Cheating Online Casino? (Data Inside)
For the last year, I've been playing at an online casino that has a built in player advantage of ~0.4%. This is not a live dealer game. It is a RNG game with rules that favor the player based on a discrepancy in the stated gameplay rules, and the actual rules programmed in the game.
I've been tracking my results for almost a year and am sharing them here. I'd like to know from the experts on this forum, is this game rigged or not?
I am currently 4.5 SD's away from expected results based on my calcs.
I cannot post link to google spreadsheet yet because I don't have 20 posts - will try to get to 20 and post it after..
Quote: WizardMeanwhile, feel free to post a summary of your results. It will be nice to see an accusation of casino cheating with numbers as opposed to insults, starting with the letter N, for a change.
Understood.
Here's the summary.
155,865 hands played
2,848,140 total wagered
Win/Loss = -$25,690
Expected player advantage 0.4%
Std Deviation per hand = 1.12 (I used 1.2544 in my calcs because I normally play two hands at a time)
Avg bet size - $18.27
Anything else you need?
Edit: I used cardcounting.com/calcrisk.htm to get this odds of this result.
Quote: Johnboy85Understood.
Here's the summary.
155,865 hands played
2,848,140 total wagered
Win/Loss = -$25,690
Expected player advantage 0.4%
Std Deviation per hand = 1.12 (I used 1.2544 in my calcs because I normally play two hands at a time)
Avg bet size - $18.27
Anything else you need?
Thanks. I'll need to know the amount bet for every hand to get the standard deviation of your play as a whole.
155,865 hands -- that is quite a few!
I do not have individual hand histories as that data cannot be downloaded from this shop. I only have data for each "day" as a whole.
Correct me if I'm wrong, is the 4.5 SD I cited via the website calculator above not enough?
Edit to ask: furthermore, if you had individual hand histories, how much could this theoretically change the SD of my play as a whole. I say this because I will admit that most sessions were in the $5 flat betting range, while very few sessions had avg bet sizes of $50-$75 when my bankroll grew quickly.
Quote: Johnboy85Hi All,
For the last year, I've been playing at an online casino that has a built in player advantage of ~0.4%. This is not a live dealer game. It is a RNG game with rules that favor the player based on a discrepancy in the stated gameplay rules, and the actual rules programmed in the game.
I've been tracking my results for almost a year and am sharing them here. I'd like to know from the experts on this forum, is this game rigged or not?
I am currently 4.5 SD's away from expected results based on my calcs.
I cannot post link to google spreadsheet yet because I don't have 20 posts - will try to get to 20 and post it after..
What are the rules of the game?
Are you sure this discrepancy is worth as much as you think?
Quote: HunterhillWhat are the rules of the game?
Are you sure this discrepancy is worth as much as you think?
I knew this question would come up and respectfully I will keep that a secret for now as I think if I divulged this, it would be a giveaway and could alert the operator of their mistake.
Quote: Johnboy85I knew this question would come up and respectfully I will keep that a secret for now as I think if I divulged this, it would be a giveaway and could alert the operator of their mistake.
Understandable.
It totally depends on the distribution of wagers - I can't be more specific. But, yes, it could easily take 4.5 under 3.Quote: Johnboy85How much would variance in bet sizing affect the true SD? Enough to drastically alter the 4.5 SD cited?
Quote: teliotIt totally depends on the distribution of wagers - I can't be more specific. But, yes, it could easily take 4.5 under 3.
Understood.
So the blackjack outcome calculator (google it if you don't know what I'm referring to) is useless? It doesn't mention anything about distribution of bet sizing, etc.
I don't know what you're talking about with Google. But, any short cut is going to err on the side of making the z-Score larger and creating more false positives.Quote: Johnboy85Understood.
So the blackjack outcome calculator (google it if you don't know what I'm referring to) is useless? It doesn't mention anything about distribution of bet sizing, etc.
Spreading to multiple hands and spreading bets is not solvable in any practical analytic way.
I've analyzed blackjack sd's for massive amounts of data for online casinos. They list every bet, dollar amount, splits, doubles, multiple hands, etc. With that full data, it's not hard to get the actual sd. I did this for years when I owned certifiedfairgambling.com I automated it with scripts and it ran very quickly over gigabytes of data. Or, I could do it by hand. But, it gave the exact sd.
