Question about variance
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
Quote: FollowCan anyone help me understand the math for a player to turn a +1.3% EV in blackjack over the course of nearly 20,000 hands without cheating? Player bets an average of $163 per hand and is winning around $2.14 per hand over 20,000 hands.
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
link to original post
Your question is not worded well enough for us to answer cogently.
1. Are the basic rules of the game so tilted towards the player that he has a +1.3% EV? I don’t think that’s what you meant.
2. The RESULTS which you describe are NOT the EV, rather, they are the RESULTS. The EV would have been determined by knowing the exact rules of the game, which you haven’t supplied.
It seems like you are saying ‘you’ won around $43k betting $3.26 million. If my math is right, your results are pretty darn good, but certainly (most likely) not extraordinary.
Hopefully I’ve been helpful. Welcome to the forum.
Game rules:
Dealer hit soft 17
Double any
Split once
Blackjack plays 3:2
Continuous shuffle
No surrender
I took the standard ROI of 99.5 for every 100 bet as my base and found the return on this run of 20k hands to look fairly extraordinary to me. Can you use this information to tell me the mathematical likelihood of this kind of run? If it matters, this is over the course of 25 sessions beating the negative almost every time, even in the few losing sessions. I have each session entered on a spread sheet if that will help you.
There is a formula for working out the variance and standard deviation for a combination of wagers. But it goes to hell in a handcart unless the wagers are all the same. You can't just plug in the average wager.Quote: FollowCan anyone help me understand the math for a player to turn a +1.3% EV in blackjack over the course of nearly 20,000 hands without cheating? Player bets an average of $163 per hand and is winning around $2.14 per hand over 20,000 hands.
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
link to original post
If you increased bankroll X into Bankroll Y using a LOW house edge game and ANY betting pattern, you can estimate how likely that was with my rule of thumb. P<=X/Y
E.g if you had the objective of turning $1000 into $1010 using $1 base martingale, with the only acceptable outcomes being success or loss of all bankroll, then P<=1000/1010 = 99%
https://wizardofvegas.com/member/oncedear/blog/7/#post1370
So if you meant that you made a 1.3% profit having put your bankroll at real risk, then P<=100/101.3 or about 98.7% likely
Quote: FollowCan anyone help me understand the math for a player to turn a +1.3% EV in blackjack over the course of nearly 20,000 hands without cheating? Player bets an average of $163 per hand and is winning around $2.14 per hand over 20,000 hands.
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
link to original post
You are very lucky, I would guess that you are about 2.5 Standard Deviations above the average, if you were flat betting (obviously you weren't).
Quote: OnceDearThere is a formula for working out the variance and standard deviation for a combination of wagers. But it goes to hell in a handcart unless the wagers are all the same. You can't just plug in the average wager.Quote: FollowCan anyone help me understand the math for a player to turn a +1.3% EV in blackjack over the course of nearly 20,000 hands without cheating? Player bets an average of $163 per hand and is winning around $2.14 per hand over 20,000 hands.
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
link to original post
If you increased bankroll X into Bankroll Y using a LOW house edge game and ANY betting pattern, you can estimate how likely that was with my rule of thumb. P<=X/Y
E.g if you had the objective of turning $1000 into $1010 using $1 base martingale, with the only acceptable outcomes being success or loss of all bankroll, then P<=1000/1010 = 99%
/member/oncedear/blog/7/#post1370
So if you meant that you made a 1.3% profit having put your bankroll at real risk, then P<=100/101.3 or about 98.7% likely
As stated, this is over the course of 20,000 hands and 25 sessions. The bets are almost always a standard 150 with the other 13 of the average coming from double downs, splits, etc...
Quote: ksdjdjYou are very lucky, I would guess that you are about 20 Standard Deviations above the average, if you were flat betting (obviously you weren't).
The bets were flat and I realize that the run is absolutely improbable. I want to know how improbable such a run is mathematically. I'm good with numbers and statistics, but figuring out this particular math is beyond my skill, which is why I'm turning to this forum and hopefully those better versed with math than I am.
Quote: FollowCan anyone help me understand the math for a player to turn a +1.3% EV in blackjack over the course of nearly 20,000 hands without cheating? Player bets an average of $163 per hand and is winning around $2.14 per hand over 20,000 hands.
