From Donovan v. Grand Victoria Casino & Resort (Oct. 30), in which the Indiana Court of Appeals so holds, and cites a 1982 New Jersey case so holding:
[The casino] may not simply take refuge in the common law right of exclusion, inasmuch as it is the public policy of this State that gambling is subject to “strict regulation,” and the Commission has been given exclusive authority to set rules of riverboat casino games. The Commission did not enact a prohibition against card counting and Grand Victoria did not seek a prohibition by rule amendment. No law, regulation, or duly promulgated rule advised Donovan that the skill of card counting was prohibited.Indiana has implemented a comprehensive scheme for regulating riverboat gambling and thus has partially abrogated the common law right of exclusion.
I think this is a bad rule, and that casinos should be free to eject card counters from their property. Nor am I sure that this is indeed the best interpretation of the statutory text; I haven’t looked closely enough at the statutes to form a reliable opinion, but the statutes that the court cites don’t strike me as persuasive on this — that the statutes control the “rules of the game” doesn’t mean, I think, that they control the casino’s choices about whom to allow to play the game. But in any event, this appears to be the law in Indiana and New Jersey, which I didn’t know until I read the case.
Anderson says:
I dunno. Can they exclude someone for winning, absent express legal authority?
I can see the argument that the “odds” are governed by the regulations, and that the casinos are not allowed to improve them in their own favor.
Is anyone requiring the casinos to offer single-deck blackjack (which I ignorantly suppose to be the only kind where card-counting can help)? Or any blackjack? If not, then if they don’t like that some people play the game well, they have a recourse: don’t offer the game.
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November 6, 2009, 3:23 pmgasman says:
The card counters merely show us that this is not a game of chance purely. There is an element of randomness that must be coped with in utilizing a strategy, but that can be said of many endeavors. The knuckle ball will break randomly in a way even the pitcher cannot predict because of the unpredictable nature of fluid dynamics when the sphere is not spinning for a smooth Bernoulli effect. Yet we would bristle at a league that banned batters who were particularly adept at hitting such a knuckle ball.
Besides that, the casinos probably are discriminatory in that they permit poor card counters or counters in training to stay and loose money. They likely don’t uniformly ban counting, only counting that is good enough to be effective. This might even create a cause for action from a sloppy counter — they might argue that the casino had a duty to enforce its rules evenly, and if the casino had, then they wouldn’t have lost all night at the table.
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November 6, 2009, 3:27 pmKazinski says:
EV,
I don’t think its too much state regulation to say that the Casino has to have grounds for ejecting somebody from a state regulated business. As long as somebody is not disruptive or breaking rules or the law, they should be allowed to play. If the State wants to change the rules so card counting is against the rules, they can do that. But the Casino’s shouldn’t be able to say that you can only play if you have half your mind tied around your back. Of course the Casino’s should also be able to use multi-deck shoes that make Card counting much harder; or not offer Blackjack at all if they can’t make a sufficient profit under the rules.
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November 6, 2009, 3:28 pmAllan says:
I thought casinos had other means for ensuring that card counters stayed out. Their names would be like Bruno or Vinny.
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November 6, 2009, 3:35 pmtroll_dc2 says:
What is so bad about card counting?
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November 6, 2009, 3:35 pmWaste93 says:
Card counting can be done with multiple decks though it becomes more difficult.
Personally I don’t see the issue with it as long as it is done in the persons head. No computers or anything like that. All card counting is, is figuring the odds that a favorable card will be drawn when you request a ‘hit’ based on what cards have already been exposed. If you ban card counting does that mean someone with a photographic memory would be automatically excluded from playing?
Card counting is routinely used in Poker in a fashion. The players bid based on their hand and what they are discarding and hoping to draw. In Texas Hold’m you have cards exposed with a couple hidden cards. The raises and decision to fold and such are based on the exposed cards and the likelyhood that a favorable card has been or will be exposed.
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November 6, 2009, 3:36 pmbyomtov says:
Anderson,
Counting can be effective with multi-deck games as well. And what gasman says is probably correct. The casinos are happy to have card counters play. The more the merrier. They only want to bar good counters.
It’s not the counting that bothers them. It’s the winning.
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November 6, 2009, 3:41 pmBlue says:
1) Blackjack is not a game of chance–it is a game of skill. There is a perfect strategy for any given set of rules/displayed cards.
2) Casinos may suspect people of card counting...but it’s not something they can prove. All they can say is that certain behaviors (e.g., increasing the size of a wager after a series of low wagers) correspond with card counting.
3) Casinos always have an option short of expulsion to deal with card counting–multiple decks and frequent shuffles prevent players from gaining the advantage.
Part of the problem is that people think card counting is related to a memory of cards being played...actually it is just keeping a mental tally of the ratio of high to low cards.
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November 6, 2009, 3:43 pmASlyJD says:
Iris: So, what are you doing in Las Vegas?
Raymond: We’re counting cards.
Iris: You’re counting cards?
Raymond: We’re counting cards.
Iris: That’s interesting.
Raymond: We’re counting cards.
