how many hands is long run?

Im currently at about 5k hands played, and am 1.5% below the expected edge. At one point i was also 1.5% above the house edge.

Question, how likely is it to not be very near the house edge at 5k hands played? When should i expect to hit the house edge? What would be considered a reasonable sample size? Its a 1 deck game btw, and im simply playing composition strategy, or when im not sure i stick to basic. no counting. Assuming i dont make mistakes.

Alas, you hit that house edge on the very FIRST HAND and also on EACH AND EVERY SUBSEQUENT hand.

i mean statistically speaking, what is a reasonable sample size to have a return as expected in the house edge?


Say if i play a billion hands it will be very likely that my bottom line is -0.5%

If i play 100 hands, it wont be so likely etc...

Quote: hoppala

i mean statistically speaking, what is a reasonable sample size to have a return as expected in the house edge?.

There is a concept known as N0 that counters sometimes use. That is the number of hands such that EV > 1 STD DEV. That's the number of hands that would correspond to a losing result being more than 1 standard deviation from expectation. N0 varies based on a lot of factors about the game, but is generally in the range of 25k to 50k hands for ordinary card counting. In other words, at 5k hands you are still experiencing a lot of statistical noise.

Is there a figure for say pass line at craps?

Quote: DeMango

Is there a figure for say pass line at craps?

In the case of a wager with a house edge, N0 corresponds to the number of decisions until the house EV is greater than 1 STD DEV, that is, for the house to be losing after that number of decisions against a Pass Line player would be more than 1 standard deviation from expectation.

The formula for N0 is (STDDEV/EV)^2. The EV for the pass line is 1.414%. The standard deviation is 0.999900. So, with no odds, N0 for the house is (0.9999/.01414)^2 = 5000 rolls.

If you include odds, then

N0 for 2x odds is 40,842.

N0 for 3x,4x,5x odds is 120,830.

N0 for 100x odds is 50,802,102

Long run? good one. Seems to me I saw 50,000 rounds referenced in one of the bringing down the house type books (law of large numbers was the phrase...lol). Like teliot said, the actual number will vary by game conditions, but since I play a variety of different BJ games with different conditions, I have opted for a bit higher number. I use 80,000 rounds for BJ. I picked this number, because I play 80 K rounds per year or more. So basically, I am figuring a year. Interestingly enough, I have had 6 month losing periods in both 2010 and 2011, so that is roughly 40,000 rounds with losing results, but for each year in total the results were pretty close to expectation.

I have had discussions with players that have endured a whole year of losing, but most play fewer rounds than myself, so I feel like this number I have chosen holds. I do find myself thinking, if I can have losing periods of 6 months, then why not a year? (80,000+ rounds) Why not 2 years? (160,000+ rounds) There has to be a point that the math kicks in and results begin to come in line with expectation. Until proven otherwise, which I hope never happens, I am going with a years results for me, 80,000 rounds.

Quote: hoppala

Say if i play a billion hands ...
If i play 100 hands, ...

If I play four hands in succession and lose, I'd walk.
If I play ten hands and am "down", I walk.
Yet each of those hands was against a house edge when dealt.

You want to know what "long run" is? Heck, why not use the casino's definition?
They switch dealers every twenty minutes don't they?

Quote: hoppala

Im currently at about 5k hands played, and am 1.5% below the expected edge. At one point i was also 1.5% above the house edge.

Question, how likely is it to not be very near the house edge at 5k hands played? When should i expect to hit the house edge? What would be considered a reasonable sample size? Its a 1 deck game btw, and im simply playing composition strategy, or when im not sure i stick to basic. no counting. Assuming i dont make mistakes.

The Wizard showed this B4.
I do not have the link. But it is simple math.

The standard deviation of the house edge is =oneUnit_sd/sqrtN
BS player
Say the one unit SD is 1.15/sqrt5k = 0.016263
Edge is say -.5% +/- 1.6% (1.6% is the 1SD error. The normal curve uses 3SD+/-)
50,000 hands the error will be
1.15/sqrt50k = 0.005143
Of course that error is over a larger number of $s bet

A counter
Say the one unit SD is 2.5/sqrt5k = 0.0353553
Edge is say 1% +/- 3.53%

It can also be done with total $SD and total $action over N bets
=TOTAL$stdev/$action = SD of the HE

Take the math from there. The EV/SD is also a good example to use.

also...
"There is a lot of talk about the long term and short term in Blackjack.
Basically the only difference is that the more you play, the more likely your actual play will match theoretical advantage"

Norm knows his stuff too
http://www.blackjackincolor.com/blackjackvariance1.htm

Keep this in mind.
The key is "theoretical advantage"
$net/total $action
NOT actual $s won

Thanks for the replies!