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
link to original post
For 20,000 hands, your profit is about (20,000)(2.14) = $42,800.
For your rules, the Wizard of Odds gives a house edge of about 0.7%, so let's use that instead of 0.5%. Your expected loss on 20,000 hands of $150 initial bet size would be (0.007)(20,000)(150) = $21,000.
I couldn't find the exact variance for your rules, but suppose for a 1-unit-bet hand of blackjack it is 1.346. Then the variance for playing 20,000 hands at $150 per hand would be (150)2(20,000)(1.346) = 605,700,000.
The standard deviation would be the square root of the variance and would equal about $24,611.
The number of standard deviations that your result is above the expected loss is: ($42,800 + $21,000) / $24,611, which is about 2.59.
The probability of being at least 2.59 standard deviations above the mean in a normal distribution is about 0.48%.
So, it looks like your luck is rare but not impossible.
Quote: FollowQuote: ksdjdjYou are very lucky, I would guess that you are about 20 Standard Deviations above the average, if you were flat betting (obviously you weren't).
The bets were flat and I realize that the run is absolutely improbable. I want to know how improbable such a run is mathematically. I'm good with numbers and statistics, but figuring out this particular math is beyond my skill, which is why I'm turning to this forum and hopefully those better versed with math than I am.
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Short answer, you had about a 1% chance of this happening (rough guess).
Note: I don't know why it says 20 SD in my original answer because I cut and pasted it as 2.5 SD (20 is obviously wrong, sorry).
Last year, 2020, my expectation for my blackjack play was more than $80,000. Since I play +EV (card counting), this $80,000 represents what I call accumulated EV of each session. So over $80,000 in expectation. My actual results a little better than $14,000. That would be $65,000 below expectation. In terms of rounds played that was about 40,000 rounds, so double what you are talking about.
And it goes both ways. This year I was on the complete opposite end, some $50,000 above expectation for the year.
Now these two years for me have been the most extreme I have ever had and weirdly they occurred back to back, one in each direction.
Your results are in the same ballpark. Since your expectation was negative (not sure how much) it looks like you finished $30,000, or $40,000 above expectation for those 20,000 rounds. Unusual yes. But the unusual happens with variance sometimes. And really nothing is unusual until you get well above 3 standard deviations. That is when you are really starting to talk unusual results.
So I wouldn't think any more about it that you finished with good positive variance. Enjoy it. :)
Quote: FollowCan anyone help me understand the math for a player to turn a +1.3% EV in blackjack over the course of nearly 20,000 hands without cheating? Player bets an average of $163 per hand and is winning around $2.14 per hand over 20,000 hands.
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
link to original post
Suppose you win $2.14 per hand over 20,000 hands, so your total winning, W = 2.14 * 20000 = $42800. To find probability of winning, W >= $42800, P(W >= 42800).
Assuming that blackajck is normally distributed, the house edge is 0.67%(6 deck and DAS) and the variance is 1.31.
μ = -0.67/100 = -0.0067, σ = 1.31^0.5 = 1.145, n = 20000 hands, bet size = $163
Z = (W - μ)/σ = (42800 + 20,000 * 163 * 0.0067)/(163* 1.145 * (20,000)^0.5 ) = 64642/26,394 = 2.45
So P(W >= 42800 ) = P( Z >= 2.45) = 0.71%.
So probability of winning more than $42800 after 20,000 hands is 0.71%.
Here you goQuote: OnceDearThere is a formula for working out the variance and standard deviation for a combination of wagers. But it goes to hell in a handcart unless the wagers are all the same. You can't just plug in the average wager.
https://wizardofvegas.com/forum/gambling/blackjack/33787-ev-and-standard-deviation-in-bj/#post746394
Quote: Romes: numbers modified by meOriginalSD = 1.15 * AvgBet
EV(x hands) = (AvgBet*NumHands)*(HouseEdge)
SD(x hands) = Sqrt(x) * OriginalSD
----------------------------------------------------------------------------
Example: $150 flat bet at .5% average blackjack game for 20,000 hands:
OriginalSD = 1.15*150 = 172.5
EV(20,000 hands) = (150*20,000)*(-.005) = -$15,000
SD(20,000 hands) = Sqrt(20,000) * 172.5 = ~$24395 ... 2SD (95% confidence) = $48790
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link to original post
As I said, this formula goes to hell if the wagering wasn't flat betting.