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November 6, 2009, 3:43 pmCard Counter says:
Intelligent card counters prefer a rule where card counters can be ejected. The other countermeasures used against card counters when ejection is not available are much more effective. I don’t know a single counter who prefers counting in AC (where no ejection is allowed) to Vegas (where ejection is allowed, and I’ve been ejected multiple times).
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November 6, 2009, 3:43 pmTheef says:
As a card counter myself, I actually prefer that a jurisdiction allow card counters to be ejected. If a casino is not free to eject me, then it must compensate for my unabated presence by offering stingier rules and practices. I prefer venues that do the former — and most counters agree. Worse, most of these measures actually harm all blackjack players, even the vast, vast majority who don’t know a thing about advantage play. (As one example, all players, counting or not, are dealt blackjacks less frequently from an eight-deck game than from a single– or double-deck game.) Thus, hamstringing the casinos in an attempt to protect the customer actually fosters a gaming climate that hurts the customer.
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November 6, 2009, 3:45 pmPatHMV says:
If you have to change the regulations to allow the casinos to eject the card-counters, then that means that you have to define card-counting as “cheating,” doesn’t it? As a practical matter, at any rate. That seems to me unwise, because it doesn’t take advantage of anything other than a rainman-like ability to keep track of which cards have been dealt.
Moreover, absent an organized team of card-counters (a la 21 using electronic assistance, how do you prove it? If you can only eject for violation of regulations, that means that you have to give some kind of due process to determine if the regulations were violated. How do you prove that Raymond was counting cards? It’s more a “I know it when I see it” sort of thing, isn’t it?
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November 6, 2009, 3:47 pmSteve says:
This is the correct ruling. NJ has a very detailed regulatory regime that effectively “preempts the field.” If casinos want to be able to exclude a given class of customers, they need to go through the rulemaking process; otherwise the presumption is that the public has access.
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November 6, 2009, 3:48 pmzuch says:
Prof. Volokh:
Do the rules set by statute/commission specify such things as types of games allowed and permitted “take”/odds? IIRC, there’s fairly strict regulation in some states as to slot machine payouts, and it wouldn’t surprise me to see similar rules for other games. How about permits for the numbers and types of tables, and on the conduct of the dealers? If so, there’s a fairly intrusive regulation of the casinos. The rules may not specify who can play (other than people over 21), but they may specify that the rules can’t be bent because some people try to take advantage of the permitted odds.
Cheers,
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November 6, 2009, 3:49 pmSteve says:
That seems to me unwise, because it doesn’t take advantage of anything other than a rainman-like ability to keep track of which cards have been dealt.
Card counting is actually pretty simple although you can use it more effectively the more rainman-like you are. In the simplest form, high cards count as –1 and low cards count as +1, and you raise your bet when the running total gets high enough. That’s pretty easy for anyone to keep track of, even at the fairly rapid pace of a typical casino game. You can get gradually more sophisticated from there depending on how well you can juggle numbers.
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November 6, 2009, 3:51 pmzuch says:
Anderson:
Usually, they try to make winners welcome, for more than one reason. They give them comps, drinks, free hotel rooms, etc.. This is not only because it’s good customer relations, but also because they know that if the person continues to gamble, they’ll probably lose their winnings back again, and the casinos will recoup the losses.
Cheers,
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November 6, 2009, 3:52 pmAnon21 says:
From my vague knowledge of blackjack, this strategy probably doesn’t work for experienced and skillful players of that particular game; as a commenter upthread noted, the “basic strategy” is a learnable collection of actions which will always minimize the house’s advantage and keep the player consistently winning. (Obviously, results from any one night may be bad, but over time the player will turn a nice profit.)
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November 6, 2009, 4:03 pmzuch says:
Theef says:
How so, pray tell?
Cheers,
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November 6, 2009, 4:07 pmzuch says:
Anon21: What I said was “usually”. Such as winners at other games. And people who aren’t suspected of being counters. Which is most of the clientele.
Cheers,
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November 6, 2009, 4:10 pmdjh5 says:
It’s well known that blackjack only surged in popularity after the publication of Beat the Dealer in the 1960s. It was the prospect that the game could be beaten that drew players in, even if most lacked the discipline to learn the basic strategy/card counting techniques and apply them consistently. Likewise a few poker players making a living off their winnings draw in more casual players.
One of the reasons that horse racing has been decimated is due to high takeouts that would require super-efficient strategies to consistently win.
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November 6, 2009, 4:22 pmrichard says:
I dunno. Can they exclude someone for winning, absent express legal authority?
It seems to be that is a very good question. Leaving aside the regulatory premption question, Professor Volokh’s comment that the casino should be free to eject card counters seems to be based on the premise that the casino has the right to eject people it doesn’t want at the table (as long as the reason isn’t because of a prohibited classification — race, religion, national origin, etc) (If there is another reason for the conclusion, can he or someone else provide the rationale?). Can the casino then decide that they will eject anyone who wins more than $1000 in an hour? (They may not want to do so figuring that winners who stay at the table eventually become losers but the question is whether they should be free to implement such a practice)
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November 6, 2009, 4:28 pmSteve says:
How so, pray tell?