This calculator only considers total amounts wagered and average bet size. Why would a calculator like this not mention spreading if it can have such a massive effect on SD as you say?
Edit: furthermore, the above calculator generally applies to card counting, where bet spreading and # of correlated hands may vary from deal to deal. If it's valid for card counting, why would the same not apply to my circumstances?
Because the person who wrote it either doesn't know or doesn't care. I work with folks all over the world who use calculators like this in their own operations. They take some stats course and think they can just use sqrt(N)*sd*(average bet). I am constantly having to correct them when they go crazy over players they think are beating them by 4 sd's and it ends up being 2.7 sd's.Quote: Johnboy85For the calculator - I am using qfit dot com slash calcrisk dot htm (sorry for formatting).
This calculator only considers total amounts wagered and average bet size. Why would a calculator like this not mention spreading if it can have such a massive effect on SD as you say?
Ask yourself this. Player 1 made 100 bets, each $1,000. Player 2 made 100 bets, 50 at $100 and 50 at $1900, Player 3 makes 81 bets of $50 and 19 bets of $5000. Which player is more likely to win $10,000 or more by chance? I am sure your intuition is exactly right.
Quote: teliotBecause the person who wrote it either doesn't know or doesn't care. I work with folks all over the world who use calculators like this in their own operations. They take some stats course and think they can just use sqrt(N)*sd*(average bet). I am constantly having to correct them when they go crazy over players they think are beating them by 4 sd's and it ends up being 2.7 sd's.
I don't mean to minimize what you're saying, you sound extremely knowledgeable on the subject, but the calculator is on the Qfit site who are the makers of the CVCX software which is like the gold standard for running simulations and calculating house edge for various BJ rules. I'm inclined to believe those calculators are built out by the same guy(s) which is why it would be a surprise if they are completely wrong (not saying it's impossible, of course).
Wizard, care to weigh-in on the subject?
We're not talking card counting here ... the OP was talking about online basic strategy, with rules that gave him an off-the-top edge (or so I thought). CVCX gives sd's for bet spreads using card counting systems. It gets these results by simulation.Quote: Johnboy85I don't mean to minimize what you're saying, you sound extremely knowledgeable on the subject, but the calculator is on the Qfit site who are the makers of the CVCX software which is like the gold standard for running simulations and calculating house edge for various BJ rules. I'm inclined to believe those calculators are built out by the same guy(s) which is why it would be a surprise if they are completely wrong (not saying it's impossible, of course).
Wizard, care to weigh-in on the subject?
As for what Norm did, I have no idea what he did. Maybe he could clarify.
Norm??
Quote: Johnboy85Hi All,
For the last year, I've been playing at an online casino that has a built in player advantage of ~0.4%. This is not a live dealer game. It is a RNG game with rules that favor the player based on a discrepancy in the stated gameplay rules, and the actual rules programmed in the game.
I've been tracking my results for almost a year and am sharing them here. I'd like to know from the experts on this forum, is this game rigged or not?
I am currently 4.5 SD's away from expected results based on my calcs.
I cannot post link to google spreadsheet yet because I don't have 20 posts - will try to get to 20 and post it after..
Are you playing for real money, bitcoins, or play money? It has been my admittedly limited experience that some games play differently when in play money mode.
Are you sure the website does not have a hand archive available to you? Many do;some you have to dig for the stats.
Are you sure you're playing the correct basic strategy for the number of decks and game rules as they actually exist? Does the game tell you when it shuffles, use a continuous shuffler, shuffle every hand, or do something else? Did you have to estimate or ignore any of the game factors when you came up with your approximate edge figure?
Sorry to reiterate basic info, but your previous posts did not specifically cover these things that I saw.
They do. At least, all the software I've audited does.Quote: AxelWolfThis brings up a question. Why wouldn't an online casino record Hand history?
OP, have you looked at the rogue list at Casinomeister?
http://www.casinomeister.com/rogue/index.php
Quote: Johnboy85I knew this question would come up and respectfully I will keep that a secret for now as I think if I divulged this, it would be a giveaway and could alert the operator of their mistake.
I'm sure they are aware of this apparent mistake.
But, they might well have gaffed the game to retain any edge of their choosing.
If this is a 'play money' game, then let's not waste our time.
If this is a real money RNG game and there is no available game history, then this sounds very much a two bit fly-by-night unregulated outfit. That't you've played so very many hands REALLY shocks me. That you have lost thousands on a game where you believe you have an edge does not surprise me at all.
