It clicked with me when somebody explained it with playing cards but they used the entire deck.
Spread out an entire deck of 52 cards, face down, on a table. Guess which card is the ace of spades. Monty then flips over to reveal 50 of the remaining 51 cards (none of which are the ace of spades) and you are given a choice to stick with your original guess or switch to the other face-down card.
Even better, do this with a card that has a higher likelihood of being chosen by the spectator—the ace of spades, for instance—and you'll see the trick work far more frequently than simple probability would suggest.
An illuminating example uses a deck of cards. You're trying to get the ace of spades. You pick a card. I don't know anything but I turn over 50 of the 51 remaining cards and they're not the ace of spades. Do you want to switch your pick to the alternative unknown card?
>To me, we can take the Ace of Hearts and the Ace of Spades, shuffle them, and deal them out, face down, one each to Bob and Sally. Bob can go a light year away. Sally then looks at her card and knows right away, nothing faster than the speed of light needed, what Bob's card is.
I don't get it. Alice knows it right away only if she knows the rules of the game, electricity in her brain doesn't need to move a light year away. Though, if she's braindamaged, it can take longer than a light year for her to figure that out or may never happen at all.
At that point, they should just use a continuous shuffle machine.
I think there is a nice psychological effect of a deck that can truly get “hot”, where the odds actually do temporarily turn towards the players favor. The life is sucked out the game if things are truly random on every deal.
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.
There's an obvious intuition that the author seems to be missing with the 'two aces' paradox.
If you have a hand with two aces, you have two chances of getting the "Ace of Spades." Having a hand with two aces doesn't make it any more likely to have "an ace" than having a hand with one ace does.
Excluding the physical elements, it still seems a poor, possibly actively misleading (or should I say misdirecting), analogy.
The better way to understand it is to use only two cards, one face up one face down, if you give one to each person randomly, how can you magically match the other person? By flipping the card, because for every down you have, the other person has one up.
I used to walk around with a queen of hearts in my pocket and, as a party trick, ask a female friend or acquaintance to "name a card, any card, just not ace of spades, everybody picks an ace for some reason". If I got it right, I'd produce the card, otherwise I'd blurt out some "character reading" bs based on what card they picked as an "out".
I learned the trick from a Derren Brown book in which he describes a much more elaborate version. You would be amazed how well it worked. It's just one of those things: A number between 1 and 5? 3. 1 and 10? 7. 1 and 20? 17. And the famous "red hammer" trick. Humans are lousy PRGs.
Of course I could hide several cards in several pockets to increase my chances but that would be "cheating".
There is a probability, it can be described based on what cards have already been dealt. It does not change whether that specific card is an ace or not.
"You, my friend, are about to witness the best card trick there is. Here, take this ordinary deck of cards, and draw a hand of five cards from it. Choose them deliberately or randomly, whichever you prefer -- but do not show them to me! Show them instead to my lovely assistant, who will now give me four of them, one at a time: the 7 of Spades, then the Queen of Hearts, the 8 of Clubs, the 3 of Diamonds. There is one card left in your hand, known only to you and my assistant. And the hidden card, my friend, is the King of Spades."
The cards are pre-shuffled at the manufacturer. It's a smart move since the casinos don't have to spend time dealing with shuffling cards manually (and losing time) or automatically (and investing in expensive machines).
The whole situation came up because the playing card manufacturer forgot to shuffle the cards before packaging. So all the cards came in the same pattern out of the box, which I'm assuming is determined by how they were cut from the sheet or whatever is done. There's no mention that they came out in suit/count order (like the packs most people normally buy in stores).
The mini-baccarat game seems to take 6-8 packs and combine them into a large shoe. The pattern would not have been obvious after the first 52 cards but when the next 52 showed up in the same order, that's when the betting started going nuts.
They mitigate that by discarding without looking several of the cards, so it's not a completely even distribution of outcomes. E.g., it's possible that 4 of the '6's won't come out at all that time through the deck.
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