Let us assume I deal to you from a single deck. The first card is an ace. The chance that your next card will complete a blackjack is 16/51.
Let’s say I deal to you from a double deck. The first card is an ace. The chance that your next card will complete a blackjack is 32/103.
16/51 is more than 32/103. Not much, but it’s more. Extend it out to 8 decks and the difference gets even bigger. You get more blackjacks with a single deck.
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November 6, 2009, 4:29 pmGuest says:
I’m not a statistician, but I assume its because the number of blackjack triggering cards (A, K, Q, J, 10) increases at a smaller rate than the number of non-blackjack triggering cards (9–2). So, the more decks you add, the greater your chances of receiving a non-blackjack triggering card.
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November 6, 2009, 4:32 pmGuest12345 says:
Seems to me that they should be able to ask a winner to leave if they so chose. It’s directly analogous to a loser leaving the table.
I think that asking a player to leave is taking your recourse of not offering the game, to that particular player. Since we don’t yet live in a society where we have a mandate to play the black jack tables, I fail to see why any particular person/group of persons should be required to provide a black jack table to any and all comers in all circumstances.
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November 6, 2009, 4:33 pmDavid Welker says:
Why?
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November 6, 2009, 4:34 pmjosh bornstein says:
As a card counter myself,...
[...]
(As one example, all players, counting or not, are dealt blackjacks less frequently from an eight-deck game than from a single– or double-deck game.)
How so, pray tell?
Well, in the casinos I’ve been in, dealers have a lot of discretion as to when they re-shuffle. And if the pit boss is looking over their shoulder, and the deck is “hot” (ie, a lot more face cards and aces remaining compared to what would normally be expected), I’ve seen dealers reshuffle after only a 1/3 of the shoe. Obviously, this makes counting much less productive.
My response has been to never play at more than a 2-deck shoe. And, when the deck is hot, rather than give a direct tip to the dealer, I (quietly) tell him that I will be placing a bet on his behalf on the next deal. Or, on the next 2 deals. This *always* works at preventing a re-shuffle, since the dealer now has a strong motive in having you win the upcoming hand(s). (This would not apply if the pit boss is hovering nearby. If so, it’s time to switch casinos, or, to come back the next day.)
When I played at Lake Tahoe (which was almost 20 years ago, so the guidelines there certainly may have changed), they played through almost the entire deck. However, if your bet was 3x the previous bet (or higher), there would be an automatic re-shuffle. My only response was to literally ‘hide’ a $50 or %100 chip under the one or two $5 chips, so that the dealer did not notice. The only issue was that, if I did win, I had to keep my hands *well* away from the table, and to point out to the dealer that he actually owed me $110, not $10.
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November 6, 2009, 4:34 pmJeff R. says:
52 cards in a fresh deck, 8 aces, 16 faces and tens. So the chance of being dealt blackjack is (8/52)*(16/51)=2.4133%
516 cards in an fresh 8-deck shoe, 32 aces and 128 faces and tens. (32/416)*(128/415)=2.3726% A small difference, but a real one. There because the difference between 52 and 51 is bigger than that between 416 and 415. Probably gets a lot bigger towards the end of the pack, too.
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November 6, 2009, 4:36 pmAnderson says:
It’s directly analogous to a loser leaving the table.
The court’s point appears to be that the casinos have no such right unless expressly granted in what is presumably a fairly rich regulatory scheme. If the casinos wanted this right, they should have negotiated for it when the regulations were being created (as they doubtless lobbied for other stuff).
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November 6, 2009, 4:38 pmGuest12345 says:
Given that gambling tables were around before the regulatory environment, it is a bit disingenuous to talk as if the regulations created the game. The ability to evict players has been around for decades. Proposing that someone should have negotiated something that has been there from the start seems to be putting the cart before the horse.
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November 6, 2009, 4:46 pmDavid Schwartz says:
The hypo is this: What if they have a policy of ejecting anyone who doubles down? The rules allow the player to double down, this improves the player’s odds (if done strategically). Prohibiting doubling down by the backdoor ejection route allows the casino to circumvent an advantage the law guarantees the player.
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November 6, 2009, 4:48 pmmrcausality says:
I don’t frequent casinos enough (or ever, for that matter) to determine if or when the end of card counting will be a reality, but it seems to me an inevitability. No matter how basic or advanced your technique, it always relies on the tracking of a few state variables of the penetrated decks. The obvious defeat of any card counting techniques, therefore, is to remove penetration. This is simply accomplished by reshuffling after every round. Electronic blackjack, as far as I know, does this. In some casinos, there are now continuous shuffling machines that shuffle one deck while the dealer administers another. In these cases, the house retains the advantage every round.
I would be interested if those with on the ground experience see this as well or believe I’ve missed something.
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November 6, 2009, 4:51 pmNunzio says:
Where’s the regulation that says casinos shall have no clocks or windows?
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November 6, 2009, 5:02 pmDJR says:
8 aces?
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November 6, 2009, 5:05 pmDan Weber says:
Yeah. You got a problem wit dat?