Quote: DeMango

Is there a figure for say pass line at craps?

To add.
oneUnitSD/SQRT N Trials

0.999900005 / SQRT 5,000 = 0.014140721
this is the 1SD value of the 1.41% pass line HE at 5k trials (same avg bet)

1.41%HE +/- 1.41% (1SD +/-) again, use 3SD for the normal surve

So 5k is a very small sample size to be even close to losing 1.41% after 5k bets
The error is just too high. Good (not great) chance of coming out ahead.

here is for 25,000 bets
0.999900005 / SQRT 25,000 = 0.006323923
3Sigma = -0.018971769 to 0.004830355
Still a very wide range... most in the negative side

Point is...
It take many trials to get the error to say .001
many will never play that many trials.
Then that small error is over a larger $ action.

I think the economist Adam Smith said "in the long run we are all dead" :)

well that means an advantage of 0.5% is still a huge gamble...


im gonna assume 80k as the target of hands played to have an ok sample size, ty for the answers, i thought 5k is pretty solid and was getting angry at the results...

Quote: hoppala

well that means an advantage of 0.5% is still a huge gamble...

im gonna assume 80k as the target of hands played to have an ok sample size, ty for the answers,
i thought 5k is pretty solid and was getting angry at the results...

Yep. It is all gambling and proper bankroll.
Always assume nothing.

Here is a better example

BS player
-.005 edge
you want the error to be .001 so your range of HE after X trials will be -.002 to -.008 (3X SD)
[unitSD / E (error)]^2 is the formula to use

BS SD about (1.15unit / .001)^2 = 1,322,500 hands
Double-check this. Do the math...

at 80,000 hands the standard error of the HE is
1.15/SQRT of 80,000
1.15/282.84 = 0.00406586

so your 3SD range to fall into after 80K hands is the HE of -.005 +/- 0.0122
-.0.0172 to +0.0072
More in the negative than positive

Still a very wide range to end up in.

Play with the math and you will see, do not just assume.

Good Luck!

For a different perspective...
Lets say you play 80 hands per hour of Blackjack, 8 hours a day, 5 days a week, 52 weeks a year for 50 years. The math indicates 8,320,000 original hands (there will be splits making additional hands played). If your theoritical advantage is 1.5%, then the expected profit upon the original hands is $124,800 for every $1 as average original bet (an average $10 bet equals $1,248,000).

This is the carrot on stick in front of aspiring 21 players.

Quote: 98Clubs

This is the carrot on stick in front of aspiring 21 players.

Of course, all aspiring 21 players, maybe 99.9992% are just underfunded. Yes, even the $10 bettors.
The bankroll is too small for the bet sizes.
Not to mention the other side of the coin, over betting small bankrolls.

$1.2M may sound good to some for 50 years of work, assuming you have the bankroll to make it that far.
$25K a year (B4 taxes) for all the work and no benefits.

Just being a Manager at a burger joint IMO is a better career.

Quote: 7craps

$25K a year (B4 taxes) for all the work and no benefits.
Just being a Manager at a burger joint IMO is a better career.

Sure, but that calculation was for $10.

If unit size is $100, you're at $250K/year, no? Or maybe "unit size" average 2 hands of $250?
Still wanna flip burgers?

See also: "team play" ;-)

deleted

Quote: 98Clubs

For a different perspective...
Lets say you play 80 hands per hour of Blackjack, 8 hours a day, 5 days a week, 52 weeks a year for 50 years. The math indicates 8,320,000 original hands (there will be splits making additional hands played). If your theoritical advantage is 1.5%, then the expected profit upon the original hands is $124,800 for every $1 as average original bet (an average $10 bet equals $1,248,000).

This is the carrot on stick in front of aspiring 21 players.