Quote: beachbumbabsAre you playing for real money, bitcoins, or play money? It has been my admittedly limited experience that some games play differently when in play money mode.
Are you sure the website does not have a hand archive available to you? Many do;some you have to dig for the stats.
Are you sure you're playing the correct basic strategy for the number of decks and game rules as they actually exist? Does the game tell you when it shuffles, use a continuous shuffler, shuffle every hand, or do something else? Did you have to estimate or ignore any of the game factors when you came up with your approximate edge figure?
Sorry to reiterate basic info, but your previous posts did not specifically cover these things that I saw.
Heard from Johnboy via PM. He wanted to respond to my and other posts publicly but is constrained by the new member post limit. So I'm going to post his reply to these questions with his implied permission.
Quote: jboyHi,
I'd like to be able to respond to yours and other comments in the thread I started last night. Is there any way you can remove the limit on my posting as a new member so I can do that?
If not, the answers to your questions are:
-This is all real money.
- I went and had another look - the site does have a hand history in the browser, but it's not downloadable/exportable, and it doesn't span the last 12 months.
-Yes, I am 100% sure I am playing perfect basic strategy for this particular game. The game shuffles after every hand. I did not estimate or ignore any game factors in my calculation. I used this calculator to ascertain the house edge (link redacted, was from beating bonuses).If the House lost every hand, they wouldn't deal the game.
Back to answer your questions tonight, I had to wait 24 hrs to post because of the limits on newbies. I'll try to answer all questions in one post in case there's further discussion.
Quote: teliotThey do. At least, all the software I've audited does.
OP, have you looked at the rogue list at Casinomeister?
p
They for sure have one, but they are not providing it to me (I asked their support team today). This is not at all a rogue casino. - it is a well known and reputable shop.
Quote: standbymymanI'm sure they are aware of this apparent mistake.
Perhaps they are. Most casual players don't even use BS and are profitable for the casino anyway.
Quote: OnceDearI respectfully suggest that they will be aware of it and it's a marketing ploy, just like when certain slot machines would pay out on certain unpublished outcomes where no win was apparently due ( Do any still do that ? )
But, they might well have gaffed the game to retain any edge of their choosing.
If this is a 'play money' game, then let's not waste our time.
If this is a real money RNG game and there is no available game history, then this sounds very much a two bit fly-by-night unregulated outfit. That't you've played so very many hands REALLY shocks me. That you have lost thousands on a game where you believe you have an edge does not surprise me at all.
It's certainly possible you're right, but on the other hand, most online casinos that accidentally-on-purpose have games with a small edge for the player are in the neighborhood of .01% edge, not 0.4% which is actually a fairly big risk IMO.
I assure you this is not play money. I wouldn't waste my time or yours on play money. I'm not sure what you're trying to convey in your last line, but I have grinded this game for a very long time expecting positive results. I'm familiar with the variance of the game, which is why I waited to post until the results looked outside the realm of normal to my sniff test.
Quote: teliotI work with folks all over the world who use calculators like this in their own operations. They take some stats course and think they can just use sqrt(N)*sd*(average bet).
This is one very good point that is not well understood by many people. It is a flat betting formula only. Varying your bet sizes means that the larger bets are going to have a greater effect on the Standard Deviation and this is because the square of the SD is proportional to the weighted average of the squares of the different bet sizes. In addition, it is also possible to take into account the effect of playing simultaneous hands by introducing multipliers as well as varying game speed but the calculations do get quite complex.
1. Add a column to the data sheet called VAR. In it put (1.12*wagerAmount)^2
2. Add all of those values.
3. Take the square root of the result.
4. That's your overall standard deviation for the hands where you played one hand only.
5. Sum all your wagers when you played one hand only and multiply by 0.4%. That's your EV
5. Compute the z-Score for your one-hand play.
The point being - you sum the per-hand variance then take the square root of that to get the overall SD.
If you like you can do this for all wagers, but you will need to use a different formula for the per-hand variance for those hands.
And/Or, file a complaint with ThePogg or at Casinomeister.
You can also do a distribution of the first 2 cards dealt to the dealer and do a chi-squared test on that. You can also do a distribution test on the dealer's third card - that is a good one. Do these tests for your first two cards and first draw card as well.