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November 6, 2009, 5:20 pmRoger says:
EV, is your point that casinos ought to be able to exclude anyone they please for any reason, or that card counters are particularly deserving of exclusion?
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November 6, 2009, 5:26 pmtraveler496 says:
EV: “...that the statutes control the ‘rules of the game’ doesn’t mean, I think, that they control the casino’s choices about whom to allow to play the game.”
I don’t see how one can distinguish the two in this context. Casinos which eject counters based on their betting or playing behavior within the rules are in effect modifying the rules (in admittedly unstated ways which furthermore vary by casino, shift, pit, table, player’s chip count, etc.). But according to the cited opinion, the rules are something which the Commission “...been given exclusive authority to set...”.
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November 6, 2009, 5:41 pmWaste93 says:
A single deck of 52 cards only has 4 aces. One for each of the four suites. Not eight.
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November 6, 2009, 5:54 pmzuch says:
Steve:
Yeah, that’s the conditional probability based of the first card being an ace. But that’s not the relevant statistic, because the number of blackjacks is over the entire deck[s], whether or not you got an ace (or ten-spot) on the first card. If you get that ace (or ten-spot), and a blackjack on the first deal, your conditional probability of getting a blackjack later is lower. If you don’t get that ace (or ten-spot) on the first card (and thus no blackjack), your conditional probability of getting a blackjack later is higher.
It’s true that your immediate probability of getting a blackjack improves considerably on the first deal after you get that ace showing on the first card (by an order of magnitude). But that hardly means that you have a much better chance of blackjack (before you’ve seen any cards) on the first deal always, compared to any other deal. Throwing in that conditional probability there is just bogus.
You play poker, by any chance? ;-)
Cheers,
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November 6, 2009, 6:03 pmCato The Elder says:
(He was affecting a rigged, shady game run by the sort of lowlife you might see in a Western, Waste)
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November 6, 2009, 6:05 pmBill says:
according to Ben Mezrich’s books about the MIT blackjack team, team card counters can effectively take advantage of multi-deck shoes even with a simple +1/-1 count per card. a multi-deck game can get much further from a neutral count than a single-deck game, and when it strays particularly far in favor of the player you can increase your bets and expect bigger payoffs.
they did this by having counters placing small bets at multiple tables and one “whale” moving from table to table placing big bets at whichever table was best at the moment.
one casino caught on to this and changed their house rules to require reshuffling (which takes time and thus reduces the casino’s take) every time someone new joined the table.
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November 6, 2009, 6:18 pmLloyd says:
Let me tell you how this works in practice. The casinos make use of a variety of other tools to defeat card counting, but all have costs associated with them. The three most prominent are:
(1) they place the cut card rather far from the back of the deck. Thus when using a 6 deck shoe rather than placing the cut card 1 to 1 1/2 decks from the back, they place it 3 decks from the back. In that way they make it far less likely that truly favorable counts will result. The cost of this to the casino is more frequent shuffling which the ordinary players don’t appreciate.
(2) they station a floor man near the dealer when a suspected card counter is present and when the count becomes favorable to the player the floor man orders the dealer to shuffle up prior to the appearance of the cut card. In addition to annoying and confusing the other players at the table this technique can be defeated. It is the rare floor man who bothers to “count” the deck and determine whether it is favorable or not. Instead he makes his determination based on the putative card counter’s bets. If the counter raises his bet the floor man orders a shuffle. So, savvy counters raise their bets when the count is negative rather than positive and thereby get fresh decks.
(3) the most delightful device that the casinos in Illinois, Indiana, and New Jersey use is to make strategic use of their state granted power to allow at their discretion selected players to exceed the table limit. So while the typical maximum bet at a $25 minimum table will be $1,000, casinos in these states ordered special signs that posted a minimum bet of $25 and a maximum of $25, $50 or $100. Then the floorman tells everyone but the counter that they may exceed the table limit. This also does little to generate goodwill with the other patrons.
Beyond all that one casino in Illinois barred me from play claiming that my actions made it too difficult for them to comply with state and federal reporting requirements. Specifically, they said I: (1) changed tables very frequently; (2) kept my chips in my pocket; and (3) cashed in quietly numerous times. While all these accusations were accurate, they were clearly just a pretext to make a colorable claim that they could bar me from the riverboat. Why? Because, I offered to amend my behavior to comport with any reasonable rules they could suggest. They declined my offer. I probably had a legal claim, but I was leaving Illinois with a couple of months so I let it go.
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November 6, 2009, 6:24 pmtraveler496 says:
zuch,
If you read Steve’s “first card” as “first card you receive in this hand,” his analysis is correct regardless where you are in the deck. Completing his analysis, the probability of being dealt a blackjack at an arbitrary point in a 1-deck game, averaged over a large number of random shuffles, is
(4/52)*(16/51) + (16/52)*(4/51), or 32/663,
where the first term covers A-first and the second term covers 10-first. And for an 8-deck game this probability is smaller, since each of the LHS numbers increases by a factor of 8 except the 51’s in the denominators which increase by more than a factor of 8 (to 8*52–1=415 > 8*51).