Looks like at 43k profit you are about 58k away from expected value. Between 2 and 3 standard deviations. Good but not remarkable.
This seems very much written as a casino employee trying to figure out if/what a player is doing because they can't fathom that they're actually "up."Quote: FollowCan anyone help me understand the math for a player to turn a +1.3% EV in blackjack over the course of nearly 20,000 hands without cheating? Player bets an average of $163 per hand and is winning around $2.14 per hand over 20,000 hands.
I have quite a bit more information than this if needed, but my basic question is about the probability of a lucky run like that.
Thank you for your time.
link to original post
Firstly, 20k hands is not enough hands to land on EV in blackjack. So if you're simply going off numbers and 20k hands is your big data dump, then sure things could trend one way, but you cannot with any certainty claim one thing or another (just going off the data you posted).
Next, others have responded and more will, but the answer to all of your questions and more are available if you do a bit more research. In the case that you might be a casino employee trying to make the life of a regular customer, or possibly an AP, worst, I won't help that. Casinos have not been very friendly to me, even though I'm friendly to everyone, so sadly, I don't see the need to help any casino continue to do that.
Quote: RomesThis seems very much written as a casino employee trying to figure out if/what a player is doing because they can't fathom that they're actually "up."
Firstly, 20k hands is not enough hands to land on EV in blackjack. So if you're simply going off numbers and 20k hands is your big data dump, then sure things could trend one way, but you cannot with any certainty claim one thing or another (just going off the data you posted).
Next, others have responded and more will, but the answer to all of your questions and more are available if you do a bit more research. In the case that you might be a casino employee trying to make the life of a regular customer, or possibly an AP, worst, I won't help that. Casinos have not been very friendly to me, even though I'm friendly to everyone, so sadly, I don't see the need to help any casino continue to do that.
This is a very interesting response. First, to answer your question, I am not a casino employee. I do run a local betting site and I am scratching my head over the records of a couple of my players who happen to be related and are posting some very questionable numbers. The numbers I'm showing here are theirs. I've been running my site for some time and I have never seen anyone with a run like this. In fact, every one of over 100 accounts and around half a decade of records eventually reaches the same expectation, then suddenly 2 related players start posting these kinds of numbers and start failing captchas at an alarmingly high frequency.
I'm not a large corporation, and I haven't done you any wrong. I came here asking mathematical and logical questions for an enigmatic problem that is causing me some concern. If it weren't all electronic, I wouldn't have any real concerns. But considering that my "casino" is all handled through an electronic medium, I thought I would look into the math issues that I couldn't figure out myself. I have many more numbers that have poured in since starting this thread and I am asking people for help on the math to understand whether people are trying to rob me, nothing more.
Your biases and telling me that you are disinclined to help me with math because I might be a "casino employee" and since others whom you identify with the same moniker haven't been nice to you seems rather prejudicial and rude to me. You make your decisions as you like, but in the end I'm trying to find a way for these numbers to show me how likely the player is to be legit rather than the other way around. I have a friendly and personal relationship with every one of my players, and it would be pretty terrible for me to uncover real cheating on my site.
I hope this clears things up and if anyone is still willing to help me work through my numbers, I would love to post some more to run through the formulas to determine how unlikely or likely they are.
Interesting.Quote: FollowQuote: RomesThis seems very much written as a casino employee trying to figure out if/what a player is doing because they can't fathom that they're actually "up."
Firstly, 20k hands is not enough hands to land on EV in blackjack. So if you're simply going off numbers and 20k hands is your big data dump, then sure things could trend one way, but you cannot with any certainty claim one thing or another (just going off the data you posted).
Next, others have responded and more will, but the answer to all of your questions and more are available if you do a bit more research. In the case that you might be a casino employee trying to make the life of a regular customer, or possibly an AP, worst, I won't help that. Casinos have not been very friendly to me, even though I'm friendly to everyone, so sadly, I don't see the need to help any casino continue to do that.
