As a break from things serious, consider this scenario:
In a New Jersey casino, you walk up to an electronic slot machine, stick in a buck and punch the buttons. You win fifty. It happens. Flush, you venture another buck. You’re still up a bunch. You win another fifty. Figuring why not, you bet again. Another win. Say, this is getting good. Another bet, another win. And so on for forty-one—that is 41—times in a row!
Ah, but then four beefy guys named Guido finger your collar, drag you back to your room and bounce you up and down a bit, hoping to dislodge a device you don’t have, a device which they imagine could have secretly controlled the slot machine. In saunters a pencil necked manager wearing an expensive but garish suit and says he’s not going to pay since he claims the machine is busted.
Out the door you go…straight into a lawyer’s office? Are you upset that you didn’t pocket the proceeds? Or do you figure that this is what happens when you flirt with fortune?
I say, write the whole thing off as a lesson in how not to gamble: viz. don’t gamble. Especially in New Jersey—New Jersey, for crying out loud.
The scenario painted above happened in a sort of way. In New Jersey at the Golden Nugget. According to the AP, several players at a game of mini-baccarat
kept seeing the same sequence of cards dealt, over and over and over again, their eyes grew wide and their bets grew bigger, zooming from $10 a hand to $5,000.
Forty-one consecutive winning hands later, the 14 players had racked up more than $1.5 million in winnings — surrounded by casino security convinced they had cheated but unable to prove how.
The Casino blamed their playing card source, Gemaco, Inc., which was supposed to send them the painted boards pre-shuffled. Only this time, they forgot. Also, this wasn’t the first time: “the Trump Taj Mahal Casino Resort used unshuffled mini-baccarat cards for 3 1/2 hours before realizing something was wrong.” You may wonder at the level of minds that take three-and-a-half hours to discover the decks of cards they’re using are unshuffled.
The Golden Nuggest, after they finally figured—after seeing forty-one straight hands with the same damn sequences over and over and over again—their cards were rigged, weren’t such bad sports about it. It “let nine of the players cash out $558,900 worth of chips.”
But poor Hua Shi of Brooklyn wasn’t one of them. He says he went back to his room after the game to knit the raveled sleeve of care, but then in busted a quartet of Planet of the Apes cast members “who pinned him against the wall and searched him and his belongings” and then kept him there overnight.
Hua Shi’s lawyer says he got the business because he was Chinese and that his treatment had nothing to do with the winnings he racked up from the stacked decks.
Recapitulation: forty-one—41!—consecutive winning hands are dealt, Casino realizes something fishy, notices unshuffled card; casino sues Gemaco, shakes down a player Hua Shi for winning too much; Hua Shi sues Casino.
I haven’t any idea how to compute the probability of 41 identical hands, because it would requiring knowing how many players played, the numbers of decks used per game, whether every player bet the same way each time, and so forth. But good grief, quantitative probability isn’t needed! Maybe, just maybe, after seeing the second hand identical to the first, we can imagine a pit boss saying, “Well, it could happen.” But after three? And then four, and even five?
The suspicion is either we’re not getting the whole story, or that casinos would not be the best hunting grounds to search for Mensa members.
If I were the judge, I’d throw out all the suits—and I wouldn’t apologize for the bad pun.
Hey! It’s NJ and everybody’s in a union and I imagine casino dealers are considered part of “everybody”. The card dealers aren’t paid to keep track of the hands dealt nor do statistics. Not in their job description. What caught their eye was likely the large amount of negative cash flow.
Interestingly the number of employees has increased. What’s the primary goal of a union?
Thinking of a previous post, I conclude this is simply a rare event! ^_^
Oh, no, the slot machine is stuck!
RE: how to compute the probability of 41 identical hands
THAT presumes fair decks reasonably shuffled, and thus misses the point:
How many such hands does it take to recognize the deck is flawed and “bets” shift from being “gambles” to “sure-thing investments”?
From the tone of the article it appears some, not all, gamblers started acting on this on the fourth deal. By what deal were all acting on this?
The corrallary question is: “How many deals did players need to recognize the deck became “fair” again (i.e. when did they recognize that “investments” shifted to “gambles”?)?” Presumably after the first or second loss due to the set pattern shifting back to random.
ASIDE: This illustrates a principle associated with optimization techniques of multivariate constrained systems, where mathematical techniques can be employed to reject broad swaths of possibilities without actually calculating their specifics. With much, or sometimes limited, experience & knowledge one is sufficiently informed to reach logical rationale actionable conclusions.