I don’t play poker but if you disagree substantially with this (and you give me some time to check my math) I think we could work out something:-)
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November 6, 2009, 6:33 pmAnderson says:
Given that gambling tables were around before the regulatory environment, it is a bit disingenuous to talk as if the regulations created the game.
Uh, no. We’re not talking about the game. We’re talking about a practice extrinsic to the game, as regards some casinos which are allowed to operate ONLY by sufferance of the state.
Sorry if it seems to me you’re being a tad willful here.
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November 6, 2009, 6:37 pmzuch says:
Nevermind. I see my error. There’s less “non-replacement” in a smaller deck.
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November 6, 2009, 6:57 pmAllan Walstad says:
In a completely free market for gambling, or even just blackjack, then sure, the owner of the establishment ought to be able to exclude whoever they want, as long as their actions don’t violate their advertising or posted rules. On the other hand, the government is deeply involved in the whole business–so, for example, other investors can’t simply build competing casinos anywhere, anytime and set up whatever rules they choose, and established casinos thereby enjoy something of a government-enforced oligopoly. So the question at hand has something of the quality of trying to figure out what combination of wrongs makes a right.
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November 6, 2009, 7:35 pmSara says:
Prof. Volohk: You don’ know the statute or the law but you think that the Appeals Court’s ruling is bad? Really?
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November 6, 2009, 7:36 pmkdackson says:
There are some canadian casinos that use a mechanical shoe that constantly recycles and reshuffles the 8 decks. Never play at those tables for obvious reasons.
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November 6, 2009, 7:38 pmTC says:
Do the casinos have to show any proof that one is counting?
I’ve never gambled but let’s say decided to try blackjack and, beginner’s luck, won hand after hand. Would that be sufficient “proof” that I was a card counter?
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November 6, 2009, 7:46 pmEH says:
TC: It’s not the winning, it’s the bet-structuring.
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November 6, 2009, 7:59 pmTweets that mention The Volokh Conspiracy » Blog Archive » New Jersey and Indiana Casinos May Not Eject Blackjack Players for Card Counting -- Topsy.com says:
[...] This post was mentioned on Twitter by Lokkju Brennr, Gene Hoffman. Gene Hoffman said: Should state regulated casinos be able to eject card counters? http://bit.ly/LEXKQ [...]
Gene Hoffman says:
No. Counters have a bit of a discernible pattern if the house is counting along with and the counter is following the correct betting strategy.
–Gene
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November 6, 2009, 8:10 pmNew Pseudonym says:
Card counting is a strategy. It has nothing to do with the rules of the game. Others have pointed out that poker involves a crude form of card counting when played successfully. Bridge involves a lot more in order to be played in a mediocre manner.
The real problem is that the rules in Blackjack were set under a presumption that every deal would progress from a new deck. This gave the House a measurable edge. When someone applied a little math to the idea that deals were not made this way in practice, the edge shifted to the player who played optimally (by counting the cards which have been played), not to a player who cheated. Some tinkering with rules was tried in the early 1970s, but the best that could be done was to deal multiple decks from a shoe (I am old enough to remember when every game in las Vegas or Reno was a single deck game).
Which brings us to the problem of determining who is a card counter. I don’t gamble a lot, but when I do, I disguise card counting by playing a modified Martingale (a procedure recommended in Beat the Dealer) at the same time. Basically, the casinos seem to be saying that anyone who varies their bets and wins is counting cards. While I agree that is likely, does it show by a preponderence of the evidence that something wrong is being perpetuated? I think not.
My final opinion is that if casinos want to continue to profit by luring in losers, they must bear the losses by people intelligent enough to beat their system. I would treat them as an inkeeper, required to accept all comers except for those who break the rules.
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November 6, 2009, 8:14 pmKevin says:
I thought there used to be a fear by the gov’t that casinos would purposely lose money to certain clients in order order to launder mob profits or payoffs, thus NV regulators were concerned with making sure the casinos adopted policies to prevent losses. Given the high ethical standards in NJ’s government it makes sense that Atlantic City abandoned these rules.
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November 6, 2009, 9:01 pmCousin Vinny says:
Which is why blackjack is so hideously boring compared to poker.
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November 6, 2009, 9:17 pmStormy Dragon says:
It seems to me the solution is for more casinos to start using continuous reshufflers (a device that takes all the played cards and randomly inserts them back into various sports in the shoe). This allows them to keep small shoes while rendering card counting nearly useless.
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November 7, 2009, 1:00 amyankee says:
I don’t know anything about the statutes either, but the general line of reasoning makes perfect sense to me. By ejecting anyone who plays using a certain strategy, the casinos are in effect imposing a new set of rules about what strategic options are available to the players.
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November 7, 2009, 4:18 amJohn Skookum says:
the “basic strategy” is a learnable collection of actions which will always minimize the house’s advantage and keep the player consistently winning.
Yes and no. Basic strategy reduces the house’s advantage to less than one-half of 1% under most sets of rules, but does not eliminate it or give the player a slight advantage like skillful card counting can do. You are guaranteed to “win” only if you play perfect basic strategy for small stakes while collecting free drinks.