Just thought I would update you on the status here. The stats now stand at:
0.4% player advantage
188 379 hands
-$28,903
16.80 Avg Bet size
According to the calculator cited earlier, this puts my results at 5 standard deviations from EV.
Would be great to hear from Norm Wattenberger on how this calculator was built.
John
Quote: Johnboy85I knew this question would come up and respectfully I will keep that a secret for now as I think if I divulged this, it would be a giveaway and could alert the operator of their mistake.
A mistake? I beg to disagree, This 'mistake' has led you to lose nearly $30k. If they did not have this 'mistake' would you be playing there? Probably not. So you have been reeled in, much like it is not a 'mistake' that an angler places a tasty worm on a hook.....
0.4% player advantage
233 614 hands
-$34,471
16.24 Avg Bet size
Now at 5.54 away SD's from the expected outcome. If it hits 6, I'll be filing a formal complaint with Casinomeister or the pogg or casinomeister.
Do you have all of this data logged, hand by hand, and/or video of you playing most of those hands? Unfortunately even if you're telling the truth, that's still not "proof" because we'd have to see it as a community with our own eyes. We can't just take everyone's word on things around here, especially with serious accusations at stake =).Quote: Johnboy85Another update here for those who were keeping track.
0.4% player advantage
233 614 hands
-$34,471
16.24 Avg Bet size
Now at 5.54 away SD's from the expected outcome. If it hits 6, I'll be filing a formal complaint with Casinomeister or the pogg or casinomeister.
Oh, btw I made $50 mill last weekend at a blackjack game in about 3 hours... Take my word for it ;-). Not saying you're not telling the truth, just that we need viable evidence past words.
Quote: RomesDo you have all of this data logged, hand by hand, and/or video of you playing most of those hands? Unfortunately even if you're telling the truth, that's still not "proof" because we'd have to see it as a community with our own eyes. We can't just take everyone's word on things around here, especially with serious accusations at stake =).
Oh, btw I made $50 mill last weekend at a blackjack game in about 3 hours... Take my word for it ;-). Not saying you're not telling the truth, just that we need viable evidence past words.
Not hand by hand, because they don't allow the player to export individual hands. I do however have logs of win/loss amounts with avg bet size for every single day over the last year or so.
What I could do is take a screenshot of the hand history to at least prove to you that the rules are what I say they are.
Quote: Johnboy85Not hand by hand, because they don't allow the player to export individual hands. I do however have logs of win/loss amounts with avg bet size for every single day over the last year or so.
What I could do is take a screenshot of the hand history to at least prove to you that the rules are what I say they are.
If someone made me bet on it, I would bet you are telling the truth. But Romes' point is valid. How do I know you don't split queens? How do I know you don't double down with a pair of 3's? How do I know you don't represent a competitor to the alleged bad casino?
But my biggest question is this.... if you have convinced yourself that the casino is rogue, why do you keep betting there?
Quote: Johnboy85Hi All,
For the last year, I've been playing at an online casino that has a built in player advantage of ~0.4%. This is not a live dealer game. It is a RNG game with rules that favor the player based on a discrepancy in the stated gameplay rules, and the actual rules programmed in the game.
I went back and read this statement a few times. It is my guess that you have made a calculation error or misread the gameplay rules or misinterpreted the 'actual rules programmed in the game'. If you are willing to share these exact details with the Wizard, I think he is by the rules of our forum sworn to secrecy, as he is not permitted to disclose information from a Private Message. So please PM him. Allow him to at least confirm that the game does have a player edge as you believe, or let him correct you and save you from dumping more money at that casino.
Quote: SOOPOOIf someone made me bet on it, I would bet you are telling the truth. But Romes' point is valid. How do I know you don't split queens? How do I know you don't double down with a pair of 3's? How do I know you don't represent a competitor to the alleged bad casino?
But my biggest question is this.... if you have convinced yourself that the casino is rogue, why do you keep betting there?
I understand the skepticism for sure. I'm not saying I play every hand perfectly, but I know advantage play when I see it and even if I play a couple of hands wrong out of every thousand hands, there's no way it would completely shave away an edge that big.
I haven't convinced myself this casino is rogue. In fact, it's quite the opposite. This is one of the biggest online casinos in the world with a pretty sterling reputation. I continue to play there because I know I'm playing with an edge, and because I believe that the law of large numbers will eventually see me close in on my expected EV. If not, then I will (hopefully) empirically prove that their game is flawed and get my money back and then some, or blow the lid on a huge scandal.
