The Casino Movie...
  • Okay I just saw this very old but very good movie and felt like asking a few questions that maybe someone here could answer. I remember this one scene where one of the pit bosses gets fired because this guy hit three big jackpots and big boss (can't remember his name for some reason) got all pissed off and fired him because he accused him of being in on a scam.

    He said that the odds were a billion to one or something like that. I was wondering though is it really impossable for it to happen? I meen the house can't always win and it seems more then likely to me that the guy that came in just got extremely lucky and wasn't pulling any form of scam at all.

    Anyone have any idea how this goes?
  • in a single-deck game, a player has two draw two cards, an A or 10, to get a BJ. He has a 4/52 chance of drawing an A, then a 16/51 chance of drawing the matching 10. He will get a BJ about 2.4% of the hands played, based on that. What is the probability of gettijng 3 in a row? .024 * .024 * .024 = .00001 or say once every 10,000 hands. I've certainly gotten 3 BJs in a row more than once, and two in a row quite a few times...
  • I agree with you're answer, but you stumbled upon it with two errors:

    first off 0.24^3 = .00001 -- I agree, but that is 1/100,000 not 1/10,000
    .1 = 1/10
    .01 = 1/100
    .001 = 1/1000
    .0001 = 1/10,000
    .00001 = 1/100,000

    Second, a ten and then an ace is just as good as ace and then a ten. So, the actual odds of getting dealt a blackjack with a single deck are:

    (4/52 * 16/51 ) + (16/52 * 4/51) = 0.04826546

    and the chance for 3 consecutive blackjacks:

    0.048 * 0.048 * 0.048 = 0.000112437 or about 1 in 10,000

    I hope this clears up any confusion.
  • Good math.

    I managed to break my nose two weeks ago fishing (another story). Just had surgery to fix it back to normal. Been on enough drugs that it is amazing I got the number of cards in the deck right... :)
  • In a single deck game the configuration space is not 52 cards. With 60%
    pen it is more like 32 cards and this fact alone tells us that we can never
    actually determine the exact mix of possibilities, given the shuffle and
    slight variances in the cut card. It appears to me that "trials" is the only
    valid approach to the problem stated unless we figure perfect pen and
    card distribution....an unrealistic approach at best.

    If we played with all possibilities(52) then I agree with Maverickaced. I
    suspect that stats on BJ's, etc are a result of sims/trials.
  • Perhaps, but even if you deal just two cards from the deck, the probability of drawing an Ace is still 4/52 off the top of the deck. Each and every card in the deck has an equal probability of being locked out of play behind the cut card. Obviously if you put the cut card in front of 20 cards, you will never get into the n/20 and below probabilities, but for N/21 and above, it should work out just fine...

    By the way, in my poor math above, I believe that I did the calculation correctly using my handly software calculator, but when I then went back and re-constructed how I came up with the 1/10000 number, my mind was numbed-up enough that the explanation was fractured, about as badly as my nose... :)
  • SSR-If I ask you to roll a four sided die the possibilities are always 1/6.
    Now suppose I erase one of the six, unknown to you. You can say nothing
    regarding probabilities because of elementary reasons. In static/simple
    probability calculations you must know the exact configuration space,
    the exact number of possibilities.

    Your example 4/52 off the top is not related to the problem posed (BJ's).

    Further, we know that the number of BJ's differ based on the decks that
    are in play. However, the number relationship (ace/10's is the same) and
    the results should not be different based on your example, but they are..

    The effect of card removal, volume of cards and position of the cut card
    are the likely factors.
  • My point was simply that 4/52 is a reasonable probability for pulling an Ace from a newly-shuffled deck. Doesn't matter where the cut card is placed, so long as it is not placed in front of the first card. :)

    Obviously, for three consecutive blackjacks, the numbers I gave were just an approximation. Because the second BJ probability is not the same as the first, unless there is a shuffle after each round. But for answering the question, the 1:10000 is probably within 1% of what a big sim would produce, which is close enough in reality.
  • If you roll a four sided die, woldn't the chance of rolling any number 1/4? not 1/6 - maybe I misunderstand.
  • Four sides plus top and bottom...you could make a case for six sides
    depending on your reference point and the position of the die, static
    or in motion.
  • Ray - I have really never heard anything like you said before. I would like to understand your reasoning. I was wondering if you could site some literature accepted by the science community. I'm a graduate level engineering student with years of expierence with Calculus, Differential equations both ordinary and partial, and probabilty of statistics with specific application to process control. My point is don't be afraid to site a book most would consider higher level. But, at the same time don't give me some book with obscure and very HARDCORE mathematics.