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November 7, 2009, 5:49 amneurodoc says:
There may be a bit of a fallacy implicit here, the same one that imagines that if a coin lands tails a number of times in a row, it is more likely that it will come up heads the next time than when a coin hasn’t land too many times heads or tails in a row. Let someone give you a coin from their own pocket, so they won’t question whether it is a “fair” coin, then invite them to bet on the next flip. Most people will be more eager to bet or bet more that they can call the next one after a run of heads or tails, demonstrating their mistaken notion that their chances have improved to greater than 50–50. Casinos want to encourage as much betting on their games as they can, since their take is a function of how much is wagered. It matters not whether the player has been on a “winning” or a “losing” streak, so long as they continue to gamble. It’s that “law of large numbers” thing taking all comers together, not looking at them individually.
“Smart” gamblers may favor those games that give the house less of an edge or even let the gambler get the edge from time to time (card counting in blackjack) rather than games like roulette or pumping the slots. But so long as the gambler isn’t going to have an edge by some means, casinos will be happy to have “smart” gamblers as well as “stupid” ones, their degree of happiness depending only on how much the gambler wages. When people are winning, they are more inclined to keep on playing than when they are losing, and that’s why the casinos want to give them an extra nudge to stay longer, wager more, not because the casino will win it back from those individuals who are ahead. The casino would be no better or worse off, and hence no happier or less happy, to have losers go on playing as opposed to winners, so long as they gambled as much, and more is always better from the casino’s perspective.
Also, when others see those who appear to be winning in their midst, they are encouraged to gamble more, so another reason for casino’s to want winners on display, the flashier the better.
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November 7, 2009, 9:27 amFantasiaWHT says:
Yes, but card counting in poker does not decrease the amount of rake the house takes on a hand. In fact, if a good card counter is up against a bad card counter (or a bad player in general), the good card counter can sucker a lot of money out of the bad player, which increases the rake the house gets.
@Neurodoc — there is no fallacy there. The odds clearly show that the house will “probably” win on the next hand regardless of how many times in a row the player wins. It’s not a coin flip between the house and the player.
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November 7, 2009, 9:46 amEli Rabett says:
And here, Eli thought this blog was rather hostile to the thought police. Another illusion shattered
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November 7, 2009, 10:13 ambyomtov says:
yankee,
By ejecting anyone who plays using a certain strategy, the casinos are in effect imposing a new set of rules about what strategic options are available to the players.
No. The rules are the same. Counting doesn’t create any new bets unavailable to non-counters.
Babe Ruth didn’t change the rules of baseball by hitting lots of home runs. He just was very good at exploiting a tactic which was always available.
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November 7, 2009, 11:49 amDavid Schwartz says:
byomtov: What if they eject anyone who doubles down? How does that not effectively change the rules to prohibit doubling down?
How is saying “we will eject you if you use strategy X” not the same as saying “our rules prohibit strategy X”?
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November 7, 2009, 1:45 pmXenocles says:
In most cases this is not true. There is a “perfect storm” of game variations that can lead to a player’s edge, but at your average table playing perfect basic strategy merely narrows the house edge to roughly 0.5%. There’s a reason most places will let you openly use a basic strategy reference right there at the table.
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November 7, 2009, 3:04 pmDavid Schwartz says:
Yeah. Minimizing the house’s advantage will not keep the player consistently winning. It will keep the player losing less on average.
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November 7, 2009, 3:40 pmbyomtov says:
David Schwartz,
In one sense you are right, but only because you are defining “rules” to make it so.
To my mind, the rules describe the mechanics of the game: the bets the players may make: how the cards are dealt, how bets are settled, how various possible irregularities are dealt with, etc. They say nothing about what decision rules players may use to determine their bets in the context of those mechanics (which may include table minimums and limits).
If you prohibit doubling down you are changing the rules. You are eliminating a betting option. If you prohibit counting you are barring a player from using a particular decision procedure which has nothing to do with the mechanics.
Another argument is that, whatever a rule is, it should apply equally to all players. If you don’t allow doubling down no one can double down, period. But the casinos don’t want to bar counters. They only want to bar good counters. That’s like saying Babe Ruth’s HR’s don’t count, but Willie Keeler can swing for the fences all he wants.
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November 7, 2009, 7:15 pmRebelyell says:
A couple of points. First, the increased chance of blackjacks at lower-deck games is not because of the greater proportion of face cards. It is because of the lower proportion of ACES. When you are dealt a blackjack at single deck, one-fourth of the aces have been dealt out of the deck, making an ace-ace pairing much less likely than in a six-deck show, where only 1-24th of the aces would have been dealt out.
Second, computers and the Internet have really changed the counting world. Today people can practice their card playing, both blackjack and video poker. And deals get burned out fast. In 1993 Stanford Wong sent his premium customers a notice that the Grand Casino in Biloxi had made a mistake on their Sic Bo felts and was paying 80–1 on a roll of 4 or 17. The actual odds are 72–1. This deal lasted almost a month after this mailed notice. Today, with the Internet, this deal wouldn’t last a week.