Your biases and telling me that you are disinclined to help me with math because I might be a "casino employee" and since others whom you identify with the same moniker haven't been nice to you seems rather prejudicial and rude to me. You make your decisions as you like, but in the end I'm trying to find a way for these numbers to show me how likely the player is to be legit rather than the other way around. I have a friendly and personal relationship with every one of my players, and it would be pretty terrible for me to uncover real cheating on my site.
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So, you run the online site and a member, or couple of members are beating your game in ways that are suspicious?
Please forgive, but expect some hostility from the AP community that gather on forums such as this.
Maybe they have discovered an anomaly in your software.... licenced from where?
They may be disrespecting your rules, but if they play the game with the features you offer, then what cheating is possible? Maybe consult your software provider?
You are going to have to do some deep dive analysis. Do they get more blackjacks than expected. Do they always get insurance decisions right? Do they wong in and out? etc etc.
Quote: FollowQuote: RomesThis seems very much written as a casino employee trying to figure out if/what a player is doing because they can't fathom that they're actually "up."
Firstly, 20k hands is not enough hands to land on EV in blackjack. So if you're simply going off numbers and 20k hands is your big data dump, then sure things could trend one way, but you cannot with any certainty claim one thing or another (just going off the data you posted).
Next, others have responded and more will, but the answer to all of your questions and more are available if you do a bit more research. In the case that you might be a casino employee trying to make the life of a regular customer, or possibly an AP, worst, I won't help that. Casinos have not been very friendly to me, even though I'm friendly to everyone, so sadly, I don't see the need to help any casino continue to do that.
This is a very interesting response. First, to answer your question, I am not a casino employee. I do run a local betting site and I am scratching my head over the records of a couple of my players who happen to be related and are posting some very questionable numbers.
link to original post
Analysts get consulting fees to analyze things for businesses, usually.
I also decline to do people's homework projects for them, generally.
I am not trying to beat you up.
If you choose to make money through gambling, you should probably pay up when you lose. Many players have paid you when you won.
If you no longer care to offer the game, that is your decision.
I think I gave you enough there to keep you busy for a while.Quote: OnceDear
You are going to have to do some deep dive analysis. Do they get more blackjacks than expected. Do they always get insurance decisions right? Do they wong in and out? etc etc.
link to original post
The mathematical formula is average is Np and the variance is Npq (q=1-p), the Standard Deviation is SQRT(Npq). Let's look at how this applies to players on this simple coin flip game.
For 1000 flips your average payback is $990, so the loss is $10. The SD = SQRT(1000*.495*.505)=SQRT(249.975) which is about 15.81. Thus quite a few people will come out ahead.
For 10000 flips to loss is $100 and the SD is about 50, so 2% of people come out ahead (as this is 2SDs away from the average).
In your example the maths only works for flat bets, so you may have to look at how many large bets they make.
One problem with bookmaking etc is rare events are eventually bound to happen and you have to weigh up the chances of someone winning by good luck and someone winning by cheating. Similar logic applies if there is accusation of the casino cheating and a player loses. The mathematics says you have to run a huge number of tests to "prove" anything like this to within a reasonable certainty.
Quote: DieterQuote: FollowQuote: RomesThis seems very much written as a casino employee trying to figure out if/what a player is doing because they can't fathom that they're actually "up."
Firstly, 20k hands is not enough hands to land on EV in blackjack. So if you're simply going off numbers and 20k hands is your big data dump, then sure things could trend one way, but you cannot with any certainty claim one thing or another (just going off the data you posted).
Next, others have responded and more will, but the answer to all of your questions and more are available if you do a bit more research. In the case that you might be a casino employee trying to make the life of a regular customer, or possibly an AP, worst, I won't help that. Casinos have not been very friendly to me, even though I'm friendly to everyone, so sadly, I don't see the need to help any casino continue to do that.
This is a very interesting response. First, to answer your question, I am not a casino employee. I do run a local betting site and I am scratching my head over the records of a couple of my players who happen to be related and are posting some very questionable numbers.
Analysts get consulting fees to analyze things for businesses, usually.
I also decline to do people's homework projects for them, generally.
I am not trying to beat you up.
If you choose to make money through gambling, you should probably pay up when you lose. Many players have paid you when you won.
If you no longer care to offer the game, that is your decision.