Quote: SOOPOOI went back and read this statement a few times. It is my guess that you have made a calculation error or misread the gameplay rules or misinterpreted the 'actual rules programmed in the game'. If you are willing to share these exact details with the Wizard, I think he is by the rules of our forum sworn to secrecy, as he is not permitted to disclose information from a Private Message. So please PM him. Allow him to at least confirm that the game does have a player edge as you believe, or let him correct you and save you from dumping more money at that casino.
If he comes here and confirms that, I'd be happy to at least send him some hand history screenshots so that he can validate my findings.
Quote: Johnboy85I knew this question would come up and respectfully I will keep that a secret for now as I think if I divulged this, it would be a giveaway and could alert the operator of their mistake.
After 4.5 SD down, you still think that's an "innocent mistake" on their side, rather than a bait?
Quote: AxelWolfThis brings up a question. Why wouldn't an online casino record Hand history?
I think I have read something like "top 10 tells that a casino is cheating on you" and one of them is "not recording hand history"
Quote: andysifAfter 4.5 SD down, you still think that's an "innocent mistake" on their side, rather than a bait?
Yes. If you knew the site I was referencing, you'd understand.
The calculator I have referenced to make that calculation may not be a proper calculation of actual SD as there have been instances during this long period where I did grow my balance and was betting much higher unit sizes. I'm willing to be proven wrong there although I think there comes a point where Wizard and Teliot among others will agree that things look fishy regardless...
Quote: andysifI think I have read something like "top 10 tells that a casino is cheating on you" and one of them is "not recording hand history"
They do record hand history, but only for a day, and the player cannot export it. I assume for sure the online casino has logs of every hand.
It seems odd that one of the largest online casino, one that has a sterling reputation would have a +EV game off the top. Only two casinos come to mind that I would put in that category(no one would get a sterling reputation). This leads me to believe your advantage is from ongoing weekly bonuses? Not that, that should matter when assessing fairness.Quote: Johnboy85If he comes here and confirms that, I'd be happy to at least send him some hand history screenshots so that he can validate my findings.
Quote: AxelWolfIt seems odd that one of the largest online casino, one that has a sterling reputation would have a +EV game off the top. Only two casinos come to mind that I would put in that category(no one would get a sterling reputation). This leads me to believe your advantage is from ongoing weekly bonuses? Not that, that should matter when assessing fairness.
My feeling is that they didn't intend it that way, but they misprogrammed the game and no one has caught it. The edge off the top would only be obvious to an advantage player or a very seasoned blackjack player.
What bothers me is that if the game is a true random RNG, i should not have lost anywhere near as much as I have. The fact I am where I am raises the possibility that the RNG is not as random as it seems.
Quote: Johnboy85
0.4% player advantage
233 614 hands
-$34,471
16.24 Avg Bet size
If 16% of your bets are $75 and 84% are $5 then your are only at -3 SD.
If your top bets were 2 hands of $75 then SD is even smaller.
The chance of a cheating game depends on your "a priori" belief of how likely the game is gaffed.
The SD result is not enough to draw an accurate conclusion.
If the results were at Harrahs, a large chain, for a small amount of money. I would still think that a 1 in 400 result is still possible on a "fair game".
--> In an AIDS example, even if a test is 99% accurate, if the tested person had a 1 in 100,000 "a priori" chance of AIDS, 99.9% of the results will be false positives.
--> However, if a person is from a population with 10% HIV+ people, then the person probably has AIDS.
IMO, the game probably is cheating.
However, "proving" a game is cheating is WAYYY different than believing P(Cheating) > P(Not Cheating).
...and what would be the point? The site might have a beatable game in the future, so why raise attention.
-----
Since SDs are based on the 2nd moment, you can do your own estimation of SD.
Just estimate what percentage of bets you made at $5, $10, ..., 2x$50, etc...
It's good practice to do calculations yourself (rather than rely on an "on-line calculator"), as it may give you a better understanding of how each betting system affects your real-life SD, RoR, bankroll requirements, etc...
Quote: mamatAt 3 SD, we're looking at 0.25% (1 in 400) chance (based on univariate normal distribution, and neglecting sequence effects from betting changes).
The chance of a cheating game depends on your "a priori" belief of how likely the game is gaffed.
