that was correct a -1 z-score would produce a -# of trials
my BruceZ uses it (where I found it first) and the formula is in many prob/stats books too
I see this in the book
Understanding Probability
Chance Rules in Everyday Life
Second Edition
HENK TIJMS
starting on page 168 (he uses z-value)
This book is fun to read too. A very nice personal touch in his writing style
for a math book
Sally
Thank you for your answer!
Would that then not create a conflict between making an absolute conclusive statement based on a non- absolute premise .
For example, say, conclusive statements like "Everyone always loses in the "long run", or, " All betting strategies are equally worthless" when referring to a non-absolute , shade of grey term "long run".
The reason I ask is because I'm wondering why some players get banned from playing blackjack because of suspicion of card counting , for example, which includes a " Betting Strategy " which results in them being banned , and were they allowed to continue playing would they eventually win or lose in the ambiguous "long run"?
What do you think?
Playing N hands, the expected win for the house is N*EV, the standard deviation is sqrt(N)*SD. So, for the house to be beating the player by K standard deviations gives:Quote: mustangsallyNo typo
N*EV > K*sqrt(N)*SD,
sqrt(N) > K*SD/EV,
N > (K*SD/EV)^2
OK then, time for a cup of coffee.
IMO, it is all about the degree of certainty that one is willing to accept for how much into the long run one isQuote: cwwbjrWhat is considered the "the Long run" when commenting that blackjack cannot be beaten in the " long run"?
Best Regards!
my math for a -5 SD
a 1 in 3,488,555.79 shot,
on average,
of showing a net profit after 1,322,500 hands played against a house edge of -.005
1 in 3,488,555.79 is a small value
That means out of 170,000,000 BJ players just going by basic strategy (using a card for each playing decision)
I would expected on average about 49 of them to have beaten the casino (showing a profit) after playing 1,322,500 hands.
even at 4SD or about 846,400 hands played the # of BS players out of 170,000,000 to still show a profit = about 5,384
would you still be impressed with each and every one of them?
They just followed a BS card for every play
someone(s) will be that lucky against a house edge
Sally
you are so sweet!Quote: teliotN > (K*SD/EV)^2
OK then, time for a cup of coffee.
so nice to see why it is
Sally
Quote: mustangsallyUnderstanding Probability
Chance Rules in Everyday Life
Second Edition
HENK TIJMS
I agree that Tijms' book, Understanding Probability is excellent and also fun to read--with a good deal of focus on gambling and includes a number of chapters on subjects that have been addressed in this forum. I would say the first section is quite easy to grasp whereas the second section is a little more difficult, though a knowledge of calculus helps.
I also recall that the author specifically refers to the Wizard of Odds website and mentions Michael Shackleford (I think in a footnote in a section on roulette).
By the way, mustangsally refers to the Second Edition. There is now a Third Edition published in 2012.
To me, even 1 mile is a long run.
All betting SYSTEMS are crap unless you have the math that adds up to over 100%. NO betting system can turn a negative game into a positive one.Quote: cwwbjrWizard,
Thank you for your answer!
Would that then not create a conflict between making an absolute conclusive statement based on a non- absolute premise .
For example, say, conclusive statements like "Everyone always loses in the "long run", or, " All betting strategies are equally worthless" when referring to a non-absolute , shade of grey term "long run".
The reason I ask is because I'm wondering why some players get banned from playing blackjack because of suspicion of card counting , for example, which includes a " Betting Strategy " which results in them being banned , and were they allowed to continue playing would they eventually win or lose in the ambiguous "long run"?
What do you think?
agreedQuote: teliot
Thanks for filling in the gaps in my post 8-) The values of N_0 are extraordinary for the basic strategy blackjack player. That's why players can think they have the edge for a long time. These values are similar to baccarat rolling chip programs, which is why baccarat players are similarly deceived. But by far, the largest values of N_0 are for pass line craps players taking full odds. Hence endless pointless arguments about DI.
Suppose you find a casino offering even money on the Banker bet in baccarat (to avoid confusion, I always capitalize the names of the bets in baccarat), which has happened before. To save you the trouble, the player (one one playing, not the Player bet) advantage is 0.0123508 and the standard deviation of one bet is 0.951153.
How many bets do you have to make to have a 95% chance of showing a profit?
In this case normsinv(0.95) = 1.644854.
So, the answer would be (1.644854*0.951153/0.0123508)^2 = 16,046.
Quote: pokerfaceMany people believe Marathon is a long run.
To me, even 1 mile is a long run.