I'm happy to pay a consultant a fee for their services. In fact, before coming to this forum I emailed "Wizard of Odds" proposing exactly that arrangement. But generally one doesn't offer something like that in a discussion forum when you're discussing the topic of the forum. If there is someone who is willing to pore over all of the data I have and give me a detailed analysis, I am more than happy to compensate them for their time. I feel like there is a certain impression of people that some of you are carrying without asking the other person if they fit the description made in your mind.
I don't know what kind of impression I've given of myself, but my operation is very small, local, and only caters to people and agents I know personally. This kind of operation generally doesn't color far outside the lines, maybe 5k here and 15k there, but the discrepancy I'm showing on my books is over 100k. That is a major difference from anything that has happened before. In consulting with other, larger books that are similar to me, they have never seen such a thing either. There is more to it than just this blackjack anomaly, but I assumed this would be a fair place to analyze the blackjack anomaly on its own.
I am well known in my community as a person who pays all debts. If these activities are found to be entirely legitimate, I will pay every penny. Even if these discrepancies are found to be cheating, I will come to a settlement for my players of some kind before banning them. In my world of poker and other forms of gambling, I am the one who never owes a soul and I pride myself on being entirely transparent and honest with everyone. My transparency is such that even the players involved in this investigation, know that I am investigating. I am paying them a small amount weekly while I am investigating. That is the reason I am here and other places trying to get this right and be fair with everyone. I think most in my situation would walk away, ban the players for cheating out of hand, and wash their hands of the situation. I am working a full time job trying to crunch numbers and analyze spreadsheets to ensure I am being fair.
As to "doing my homework" for me, I am perfectly willing to take any time necessary to do the math myself, but I find myself incapable, which is why I'm here. Most of the time when people link some kind of primer on how to do whatever kind of math, it is appreciated, but they require a certain initiation that comes from formal education. I don't have that, and therefore can't understand the symbols which puts a stop to most of what I'm trying to accomplish. All of my ability comes from self teaching, I have no degrees and very little formal education.
Quote: OnceDearQuote: FollowQuote: RomesThis seems very much written as a casino employee trying to figure out if/what a player is doing because they can't fathom that they're actually "up."
Firstly, 20k hands is not enough hands to land on EV in blackjack. So if you're simply going off numbers and 20k hands is your big data dump, then sure things could trend one way, but you cannot with any certainty claim one thing or another (just going off the data you posted).
Next, others have responded and more will, but the answer to all of your questions and more are available if you do a bit more research. In the case that you might be a casino employee trying to make the life of a regular customer, or possibly an AP, worst, I won't help that. Casinos have not been very friendly to me, even though I'm friendly to everyone, so sadly, I don't see the need to help any casino continue to do that.
Your biases and telling me that you are disinclined to help me with math because I might be a "casino employee" and since others whom you identify with the same moniker haven't been nice to you seems rather prejudicial and rude to me. You make your decisions as you like, but in the end I'm trying to find a way for these numbers to show me how likely the player is to be legit rather than the other way around. I have a friendly and personal relationship with every one of my players, and it would be pretty terrible for me to uncover real cheating on my site.
Interesting.
So, you run the online site and a member, or couple of members are beating your game in ways that are suspicious?
Please forgive, but expect some hostility from the AP community that gather on forums such as this.
Maybe they have discovered an anomaly in your software.... licenced from where?
They may be disrespecting your rules, but if they play the game with the features you offer, then what cheating is possible? Maybe consult your software provider?
You are going to have to do some deep dive analysis. Do they get more blackjacks than expected. Do they always get insurance decisions right? Do they wong in and out? etc etc.
I don't know what "wong in and out" means, but I think I can answer most of your other questions here.
1. Yes, these players are showing wins that are far outside of the norm. The blackjack aspect of this is showing a player who is posting wins in approximately 75% of sessions with only something like 8% (these are rough numbers from memory) reaching the expected -0.05% loss. The play itself is not perfect strategy and bets are flat. So realistically, their loss should be even greater than the -0.05%.
2. The software is an afterthought on a sports betting site rented from an offshore company. They won't give me too many details of the inner workings of the software, but they have told me enough to know that their RNG is a Pseudo RNG and not a True RNG. Do you feel that cracking a Pseudo RNG with a bot or similar software is "playing the game with the features I offer?" If cheating is happening, this is my leading theory.