Third, I think there are some state and federal statutes about discriminating against passengers on riverboats. Not just racial, I’m talking about statutes going back 100+ years. This ought to include gamblers on boats as well.
Finally, it is not really hard to count a big shoe. The problem is that a single-deck will swing somewhat positive or negative after the removal of a single card. For a six-deck shoe generally two decks have to be dealt out before you will have a single advantageous play (if any).
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November 7, 2009, 7:45 pmreadery says:
The common law prohibits gambling. By legalizing gambling, Indiana partially abrogated the common law. Any rights gambling businesses may have and exist only by virtue of the statute. Thus it’s perfectly reasonable for the courts to look to the gambling statute, and not the common law, to determine the rights gambling business have.
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November 7, 2009, 11:09 pmreadery says:
After, the Nevada Supreme Court held some time ago that the legislature made gambling legal didn’t make gambling debts enforcable in court. Nevada took the position that the common law’s basic anti-gambling stance held unless specifically abrogated by he legislature. Indiana is simply following this long-standing position.
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November 7, 2009, 11:12 pmPintler says:
@neurodoc:
You are absolutely correct that the odds on the next flip of the coin aren’t affected by a prior run, but if the previous ten flips have by chance had many heads, say, the odds are that the next ten will have fewer heads. The term is ‘regression to the mean’.
This can lead to interesting results — some recent book (‘Predictably Irrational’??) discusses a study of pilot instructors. When a student makes a worse than average landing, the instructor can either respond positively (helpful hints, encouragement, etc) or negatively (derision, threats of washing out, etc). Some instructors adopted one strategy, some the other. Both feelings were reinforced because if the student had just made a much worse than normal landing, the next landing was likely to be better than the previous, regardless of what the instructor did.
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November 8, 2009, 10:01 amDavid Schwartz says:
I disagree. Prohibiting card counting changes the bets a player may make by prohibiting particular betting and playing patterns. Casinos don’t read people’s minds to determine that they’re counting cards, they infer it from the bets they make.
In fact, the reason rules say nothing about what decision rules players may use is because they don’t restrict them. A rule need not specifically state that a player may choose to double down using any set of rules he or she pleases, all it need do is not prohibit particular rules or strategies.
The casinos, by prohibiting a particular playing strategy, are effectively adding a rule that prohibits that strategy.
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November 8, 2009, 10:11 amnormal human being says:
Whats the big deal, they have the right to add more decks, shuffle up each hand, change the limits at the table, why do they need the right to ban a card counter when they can effectively (just with the shuffle up right) ruin their odds? I always thought this was stupid anyway. The casino should advertise when card counters show up. Even if they lost $1 mil to a card counter, the PR from it would make all the 99% of the people who think they can count, but can’t, go to the casino and lose tons.
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November 8, 2009, 10:24 amLloyd says:
Exactly right. Indeed that reflects the history. When card counting began in the 1950s the casinos were initially welcoming. Thinking that this was another stupid losing strategy. Then they became frightened that this would bankrupt them in the same way a single cheating dealer could. Eventually most learned that there were very few really disciplined and skilled counters with large enough bankrolls and even they had only at best a 2% advantage. Even the best card counters will have horrendous runs and hemorrhage tens of thousands of dollars in a day. On the other hand the average player operates at a 6% disadvantage. And the numbers of those players have multiplied many times over by knowledge that blackjack is a beatable game.
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November 8, 2009, 11:23 amlucia says:
I don’t know the rules of black jack, so I was wondering if this proof is sufficient to show that multi-deck shoes are worse for players. I looked up and saw that when the player gets a blackjack, they are supposed to win 3:2 odds. I assume the player only loses their wager after 2 cards if the dealer gets a black jack and the player does not.
Could you tell me what happens if both the dealer and the player draw a blackjack? Does the player still get the payout? Or does the player just keep his money but lose nothing? Or does the player still lose his money.
I know that if neither gets the blackjack, the round continues. I just want to be clear on the math related to the winning status after only 2 cards are dealt. However, I can’t unless I know the rules!
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November 8, 2009, 12:47 pmLloyd says:
There have been a number of comments on the advantage to the player of fewer versus more decks (or in the extreme continuous shuffling) being employed by the casino. It is true that the player gets an advantage in terms of the number of blackjacks that will be dealt and the assymetry in payoffs for blackjack, but this is trivial in magnitude.
The big payoff for the card counter in facing fewer decks comes as a result of: (1) the greater variations in the “true count”, that is in the density of high and low cards remaining in the cards to be played; (2) the effect of this on the player’s expected probability of winning the hand; and (3) the player’s ability to ratchet up his bets.
For example, whether using 1 deck or 8 decks, if one could magically remove all the fives from the deck the player’s expected return would move from about –1/2% to +3%. The likelihood of all the fives coming out in the first hand of a deal with one deck is enormously greater than the likelihood that they will come out in the first eight hands dealt from an eight deck shoe. This is illustrative of the fact that the number of truly favorable betting opportunities becomes trivially few as the number of decks increase.