*snort*
I'm in real estate finance. In that field, one valuation metric you use is the cap rate. Basically, this means that an investor expecting a 10% return will pay $1,000,000 for a property he thinks will earn $100,000 per year. The simple mathematical formula is income / rate ... in this example, $100,000 / 0.10 = $1 million.
This formula represents the mathematical convergence of all of the years of $100,000 income discounted for time value, to infinity years. While the discounting eventually overwhelms the $100,000, it never takes it to zero. But when you add 1 thru infinity, the sum converges to (income / rate). (Kind of like that old problem, walk halfway to the door, stop, walk halfway to the door, stop, etc. ... even though you never mathematically get out of the room, you somehow physically get out of the room.)
Since real estate improvements don't last infinity years, there's a practical time horizon of 20 years to where the summation of 1 - 20 is so close to the convergence at infinity that there is no practical difference. I haven't done the math, but I understand it to be on the order of a few hundredths of a percent. Since the formula (income / rate) is so close to summing to infinity, we just do the formula. Ironically, many folks in my field don't know this!
So ... in my field, 20 years is the "long run" in that, it's so close to "forever/infinity" that it makes no economic difference.
That's my suggestion for the practical definition of the "long run." "Economic difference" can mean different things to different people, but when you start getting to the point where we're just talking about maybe 0.1% difference in EV after N trials and after infinity trials, maybe N becomes the "long run." In real estate, N = 20.
What does it equal in this context?
Another way of viewing this is that 5% of the players are still beating the house by pure luck after this number of hands.Quote: WizardHow many bets do you have to make to have a 95% chance of showing a profit?
For similar reasons, when evaluating "Net Present Value," (NPV) the computations rarely exceed 7 years.Quote: MrWarmthSo ... in my field, 20 years is the "long run" in that, it's so close to "forever/infinity" that it makes no economic difference.
It is well known that a 95% CL = 1.96Quote: WizardThe general formula is (normsinv(p)*std/ev)^2, where normsinv is an Excel function for the number of standard deviations from zero where p is on the standard normal curve.
In this case normsinv(0.95) = 1.644854.
1.644854 is for 90%
I think this works in Excel (at least my version)
=-NORMSINV((1-0.95)/2)
z-score
1.959963985
better yet
=NORMSINV((1+0.95)/2)
do not really know much about that function right now
Sally
Quote: teliotFor similar reasons, when evaluating "Net Present Value," (NPV) the computations rarely exceed 7 years.
The real estate calculation is just one particular industry's calculation of NPV. 7 years is not all that long a holding period ... I'm not sure which robber baron in days past set real estate at 20, but yeah, you're right, I haven't done the math but the sum is still probably pretty close at 7 years.
Quote: teliotPlaying N hands, the expected win for the house is N*EV, the standard deviation is sqrt(N)*SD. So, for the house to be beating the player by K standard deviations gives:
N*EV > K*sqrt(N)*SD,
sqrt(N) > K*SD/EV,
N > (K*SD/EV)^2
OK then, time for a cup of coffee.
Exactly. Wait, what?
Quote: mustangsallyIMO, it is all about the degree of certainty that one is willing to accept for how much into the long run one is
Yes, exactly.
When someone asks, how long is the long run, the question you need to ask them is, how sure do you want to be that you will lose? The more sure you want to be, the longer you need to play.
To the OP: how much do you jump your bets around? How do you decide when to raise or lower your bets? Blackjack is an extremely low-variance game but if you move your bets around a lot the swing can be big. When i play, my expected win-rate is around $300 an hour, but that doesn't mean that I can't blow off $10k in a shoe.
Quote: mustangsallyIt is well known that a 95% CL = 1.96
1.644854 is for 90%
That is for both sides of the bell curve. I was asking about being in one side only.
From the point of view of a Counter with a Modest Advantage (say 1%), I tell people who ask me the following with regard to the 'long run' (ie when it is guranteed to be in front)
10 hours = Random Fluctuations
30 hours = You start to see a trend, more often in front
100 hours = Most of the time you are in front
300 hours = Almost all of the time you are in front
1000 hours = If you are not in front, then you are really unlucky.
The thing is that for a new counter, you never know whether bad results is just being on the wrong side of the curve (being unlucky) or you are just not a good counter. As you play more and more hands if you results do not improve then it is more probable that you are a bad counter as opposed to unlucky. You are never sure. And there is a point that the results give a definite strong indication about the skill level (as opposed to unlucky) , which I would estimate at around 300 hours.
Similar thing should apply from the other side, like the poster who played around 300 hours. But if he plays BS and games with low HE (say -0.4%), then the above rule of thump numbers from teh other side would be a lot bigger. So at 300 hours being in front, he is quite lucky (but not extremely lucky)
>10x craps (n0=587,669).