    Thanks,
    mav
  • ray, you are overlooking an important detail on card removal effect...

    in a single deck, after I have received one ace, my probability of getting another is 3/51. In a 6D shoe, it is 23/311.

    3/52 = .0577
    23/311 = .074

    The reason is that there are more cards of all types, and removing one has a lesser overall effect as the above shows... The denominator shrinks more slowly with more decks, as does the numerator.
  • Here is what the Wizard has to say about the BJ question. Note that
    his assumptions are not very clear, no shuffle and I'm not sure if he
    considers the cut card at all.

    As I see it, you will get a BJ about 5% of the time and this is about
    right with other results that I've seen.

    If he uses the same assumptions (whatever they are), three in a row
    should occur about every 22000 or so....From these results, I can't
    determine if my argument has validity or not.

    SSR- Yes I agree with you, card removal is the big difference while pen
    and the effect on card vol is very small.

    Mav-My background is physics and engineering in the computer science
    field ( circuits, OS's and heavy process control (computer intergrated
    mfg(CIM) and robotics. I would say we could share a few experiences
    and company names.....................


    WIZARD************************************************

    What are the odds of getting 3 blackjacks in a row with 1 deck 4 players and one dealer. - Joe P from Parma Heights, USA

    I'm going to assume there is never a shuffle between hands. The three other players don't matter. The answer would be 23*(16/52)*(4/51)*(15/50)*(3/49)*(14/48)*(2/47)= 0.00004401, or about 1 in 22722. If there were a shuffle between hands the probability would increase substantially. Mar. 6, 2002

    Under the card game 21(A.K.A. Blackjack), you win if your two cards are an ace and either a 10, jack, queen, or king. What is the probability that you draw such a 21?

    It depends on the number of decks. If the number of decks is n then the probability is 2*pr(ace)*pr(10) = 2*(4/13)*(4*n/(52*n-1)), which is conveniently about 1 in 21. Here is the exact answer for various numbers of decks.
    1
    0.048265
    2
    0.047797
    3
    0.047643
    4
    0.047566
    5
    0.047520
    6
    0.047489
    7
    0.047468
    8
    0.047451 Mar. 6, 2002
  • glddraco said:
    He said that the odds were a billion to one or something like that. I was wondering though is it really impossable for it to happen? I meen the house can't always win and it seems more then likely to me that the guy that came in just got extremely lucky and wasn't pulling any form of scam at all. Anyone have any idea how this goes?


    That scene revolved around slot machine jackpots being won in one bank of slot machines. Three consecutive BJs to one player has happened right in front of me. I don't know if it was a scam but as far as the movie 'Casino' is concerned, it certainly seemed like a scam. The floorman which happened to be a relative of some elected official made that case that it's a casino and people have to win sometimes.

    In my opinion this would never happen in a successful casino. They and the gaming commissions can say all they want about it being random but why does it seem looser machines tend to be around larger denomination areas and usually on the outside of a very busy aisle? I think they are set up in a way to maximize profit for the casino. If you ask me, anyone who plays slots is giving their money away.
  • I'm a dealer and have dealt three consecutive blackjacks to one player. I've also seen dealers deal three to themselves.
  • last week i'm playing head to head and the dealer dealt himself 3 bj's in a row,i don't know what the odds are but it sure happened.
    Prog
  • Didn't see any three-in-a-rows recently, but I saw three two-in-a-rows (dealer 21) over two consecutive sessions... That was more than enough since the count was up, my bet was up, it went into the dealer's tray. :)
  • TylerDurden said:

    In my opinion this would never happen in a successful casino. They and the gaming commissions can say all they want about it being random but
    why does it seem looser machines tend to be around larger denomination areas and usually on the outside of a very busy aisle? I think they are set up in a way to maximize profit for the casino. If you ask me, anyone who plays slots is giving their money away.


    Actually, as far as I know, the law in Nevada makes two demands:
    1) That gaming machines have a built in house advantage of less than 25% (which is still a lot, especially when this figure includes the jackpots)
    2) That gaming machines that use representations of real objects (i.e., cards and dice) will ensure that they behave like their physical counterparts (i.e., random). Thus, that your chances of being dealt a blackjack in video BJ or a royal flush in video poker are the same as if someone was using the cards. The machine is not allowed to tweak the numbers.

    So as to your complaint about slots, I agree that they are a sucker's game, but they are in accordance with the law. As for video BJ, video poker, I doubt they are crooked. VP full-pay machies are rare and require huge bankroll and lots of concentration. Video BJ has crappy rules all around the world (e.g., 2:1 blackjack).
    In Atlantic City, however, the second rule for machines does not apply, so the machines can further screw you up (e.g., give you less blackjacks than you should), as long as they are still under 25% HA.

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