1.5% advantage is impossible though no?

deleted

Even if the 52 week per year/50 year $10 player were to achieve the theoretical, he wasted his time BIG TIME. That's what aspiring BJ players need to look at above all else.

deleted

Quote: 7craps

To add.
oneUnitSD/SQRT N Trials

0.999900005 / SQRT 5,000 = 0.014140721
this is the 1SD value of the 1.41% pass line HE at 5k trials (same avg bet)

1.41%HE +/- 1.41% (1SD +/-) again, use 3SD for the normal surve

So 5k is a very small sample size to be even close to losing 1.41% after 5k bets
The error is just too high. Good (not great) chance of coming out ahead.

here is for 25,000 bets
0.999900005 / SQRT 25,000 = 0.006323923
3Sigma = -0.018971769 to 0.004830355
Still a very wide range... most in the negative side

Point is...
It take many trials to get the error to say .001
many will never play that many trials.
Then that small error is over a larger $ action.

i dont understand a single word youre saying.

could you give me a few hints?

What is sigma, sqrt and he? I guess sd means standard deviation, reading up on that now.

So on a small sample size, im more likely to be below EV?! What sourcery is this, i thought deviation means, +-, could go either way....

Quote: hoppala

What is sigma, sqrt and he?

sigma = standard deviation [by convention the Greek symbol is often used, spelling 'sigma' in Eng. not so much]

sqrt = square root

he = house edge

Quote:

What sourcery is this.

Very good! perhaps unintentional?

Quote:

So on a small sample size, im more likely to be below EV?!

Not sure what you are quoting, but the gist of it is that sample sizes need to be huge in order to expect to have results close to the theoretical HE by percentage.

Quote: odiousgambit

sigma = standard deviation [by convention the Greek symbol is often used, spelling 'sigma' in Eng. not so much]

sqrt = square root

he = house edge



Very good! perhaps unintentional?



Not sure what you are quoting, but the gist of it is that sample sizes need to be huge in order to expect to have results close to the theoretical HE by percentage.

thx for clearing that up.

what i meant is, if house edge is 2% the outcome according to the standart deviation should be either above or below that, with equal probability.

So after x hands i could be at -3% return, just as likely as i could be at -1%.

Quote: hoppala

what i meant is, if house edge is 2% the outcome according to the standart deviation should be either above or below that, with equal probability.
So after x hands i could be at -3% return, just as likely as i could be at -1%.

You seem to have that right.

Quote: DBJT

Sure, but that calculation was for $10.

If unit size is $100, you're at $250K/year, no? Or maybe "unit size" average 2 hands of $250?
Still wanna flip burgers?

See also: "team play" ;-)

One of the reasons I quit bj21.com and other blackjack websites is that you can't verify the poster's results, i.e. there is no INDEPEDENT third party verification process. Anyone can make a handle, and brag how much they make. I have been around card counters for a long time -- some of the damn best card counters in the US -- and they all they me how hard it is to play black (chips) and get away with it.

Going from red to green is easy, but going from green to black is not. Too much heat, need a good act, few good games in the US (just check my CBJN to be sure), casino workers are smarter, better anti-counter devices, BJ pays 6:5, etc.

Team play??? Oh please -- talk about dishonesty, record keeping, etc. I know one guy who bankroll teams and it's a hassle factor getting the counter to push the bet out when the count calls for it.

Every once in a while, I'll get tipped off on a BJ pays 2:1 special, otherwise, I don't play BJ at all. I don't miss it at all.

Quote: hoppala

Im currently at about 5k hands played, and am 1.5% below the expected edge. At one point i was also 1.5% above the house edge.

Question, how likely is it to not be very near the house edge at 5k hands played? When should i expect to hit the house edge? What would be considered a reasonable sample size? Its a 1 deck game btw, and im simply playing composition strategy, or when im not sure i stick to basic. no counting. Assuming i dont make mistakes.

The industry standard in Blackjack (when I used to play BJ) is to look at Brett Harris' N(0) concept. For 1 SD, it's 1X the number of hands, for 2SD, it's 4X the number of hands, and for 3SD, it's 9X the number of hands.

Also, as you pointed out, it really depends on your average advantage. Most card counters get 0.5% to 1% advantage and that makes it hard to reach 1 SD. Basically, the bigger your edge, and N(0) shrinks.