The SD result is not enough to draw an accurate conclusion.
If the results were at Harrahs, a large chain, for a small amount of money. I would still think that a 1 in 400 result is still possible on a "fair game".
--> In an AIDS example, even if a test is 99% accurate, if the tested person had a 1 in 100,000 "a priori" chance of AIDS, 99.9% of the results will be false positives.
--> However, if a person is from a population with 10% HIV+ people, then the person probably has AIDS.
IMO, the game probably is cheating.
However, "proving" a game is cheating is WAYYY different than believing P(Cheating) > P(Not Cheating).
...and what would be the point? The site might have a beatable game in the future, so why raise attention.
-----
Since SDs are based on the 2nd moment, you can do your own estimation of SD.
Just estimate what percentage of bets you made at $5, $10, ..., 2x$50, etc...
It's good practice to do calculations yourself (rather than rely on an "on-line calculator"), as it may give you a better understanding of how each betting system affects your real-life SD, RoR, bankroll requirements, etc...
Well here's what I've tracked. Perhaps you can make some assumptions from that.
try https://docs.google.com/spreadsheets/d/1TkxZ8vkWEcHmykw_3QObw3io-UxkFGQfLPnwiH_2-XM/edit?usp=sharing
Quote: mamat
IMO, the game probably is cheating.
However, "proving" a game is cheating is WAYYY different than believing P(Cheating) > P(Not Cheating).
...and what would be the point? The site might have a beatable game in the future, so why raise attention.
It's good practice to do calculations yourself (rather than rely on an "on-line calculator"), as it may give you a better understanding of how each betting system affects your real-life SD, RoR, bankroll requirements, etc...
I can't necessarily prove that they are cheating, but at the very least I can prove that their game isn't actually programmed according to the rules stated on the website. That in and of itself is worrying, but I've up to this point assumed I was playing a fair game and that I could take advantage.
For what it's worth, no one has of yet come here and dispelled this calculator (https://www.card-counting.com/calcrisk.htm), which is the basis of my 5.5 SD assertion. It is a card-counting calc tool, so it must assume fluctuation in bet sizing.
Honestly the math behind all that stuff is a little beyond me. I've just been assuming that eventually my results will approach EV. I'm at nearly 250 000 hands played. How many more before I get there?
I know you can blaze though video BJ super fast.Quote: Johnboy85Well here's what I've tracked. Perhaps you can make some assumptions from that.
try https://docs.google.com/spreadsheets/d/1TkxZ8vkWEcHmykw_3QObw3io-UxkFGQfLPnwiH_2-XM/edit?usp=sharing
At one point you played over 1900 hands per hour, I would assume you made more mistakes than you think.
I would even go so far as to say that you probably made some major button mistakes along the way.
That's not to say I dont think its gaffed anyways.
You're not getting the math. Which is why doing the math by hand would be helpful.Quote: Johnboy85For what it's worth, no one has of yet come here and dispelled this calculator (https://www.card-counting.com/calcrisk.htm), which is the basis of my 5.5 SD assertion. It is a card-counting calc tool, so it must assume fluctuation in bet sizing.
Try calculating the SD of some artificial bet spreads:
80% 1 unit, 20% 2 unit
80% 1 unit, 10% 2 unit, 10% 3 unit.
And see what happens...
All hands at $5. Do this twice, once for the # of hands you played and another time for how much $$$ wagered.
All hands at $75 bet. Do this twice, once for the # of hands played and again for how much $$$ wagered.
Basically, looking for a best case and worst case scenario.
Then do it again, but do half of hands at $5/bet and half hands at $75/bets. Then again, such that you get an $18 avg bet.
Then do some more and guess at different size bets you could have had. Make sure the sum is the 155k hands it says you played AND the sum is the $$$ wagered it says you wagered. There are many different combinations of bet sizes you could have had. IE, $100 in action over 5 hands could be:
20, 20, 20, 20, 20
20, 20, 20, 25, 15 (same thing as 20, 20, 20, 15, 25 or 20, 15, 20, 25, 20, etc.)
5, 5, 5, 5, 80
But cannot be
25, 25, 25, 25, 25 ($125 total)
20, 20, 10, 25, 15, 10 (6 hands)
Etc.
I have finally managed to acquire the full hand history from the casino and was wondering if anyone here might want to help corroborate/verify the data to make sure my calcs are accurate.
Best,
John
