Actually slightly lower, 15/49. (The difference is like 0.15%.)
(I mainly mention this because I used to think my odds of drawing to a flush in poker were 1/4 per draw. It took me embarassingly long to realise that I needed to remove the cards I could see from the deck.)
It was at this point that the guy at the end took a hit when he shouldn’t have and I almost jumped over the table and punched him.
Public service announcement – if you’re going to gamble in a casino where other people depend on your play (like in Blacjack), spend an hour or two beforehand learning how to play properly, or ask the others at the table for advice so you don’t screw them over. We gamblers thank you. The more you know...
The actions of other players don't affect you statistically. Assuming the deck is fairly shuffled, it makes no difference to your expectation whether you get dealt the 10th or 11th card.
I would have turned the 5 card too. Why? Because it says to test the truth of the proposition. So it's saying all bets are off, whatever I told you may or may not be true. Only what you see (the table with the 4 cards) is real.
If you still assume that each of which has a number on one side and a colored patch on the other side holds, then no need to check 5. But if you focus on testing the final proposition, I'm not sure anymore of what I should assume...
This is one of the major life-lessons I've taken away from card games, summarized by Captain Jean Luc Picard: "“It is possible to commit no mistakes and still lose. That is not a weakness; that is life.”
You can make the best choices and chance still happens. It doesn't mean what you did was the wrong choice. You do what you can to increase your chances but the universe doesn't give a crap. It's not malicious or benevolent; it just is. The deck is just 52 apathetic cards.
However, I would actually say life is more like Magic: the Gathering (or the many clones or similar games) where some time-traveling quantum supercomputer could probably give you a guess, but don't hold your breath for that to come around.
At least in poker, the "eye in the sky" that can see all the cards in people's hands can predict winning percentages. Even if you don't know your opponents hands, based on what you know, you can calculate some good odds.
But life isn't that nice. We don't know the odds or even a wild ass guess at the odds for applying for that job or asking that person out.
Because then I have no advantage over the casino. With a hand shuffled deck, you get clumps of high cards together from the last set of hands, which gives an advantage to the player. If you can ride out waiting for the clumps, you can beat the house.
I hope you can at least understand how it would be more broken by actually having different cards, because again, even after shuffling the events that took place here are still possible. No amount of shuffling or not shuffling can change how many face cards in a deck.
With regard to it being "certain enough", consider whether you would have done the same thing as these people. I can tell you that had I sat at that table, I would have not continued betting higher and higher with the possibility that the next deck is not in my favor and thus possibly losing everything. It of course looks certain in retrospect knowing the whole story of how they were actually unshuffled -- but when you are actually at the table, without this knowledge -- it is again just a chance. You have no idea how many decks come from what company or anything thats going on to result in this. For all you know it might have just been two decks that had the same order due to some weird malfunction. I am sure in the history of gambling lots of people have thought they've seen a pattern recur, bet a lot on it, and LOST -- again, to the favor of the casino.
In other words, consider it from a game theory perspective -- the casino's "long term" winnings absolutely rely on this kind of behavior from patrons. If patrons were to think to themselves "uh oh, something is fishy and this might be unfair, better stop betting" every time they thought they had spotted a pattern or had a system, then the casino would lose tons of money, since they are 99.99% of the time wrong. Casino's winnings fundamentally rely on greediness. That's the basic point I'm trying to make: you can't have it both ways, you can either have greedy patrons who almost always lose everything because of it, or weird bizarro-world patrons that are looking out for the casino.
How did you get there? GP is talking about being dealt it, I think you've calculated the chance of it occurring in a round or something?
Wikipedia has GP's at 649739, so yeah 'almost' a million, roughly speaking. 4 / ((52 nCr 5) - (4 nCr 1)). (Four suits, one way to do it in each suit, deck of 52, five card hand.)
The analogy that came to my mind was that if you take a deck of playing cards and lay all the cards out on a table, face down, the table weighs a certain amount (the table's weight, plus weight of the cards). Then, if you flip over five cards at random, you have created enough new information to make a poker hand. But, the weight of the table did not change when you created that information.
You wouldn't get to see the shuffle though, as most casinos will use an auto shuffler that shuffles one shoe while the other is in play.
6-8 decks would be hard to figure out until maybe halfway through. Could do some analysis on the probability of a face card though that would really pay off towards the end of the shoe.
Incidentally, if I wanted to put my math skills to work in a casino, I would play poker. This game is one where the odds have not been stacked against me and a little math drastically alters my expected values.
reply