Quote: Ardent1

...you can't verify the poster's results, i.e. there is no INDEPEDENT third party verification process.

Umm, and someone needs to prove something to you, why again? This is the INTERNET, man, nobody's gonna spoon feed you anything. Gotta do your own due diligence on anything and everything. Grow up, it's almost 2013, where you been? LOL

Quote: Ardent1

...they all they me how hard it is to play black (chips) and get away with it

Oh, for individual counters alone, maybe, sure. But teams? Not so much. Recruiting trustworthy gorillas is probably one of the easiest things can be done. How many decent basic strategy players even right here reading this thread right now would do it in a heartbeat, if given the chance, just for the comps they'd add to their player's card? Child's play, LOL. And there's way more than one way to skin a cat here for that "little problem" too, no biggie hardly.

Bottom line, to quote the current website of Semyon Dukach (a guy who's opinion on beating blackjack I'd take with much more value than your opinion) :

"I joined the MIT blackjack team which is the subject of this book and spent several years with my
teammates feeling smug about being able to beat casinos around the world out of a few million
dollars before finally realizing that it's not as much of a challenge as it might seem."

You can see the quote above here:

Quote: Ardent1

Team play??? Oh please -- talk about dishonesty, record keeping, etc. .

So, what's the tl;dr version of this post?

Just because you can't do it, Mr. Ardent, don't mean it ain't bein' done by others, with more skillz or resources ;-)

Quote: Ardent1

...otherwise, I don't play BJ at all. I don't miss it at all.

Uh huh. And I'm sure it doesn't miss you, LOL. To each his own.

Quote: Ardent1

One of the reasons I quit bj21.com and other blackjack websites is that you can't verify the poster's results, i.e. there is no INDEPEDENT third party verification process. Anyone can make a handle, and brag how much they make. I have been around card counters for a long time -- some of the damn best card counters in the US -- and they all they me how hard it is to play black (chips) and get away with it.

Going from red to green is easy, but going from green to black is not. Too much heat, need a good act, few good games in the US (just check my CBJN to be sure), casino workers are smarter, better anti-counter devices, BJ pays 6:5, etc.

Team play??? Oh please -- talk about dishonesty, record keeping, etc. I know one guy who bankroll teams and it's a hassle factor getting the counter to push the bet out when the count calls for it.

Every once in a while, I'll get tipped off on a BJ pays 2:1 special, otherwise, I don't play BJ at all. I don't miss it at all.

It is true, there is a lot of BS floating around on the different BJ sites. But it usually doesn't take long to sort out who is credible and who isn't. I have learned a lot from BJ21 and other sites, but perhaps the best feature is the contacts that you make and networking that can be extremely beneficial.

When you talk about the difficulty in playing black chips, I am not sure if you are talking spreading green TO black or spreading black. There is a big difference. Tolerance levels are different at different locations as well as different stores within each location, obviously. Here in Vegas, a solo player can spread green to mid black without too much difficulty at most stores. Especially if you keep your sessions short. To me this level is the 'sweet spot', pretty well tolerated by many casinos. Again, this is dependent on your style of play. If you like to camp out at one table for a couple hours, then No, you will have problems. If you limit your sessions to 45 minutes or so, you can fly under the radar. I go even further to the extreme. One time through bet cycle. I NEVER retreat to smaller bets after showing larger bets.

I think the problem with this level of play is your yearly expectation is mid to high 5 figures, depending on just how much time you put in. Once players acquire the BR to play higher, they want to move up in stakes and make more money and that is a whole new ball game. I don't believe you can achieve the same kind of longevity playing higher stakes.

I should qualify that my comments pertain to Vegas play, which again, is what I am familiar with. The advantage of Vegas is quantity not quality of games, so you have a much bigger rotation of 'playable' games, which contributes to being able to fly under the radar.

Quote: kewlj

It is true, there is a lot of BS floating around on the different BJ sites. But it usually doesn't take long to sort out who is credible and who isn't. I have learned a lot from BJ21 and other sites, but perhaps the best feature is the contacts that you make and networking that can be extremely beneficial.