3. A deep dive analysis is tricky. As you know, there are over 20,000 hands to look at so it is a monumentally large amount of data to click through one at a time. Also, such detailed data are not carried after 3 weeks of time. We are looking at a time frame of around 1.5 months here, which means roughly half of the hands are no longer available.
To close, I still have many other active players that are showing normal numbers with some expected anomalies here and there. There are many others who are using the blackjack software as well, showing pretty normal runs, up a little/down a little, etc... I've had some people go on big runs winning 2k or 4k in short terms from tiny starting bankrolls. But, in this case I have 2 players who are related breaking the curve entirely in ways that I have never seen nor have any of my colleagues. More importantly, the run for both of these related players continues for nearly 2 months of posting extremely unlikely wins including the two accounts being related in wins and losses too. Again, this is only one part of my investigation just from a purely mathematical point of view. I am also looking into this issue from other angles as well.
Just how flat are they betting? Most live players will spice up their sessions with some bet variation.
Wong in or out: I'll give you that as a freebie. A card counter would classically ramp up his bet in a favourable count and min bet in an unfavourable account. But taken to an extreme, he may 'wong out' = simply desist from playing when unfavourable and 'wong in' Restart playing when the count is favourable.
Quote: OnceDearOK...... Winning percentage of sessions would not be a meaningful measure if they were employing some money management process, such as chasing losses with a Martingale or similar. E.g, if the come to your game prepared to lose 100000 or profit by 1000, they would win about 98% of sessions. See https://wizardofvegas.com/member/oncedear/blog/7/#post1370 for an explanation of that. My 'Oncedear rule of thumb; is mostly used to debunk money management systems, but does actually apply to flat betting.
Just how flat are they betting? Most live players will spice up their sessions with some bet variation.
Wong in or out: I'll give you that as a freebie. A card counter would classically ramp up his bet in a favourable count and min bet in an unfavourable account. But taken to an extreme, he may 'wong out' = simply desist from playing when unfavourable and 'wong in' Restart playing when the count is favourable.
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OP has said that the game is continuous shuffle, so card counting tactics and wonging should not be a valid hypothesis. Money management is clearly not a viable explanation and nobody has suggested that.
I think that it is likely/probable that the player in question is exploiting some vulnerability in your software.
I have analyzed files of 1 million hands for other online casino operators, If OP can download the 20,000 hands as an excel file I will look at them for free. Send me a message on this site 's PM system if there is an interest..
Quote: FollowI don't know what kind of impression I've given of myself, but my operation is very small, local, and only caters to people and agents I know personally.
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(context trimmed)
Sounds to me like you're doing mostly the right things.
I apologize for preemptively assuming it might be otherwise.
Best of luck in your research,
-D
You'll find regular gamblers on any forum but you'll also find quite a few people on this forum that it is also their business, like yourself. However the vast majority of people whom are professional gamblers on this site aren't on the casino side, and the casino side has for decades before me (and I'd be willing to bet for decades after me) not been very kind to people who legally beat the games that are offered. As such we've seen tons of casino employees come through the forums over time asking for similar help to try to "get" or "nail" an AP, or just someone they don't know that happens to be winning. 9/10 times these employees are baffled that ANYONE COULD EVER WIN EVER so forgive us if we did in fact judge you a bit as one of these types.
I still answered your question btw. The answers you seek are all readily available, even on this forum. It has a nice search functionality and if you check out other threads you'll quickly learn who the pro's and who the joe's are and thus who's post to search through for your information. That's another reason I responded as such. There's a lot of info on this site, and if we just spoon fed answers to everyone that asked the same repeating questions then they'd come here, post once, get an answer, and then leave... but if you stick around, check the site and other threads out, and possibly participate in sharing interesting information about your experience, then you might find a lot more answers and helpful faces.
Again, I responded with no mal-intent, but on this forum and others that promote mathematical/advantage gambling you'll often find that people don't want to help as much because the casino industry has treated 100% legal advantage gamblers so poorly. So I still stand by my initial response of just pointing you in the right direction.
I had 2 players that were far too "lucky" playing blackjack. I suspected collusion between these two players and the offshore company.