Game EV SD n0
Craps 100x 0.014 101 51,049,505
Jacks or Better (Full pay, 100 draw) 0.005 15 10,122,277
Jacks or Better (Full Pay) 0.005 4 923,270
Keno pick 10 0.396 332 703,406
Craps 10x 0.014 11 587,669
Double Zero Roulette (single number) 0.053 35 442,756
Blackjack liberal rules 0.003 1 168,686
Craps 3-4-5 0.014 5 121,509
Slot machine (estimate) 0.050 9 32,400
Let it Ride 0.035 5 21,695
Let it Ride $1 bonus bet 0.230 32 19,357
Blackjack standard rules 0.010 1 13,225
Baccarat banker 0.011 1 7,698
Baccarat player 0.012 1 5,870
Blackjack 6:5 0.025 1 2,116
Casino War (tie) 0.187 8 1,990
Casino War 0.029 1 1,329
Double Zero Roulette (even bet) 0.053 1 725
Baccarat tie 0.144 3 338
Keno pick 1 0.250 1 27
The pay-table on some of these games are pretty skewed.. so the normal approximation won't be totally accurate (i.e n0 won't be 84% chance) .. but n0 is still a good index i think.
oh, duh meQuote: WizardThat is for both sides of the bell curve. I was asking about being in one side only.
yes you did
I have always mixed up under and outside
N=16045.9449
ev=198.1802562
sd=120.4850134
ev/sd=1.644854
0.950000038=NORMSDIST(1.644854)
sweet!
Quote: cwwbjrWould the 5% of players who are beating the casino after this number of hands be the same individuals repeatedly or would the 5% be different individuals from each sample and then would it still be luck respectively, like for example" winning hands vs the dealer" ( versus)" winning money vs number of hands won or lost" ( by bet variation as in card counting)
Different in each sample.
If I understood the question.
Quote: cwwbjrAre these people on this board with that amount of play also profitable up to and including that time period ?
Quote: cwwbjrAre these people on this board with that amount of play also profitable up to and including that time period ?
Yes.
Now back to you. Lol. 67 trips x 5 hours per trip is 335 hours, x 80 rounds per hour (I doubt you are getting 100) is 26,000+ rounds. That is not the long run. I have had several runs longer than that where I was down and still ended up significantly up for the year, and a year for me is in the neighborhood of 80,000 rounds.
So, what are we getting at here? You have hinted at card counting, but mentioned conditions and games that aren't playable by traditional card counting methods, like 6-5 BJ and CSM. So are you indicating that your being ahead after 2 years and sort of a less formal statement that you are ahead after 10 years is the result of some sort of play with an advantage or is it just positive short term variance, mixed in with some 'fuzzy' and 'selective' record keeping? I am wondering this because, again, that statement that you are about $10,000 ahead after 10 years just doesn't sound so definitive.
Not splitting 88 v 10 or A or never hitting 16 is the key to a winning BJ strategy. Get drunk and toss in some doubling 13 vs 2 and 3 and BOOM you have the key for success. Occasionally you wake up the next morning with 2k extra and don't even know where it came from.Quote: kewljYes.
Now back to you. Lol. 67 trips x 5 hours per trip is 335 hours, x 80 rounds per hour (I doubt you are getting 100) is 26,000+ rounds. That is not the long run. I have had several runs longer than that where I was down and still ended up significantly up for the year, and a year for me is in the neighborhood of 80,000 rounds.
So, what are we getting at here? You have hinted at card counting, but mentioned conditions and games that aren't playable by traditional card counting methods, like 6-5 BJ and CSM. So are you indicating that your being ahead after 2 years and sort of a less formal statement that you are ahead after 10 years is the result of some sort of play with an advantage or is it just positive short term variance, mixed in with some 'fuzzy' and 'selective' record keeping? I am wondering this because, again, that statement that you are about $10,000 ahead after 10 years just doesn't sound so definitive.
Quote: AxelWolfNot splitting 88 v 10 or A or never hitting 16 is the key to a winning BJ strategy. Get drunk and toss in some doubling 13 vs 2 and 3 and BOOM you have the key for success. Occasionally you wake up the next morning with 2k extra and don't even know where it came from.
Don't forget to never split 9s. 18 is a good hand, after all.
Quote: Wizard*snort*
No objection!
However, I feel that, in "the long run", my answer is closer to the OP's question than most math jargon.
In fact, it seemed to me the OP was not asking a question at all.
Quote: pokerfaceNo objection!