When you talk about the difficulty in playing black chips, I am not sure if you are talking spreading green TO black or spreading black. There is a big difference. Tolerance levels are different at different locations as well as different stores within each location, obviously. Here in Vegas, a solo player can spread green to mid black without too much difficulty at most stores. Especially if you keep your sessions short. To me this level is the 'sweet spot', pretty well tolerated by many casinos. Again, this is dependent on your style of play. If you like to camp out at one table for a couple hours, then No, you will have problems. If you limit your sessions to 45 minutes or so, you can fly under the radar. I go even further to the extreme. One time through bet cycle. I NEVER retreat to smaller bets after showing larger bets.

I think the problem with this level of play is your yearly expectation is mid to high 5 figures, depending on just how much time you put in. Once players acquire the BR to play higher, they want to move up in stakes and make more money and that is a whole new ball game. I don't believe you can achieve the same kind of longevity playing higher stakes.

I should qualify that my comments pertain to Vegas play, which again, is what I am familiar with. The advantage of Vegas is quantity not quality of games, so you have a much bigger rotation of 'playable' games, which contributes to being able to fly under the radar.

kewlj, if you don't mind my asking, how many hours do you log in a typical year? I would be interested in 2 numbers: actual playing hours, at the table, and total hours spent pursuing BJ, including travel time to/from/between casinos, scouting, etc. I know that it is your primary source of income and you make enough off of which to live, so I'm curious how much time you put in to in compared to a "straight" job.

" "straight" job. Sometimes that can be a life sentence !

Quote: AcesAndEights

kewlj, if you don't mind my asking, how many hours do you log in a typical year? I would be interested in 2 numbers: actual playing hours, at the table, and total hours spent pursuing BJ, including travel time to/from/between casinos, scouting, etc. I know that it is your primary source of income and you make enough off of which to live, so I'm curious how much time you put in to in compared to a "straight" job.

I don't track time. I used to. But I play very short sessions, Ace. One time through bet cycle or an aggressive wong out point. That makes for VERY short sessions. So I used to have all these small segments of time. 6 minutes, 11 minutes, 4 minutes, 17 minutes, 25 minutes (a marathon session...lol). Just too much of a hassle. I now track my results by an estimate of hands played. After all, your results will really be determined by how many hands or rounds that you play. Again I estimate each session, so my number is not exact, but I come pretty close. Short sessions are easy to estimate. Sometimes you play so few hands when the count tanks immediately, you know for sure. If I am lucky enough to make it through a shoe until shuffle (or unlucky, because that means the count has not gone significantly positive), I then estimate my rounds by dividing number of cards played by number of players x 2.7 cards per hand. This 2.7 number is from BJA3. example 6 deck game, dealt to 5 decks. That means 260 cards played. myself and two other players plus dealer. That is a total of 4 hands per round x 2.7 cards per hand = 10.8 cards per round. I divide 260 by 10.8 equals 25 rounds played. It's actually 24+, but that means the cut card came out during the 25th round so that is 25. And yes I do round off. So in the case I just mentioned I would divide 260 by 11 (rather than 10.8), so I would end up recording that session as 24 rounds, when it might have been 25. I am sure I made that seem more complicated than it is. In the end I have 2 numbers for each session, hands estimate and w/l.

Now time I spend playing? Boy, if you think the last answer was complicated...lol. I have no way of knowing. I play a lot, but it is mixed in with other activities. Most days I hit 8-10 stores over a 6-8 hour period. But it's never just blackjack. I have a second game that I play at times, usually weekends though. I have bonus chasing activities that I do. So I may have to go to this store to play some VP. There is down time and travel time and scouting time and breaks for lunch and breaks for shopping and people watching. Sometimes a break to watch a sporting event. Love my Phillies! Sometimes I go out to dinner, planning only to eat and end up playing 100 hands of BJ. Sometimes I go out to Red Rock canyon for the day and end up hitting a couple casinos on the way home. It isn't just a 9-5er. It is a lifestyle for me. In the end, I average 80,000 rounds per year. About, 260 rounds per day six days a week, but I may hit a heads up table or two and rack up 5 or 6 hundred rounds one day and the next day, scout and look and just can't find many playable games and end up with 75 rounds after 7 hours. As all I can safely say is that I think I put in more than 40 hours a week, but I am down closer to 40 hours than I used to be a year or two ago. lol

Quote: 16sux

Umm, and someone needs to prove something to you, why again? This is the INTERNET, man, nobody's gonna spoon feed you anything. Gotta do your own due diligence on anything and everything. Grow up, it's almost 2013, where you been? LOL

You are the perfect example of what I am talking about -- hiding behind a handle and making unsupportive claims. Thank you for reinforcing my comments.