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November 8, 2009, 1:10 pmreadery says:
The card counter’s reduced advantage with more decks is an example of the Central Limit Theorem. The card counter only has an advantage when the the deck is rich in advantageous cards, 10 though Ace. But the Central Limit Theorem says that the larger the sample size, the less the variation will be — something close to the mean occurs more often, and a situation far from the mean occurs less and less often. Increasing the number of decks in the shoe is simply a way of increasing the sample size. It’s a straightforward example of the Central Limit Theorem in action. The more decks there are in the shoe, the more often the percentage of 10 through ace cards in the deck at any given time will be close to the mean percentage where card counting is useless, and the less often the deck will be rich enough in 10 through ace cards for a card counter to have an advantage. The card counter’s expected advantage is therefore considerably less.
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November 8, 2009, 1:33 pmHyman Rosen says:
Pintler, you are incorrect. There is no regression to the mean when outcomes are based on independent trials, which is the case in a sequence of fair coin flips. Regardless of previous outcomes, the next coin toss still has exactly the same chance of landing heads as tails.
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November 8, 2009, 5:58 pmLloyd says:
readery says:
The card counter’s reduced advantage with more decks is an example of the Central Limit Theorem.
Not quite correct I think. The central limit theorem speaks to the approaching normality of the distribution of a sample mean as sample size increases. It is the much simpler and accessible law of large numbers that speaks to the smaller variance of a sample mean as sample size increases.
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November 8, 2009, 7:38 pmreadery says:
Lloyd, indeed you’re right, I was speaking somewhat loosely. In addition, the weak law of large numbers is sufficient for the result, the strong one is not required.
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November 8, 2009, 8:57 pmDavid Schwartz says:
This is incorrect. While it’s true that the next coin toss still has exactly the same chance of landing heads as tails, they will not have an equal affect on the regression to the mean. If the past has been predominantly heads, one more head will not take us as much further from the mean as one more tail will take us closer to it.
For example, suppose we have flipped 100 coins, and by luck we’ve had 80 heads. There are several different ways to measure how exceptional this is, but by any measure, if we flip 100 more coins, and we have, say, 50 more heads, it will be a lot less exceptional. Even with independent trials, outcomes still regress towards the mean.
In other words, given two slot players, one having incredible good luck and one having incredible bad luck, it’s a safe bet that the one having incredibly good luck will see worse luck and the one having incredibly bad luck will have better luck. The more exceptional the luck so far, the more likely it is that it will seem less exceptional with more trials. (Think about it if this is not obvious to you.)
Or, as an example of reductio ad absurdum, with a single flip of a fair coin, whatever outcome you get is exceptional — all one and none the other. With 50 flips, all one and none the other is much less likely.
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November 8, 2009, 10:22 pmsilverpie says:
lucia: Under standard rules, if both dealer and player get blackjack, the result is a push (no one wins or loses).
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November 9, 2009, 8:17 amSoronel Haetir says:
If you actually had the case of a coin flip with 80% after 100 flips or 100% after 50 flips I would be questioning the fairness of either the coin or the flip procedure.
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November 9, 2009, 9:40 amDavid Schwartz says:
SH: Of course. My point was simply to illustrate the central limit theorem. To put it in simple terms, if the results so far have been statistically unlikely, the most likely outcome of adding more results is to make them less unusual. This does not require any “memory”, it’s simply a less-than-obvious consequence of the tautology that likely outcomes are more likely.
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November 9, 2009, 10:32 amepeeist says:
Whether or not casino gambling should be so highly regulated, it is, creating an oligopoly — you can’t just go and decide to open up a competing casino in the way you can with most business (nor, under U.S. law, can you just decide to start offering casino services over the Internet...). Under those circumstances I think it fair and appropriate for the normal right of exclusion to be limited, it’s part of the “price” of doing business in a highly-regulated environment.
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November 9, 2009, 11:04 amzuch says:
neurodoc:
There may be a bit of a fallacy implicit here, the same one that imagines that if a coin lands tails a number of times in a row, it is more likely that it will come up heads the next time than when a coin hasn’t land too many times heads or tails in a row.
No. I’m quite familiar with the Gambler’s Fallacy. Note I said “usually”. If they suspect you of counting, they won’t do this; in fact probably the opposite. But if you’re not counting, the house has the edge, so the law of large numbers says that your overall winnings (or losings) will most likely approximate the expected mean (which is a loss for you), given enough trials. Particularly if you’re given both alcohol and other inducements to make you feel “good” and “lucky” (read: “foolish” and/or “less competent”).
Cheers,
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November 9, 2009, 1:07 pmDan Weber says:
I initially rejected Pintler’s premise, but now I realize what he is saying:
“If you get 8 heads out of 10 flips, then on your next 10 flips, you are very likely to get less than 8 heads.” The more amazing your first 10 flips, the harder it will be for your second 10 flips to match that.
Exceptionally lucky or exceptionally unlucky performances are unlikely to repeat.
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November 9, 2009, 1:40 pmlucia says:
Thanks silver pie! I asked at my blog too.
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November 9, 2009, 4:08 pm