This also illustrates how a person with rigid thinking and/or too much narrow knowledge can be impeded by that: the average person, and every gambler, would very quickly (three deals or so) conclude that a repeat pattern in multiple decks MUST be the result of a processing failure of some sort as the odds are so astronomical the possibly it is random is nil. This ilk, unlike our statistician, would never bother to wonder what the actual odds were much less how to calculate them.
It is THAT ability to synthesize mulitple diverse inputs (card randomness & knowing cards are made in an order and then need to be shuffled, which is the step more likely to be skipped–a non-mathematical data point), which human intuition (especially intuition built on breadth & depth of experience) CAN exploit (as the gamblers did).
AND, it is that same ability which effectively negate’s any need for the sort philosophizing such as Feser’s “The Rationality of Induction,” which has limited or no real-world (non-academia) practical application. Feser’s & related philosophicl constructs (models/architectures) and analytical methodologies are invariably artificial and limited to that never-never-land of the imaginary construct. Real people in the real world contending with real issues always bring other factors, unique to the situation and individual experience, into play. No philosophical construct can account for that, which is why they suck.
I suspect the winning players were passing hefty tips to the dealer along the way to help him not notice what was happening.
What this demonstrates is micro-focus, which used be known as being unable to see the forest for the trees. Concentrating on how the cards were being manipulated, the casino didn’t look to see what the values of the manipulated cards were.
From a probability point of view, there chance that the actual values of the cards coming up would provide any information about how customers are winning so much is so low that it doesn’t make sense for the casino employees to waste time looking at the values of the cards. Instead of concentrating on the probability of 41 identical deals, consider the likelihood of winning games being dealt because of unshuffled cards. At 41 hands, unshuffled cards is a high probability but at 7 hands not so much, and even at 20 hands the probability of unshuffled cards being the cause of the winning hands is still pretty low.
OTOH, a friend of my then wife-to-be once found the entire Pabst Brewery payroll deposited to her checking account. Banking laws are very clear on this. If it is unmistakably an error, even on the bank’s part, the depositor has no right to the money. You better not spend any of that unexpected cash. Especially to send a postcard from Brazil.
It would seem this fell into the same category.
“… wonder at the level of minds that take …”
Brain vs mind descriptors: addressed above.
YOS,
Except in this case the casino is an active participant in the “mistake” through on-going acceptance of bets. Winning $1.5M at $5000/hand had to take a noticeable amount of time. Apparently the casino watched for some time. It shouldn’t be up to the players to decide what hands “aren’t kosher”.
They should pay if only for customer good will. Reneging on a bet is bad business. It sends the wrong message: come give us your money; we guarantee no return; no winners allowed — big winners in particular. They don’t seem to understand that somebody winning big draws people. You can always tell when a craps table has a good shooter. It has the biggest crowd. Good advertising.
Years ago, the Pennsylvania daily 3-pick was being rigged by the host. On one particular day, the state closed the drawing and refused to pay. In that case, the state argued that the majority of those playing the winning number where knowledgeable about the fix. Given that the winning combo had an unusual number of players, they may have had a point.
In the casino case, it’s a little hard for the casino to claim the players were in on some scam. It’s effectively the casino’s mistake and they should man up.
That something like what you describe could happen is reassuring that the games are not rigged. That the casino lacked a sufficiently alert monitoring system to detect anomalies in either direction is astonishing.
High school classmate put himself through MIT by timely visits to Vegas. the trick was never to go home with more than he needed. A couple of the houses finally recognized him, talked to him, but let it happen because he wasn’t greedy and they apparently thought that a bit of winning encouraged the others.
There’s another lesson here. The evidence that something isn’t working has to build up to a thunderous extent before most people quit doing whatever they’ve been doing. One would have thought that 4 or 5 wins would have done it, but the house apparently had no program for dealing with something like this.
How is it that 14 players can figgure out that there is something unusual to the pattern of the cards comming to them, but the casino security, which is watching them cannot figgure it out?
I don’t know the game, but does the deeler also play in the game? Did he not recognise that he got the same cards every time? Or the one card got turned up every game?
There are so many things that should have been obvious to the dealer.
I don’t think the casino has any claim at all. It is up to the casino to refuse the game to continue. But since the casino allowed the game to begin, progress and end. It’s the casino’s responsibility to pay the winnings.
Someone should have been busy calculating the p values for H0. H0 being, like, It can’t happen.
Also sounds like a good application for real-time monitoring software. Hook up a pattern recognition code having a card-data database to the always-on surveillance cameras and a background code running p values for H0.
Maybe there’s consulting opportunities, Matt.