Quote: kewlj

When you talk about the difficulty in playing black chips, I am not sure if you are talking spreading green TO black or spreading black. There is a big difference. Tolerance levels are different at different locations as well as different stores within each location, obviously. Here in Vegas, a solo player can spread green to mid black without too much difficulty at most stores. Especially if you keep your sessions short. To me this level is the 'sweet spot', pretty well tolerated by many casinos. Again, this is dependent on your style of play. If you like to camp out at one table for a couple hours, then No, you will have problems. If you limit your sessions to 45 minutes or so, you can fly under the radar. I go even further to the extreme. One time through bet cycle. I NEVER retreat to smaller bets after showing larger bets.

As you know, the secret to catching a counter is to look at his average bet and the corresponding average TC -- that can be discerned by software so no act can fool this simple cross-correlation.

Today, they have more sophisticated card-counter software, they have chips with RF, etc. The list goes on. I recall hearing through my network how T-Hopper got caught by Mindplay when first came out (yes that software can be fooled). These short sessions are just a fool's errand.

I remember when Ian Anderson released his second book "Burning the Table in LV" and he wrote about the difficulties of playing black chips.

In summary, as you noticed I was making a general comment and there are isolated cases of people succeeding in BJ playing black chips, but as a general comment, you would agree today's environment is a lot different than from 20 years when I started counting cards.

Quote: Ardent1

As you know, the secret to catching a counter is to look at his average bet and the corresponding average TC -- that can be discerned by software so no act can fool this simple cross-correlation.

Today, they have more sophisticated card-counter software, they have chips with RF, etc. The list goes on. I recall hearing through my network how T-Hopper got caught by Mindplay when first ame out (yes that ofteare can be fololed). These short sessions are just a fool's errand.

I remember when Ian Anderson released his second book "Burning the Table in LV" and he wrote about the difficulties of playing black chips.

In summary, as you noticed I was making a general comment and there are isolated cases of people succeeding in BJ playing black chips, but as a general comment, you would agree today's environment is a lot different than from 20 years when I started counting cards.

I haven't heard the T-Hopper story. Maybe I should search the archives at BJ21. How did he get caught? Mindplay isn't very reliable and is almost extinct isn't it? Several surveillance people that I talk with have told me that even with some of the more recent software, it still takes time to evaluate the player. They need a number of high counts. Short sessions and exiting after showing your spread, eliminates this, especially if playing unrated, where it becomes harder, not impossible, but harder to go back and track previous play.

I can't comment on 20 years ago. before my time. I have only been in the game 9 years. My first few years were really crappy games in AC, so vegas today is a step up for me. I often hear longtime vegas players complaining, but as I said, my 3 years since relocating to vegas have been an improvement in game conditions for me. lol I am sure you are right though. Conditions 20 years ago were no doubt better. Look on the positive and consider yourself lucky to have had the opportunity to have played in that era. :)

Ardent1, do you or did you support yourself from BJ and/or AP play? Do I know you from another forum, either the closed BJinfo or BJ21 by a different handle? (not asking you to say the handle). I really have only nbeen a member at BJ21 for about 2 years, so maybe your frustration drove you away before my time.

Quote: kewlj

...

Cool, thanks for the response. Makes a lot of sense. When I'm in Vegas I play similarly short sessions, but I still try to record "minutes played." I like your approach but I would have to tweak my habits a bit to switch over.

Quote: Ardent1

...hiding behind a handle and making unsupportive claims.

Um, yeah sure, quoting Semyon Dukach who directly contradicts your whole premise and who is one of the undisputed true GREATS of this game is an unsupportive claim. LOL

Quote: 16sux

Um, yeah sure, quoting Semyon Dukach who directly contradicts your whole premise and who is one of the undisputed true GREATS of this game is an unsupportive claim. LOL

Thank you for your unctuous bloviation.

You are entitled to your opinion, and as you know, opinions ARE NOT facts.