However, I feel that, in "the long run", my answer is closer to the OP's question than most math jargon.
In fact, it seemed to me the OP was not asking a question at all.
Yes, this thread certainly has taken a trollish twist. "Mathematician's fallacy", revisited. I wonder if it's the same guy.
My question was "what is considered to be the "long run" with respect to the statements," Blackjack can't be beaten in the long run... and "all betting strategies are equally worthless". My personal limited play, as a purely recreational player, I realize is minimal in both time and money compared to more serious / professional players.
My meager $12,000 profit over 12 years is only of significance to me and my reason for asking was to get the The Wizard's definition of the "long run".
I don't drink when I play and I keep meticulous records, otherwise , I feel I would only be cheating myself.
And by the way , congratulations on your longer run wins.! Are you also ahead in your blackjack play?
Best of luck to you!
Quote: AxiomOfChoiceWhen i play, my expected win-rate is around $300 an hour, but that doesn't mean that I can't blow off $10k in a shoe.
That is a prodigious hourly win rate. Are your stakes really that high? I'm not doubting you, just didn't get the impression you played that big from your threads here.
Quote: AcesAndEightsThat is a prodigious hourly win rate. Are your stakes really that high? I'm not doubting you, just didn't get the impression you played that big from your threads here.
I've raised my stakes significantly recently.
Actually, I should really take the time to run some sims, the $300 number is mostly out of my ass. It actually seems conservative though.
Quote: AcesAndEightsThat is a prodigious hourly win rate. Are your stakes really that high? I'm not doubting you, just didn't get the impression you played that big from your threads here.
That is a nice hourly. I'm very jealous. I am not doubting him either. One only need read through some of Axioms posts to know he knows of what he speaks.
Quote: AxiomOfChoiceI've raised my stakes significantly recently.
Now, since you have shared this info, I would like to hear your reaction to the significant increase in stakes in regards to longevity and heat concerns. I realize being a recent development, you may not have formulated a complete opinion, but I would like to hear your early impressions.
I ask because I play at a level that I believe is well tolerated at my locations. I have the bankroll to move up in stakes, but that would put me in a whole different ball game as far as drawing attention and casino tolerance levels.
Quote: teliotAwesome Chrisr!
Double Zero Roulette (single number bet) 0.053 35 442,756
Blackjack liberal rules 0.003 1 168,686
I'm surprised my assertions that keno is better than 10x craps
and roulette is better than a good game of blackjack went so unchallenged.
Quote: kewljNow, since you have shared this info, I would like to hear your reaction to the significant increase in stakes in regards to longevity and heat concerns. I realize being a recent development, you may not have formulated a complete opinion, but I would like to hear your early impressions.
I ask because I play at a level that I believe is well tolerated at my locations. I have the bankroll to move up in stakes, but that would put me in a whole different ball game as far as drawing attention and casino tolerance levels.
I really don't play very much. We are in such different situations. You play for a living; if you get backed off or barred at too many places it threatens your livelihood. I play for a hobby that I'm trying to make profitable; if it doesn't work out I'll spend more time playing video games or something. I would be a lot more careful if I was in your situation. I've never encountered anything that I would classify as heat, but maybe I just haven't noticed.
I also haven't played anywhere near enough hours to tell if I'm actually getting that hourly rate. It's all theoretical, and, not even based on my own simulations -- a lot of it is based on published work of others. I should really take the time and do it myself. I am not that confident in that number (I'm fairly sure that I'm beating the game, though)
Quote: AxiomOfChoiceI really don't play very much. We are in such different situations. You play for a living; if you get backed off or barred at too many places it threatens your livelihood. I play for a hobby that I'm trying to make profitable; if it doesn't work out I'll spend more time playing video games or something. I would be a lot more careful if I was in your situation. I've never encountered anything that I would classify as heat, but maybe I just haven't noticed.
I also haven't played anywhere near enough hours to tell if I'm actually getting that hourly rate. It's all theoretical, and, not even based on my own simulations -- a lot of it is based on published work of others. I should really take the time and do it myself. I am not that confident in that number (I'm fairly sure that I'm beating the game, though)
I see. Thank you for sharing, AxiomOfChoice.
Quote: AxiomOfChoiceI've raised my stakes significantly recently.
Actually, I should really take the time to run some sims, the $300 number is mostly out of my ass. It actually seems conservative though.
Cool, good luck. When I'm in Vegas my hourly is in the $30-50 range, depending on the game and the location. But i'm providing for two people now, so the amount of money I'm willing to lose on a trip is pretty small, and isn't getting any bigger.
I echo kewlj's curiosity about heat at that level. Good luck :)
