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I think you have misunderstood the point Alan was making.
You say that by random leaping you are twice as likely to receive the second sequence, So if I have 100 decks of cards and we choose a deck, and we will get the top card, are you saying we are twice as likely to receive the same value?
Nothing to do with random leaping. You are twice as likely to get the second set because it contained one less binary element!If you had said 1212112112, which contains 10 elements, it would have had exactly the same probability as 1111111111, which also contains 10 elements, i.e. 1 in 2^10. That said, even if you made 1024 trials of 10 coin tosses, there is no certainty that either sequence would turn up once or once only, you'd just be a bit surprised if it didn't. And you have no prior knowledge of where in that 1024 trials it would turn up, so looking at random or sequentially would have exactly the same probability of finding it. Here's a real-world example of the "significant number delusion". Many years ago I rebuilt a laboratory rig that originally included an analog voltmeter. For about 10 years, people had recorded its readings to 3 figures, e.g. 38.6V. I replaced it with a digital voltmeter and printer that displayed 5 figures, up to 99.999 volts. My boss complained that the rig wasn't working properly because it often reported "repeated digits" like 16.885, 17.793, 22.541 and so forth. It was working of course perfectly: if you take 5 random digits, the probability that the second matches the first is obviously 1/10, and that the third matches the second, 1/10.... i.e. there is a 40% probability that any 5 digit random number (such as a digital voltmeter reading) will include a repeated digit.There is a similar problem with "significant sequences" and "significant cards". It is noticeable that throughout these discussions you have concentrated on the probability of finding aces whereas form the point iof view of the cards themselves, and indeed of the dealer (who can't see the faces) an ace is no more significant than a 6. So whilst 123 or AAA may mean something to you, it means nothing to the shuffled pack. Furthermore, you are not signifcant to the dealer who is also supplying cards to Alf, Bill and Charlie
What I think you are trying to say by "P(a)/X(A)" is that the probability of a named card N being first in the first deal is 1/52.It is clear that the probability of N being the first card in the second deal is also 1/52.So the probability of N being the first card in both deals is (1/52)2But if you don't name the card in advance, the first card in the first deal defines a value n, and the probability of n being the first card in the second deal is 1/52. yesThus if I want the ace of spades to be the first card, the probability of getting AS in any one deal is 1/52 and the probability of getting it in two consecutive deals is (1/52)2. However suppose I get 10C onhe first deal, and manage to win the hand with it. 10C has now become a "special" card and the chance of getting "my special card" on the next deal is 1/52 yesNow I see your delusion. You think that by choosing "nonconsecutive" deals you can increase the probability because 1/52 + 1/52 = 2/52. There's the error. The probability of getting one AS in two deals is indeed 2/52 because the desired result is "a OR b". But the probability of getting two AS in two deals is 1/522 because the desired result is "a AND b". George Boole is credited with laying the mathematical foundations for machine logic, which starts with the realisation that "+" describes "or" relations and "x" describes "and" relations.no
I'm sorry you disagree with Boolean algebra. It's the basis for all computer hardware, and seems to work for everyone else. Beyond that, I have no idea what you are talking about.
Maybe you will understand this, at any specific point in time whilst playing live texas holdem poker there is only ever 1 of 52 variants aligned to your seat. On the internet playing internet texas holdem poker, there is 1,000,000 unknown variants aligned to your seat at any specific time.
OK, I understand where 52 variants comes from in live game = 52 different card faces.I don't understand where 1,000,000 comes from in Internet game. If you only play with one deck at a time in any one game then it's the same as live. For it to be different you would need to play with a single deck of 1,000,000 cards each with a different face value. So no I don't understand.
Quote from: Colin2B on 05/09/2015 09:35:53OK, I understand where 52 variants comes from in live game = 52 different card faces.I don't understand where 1,000,000 comes from in Internet game. If you only play with one deck at a time in any one game then it's the same as live. For it to be different you would need to play with a single deck of 1,000,000 cards each with a different face value. So no I don't understand.Yes you do understand, because in bold on the internet that is exactly what you do by the alignment of seat to card order,
Quote from: Thebox on 05/09/2015 10:59:31Quote from: Colin2B on 05/09/2015 09:35:53OK, I understand where 52 variants comes from in live game = 52 different card faces.I don't understand where 1,000,000 comes from in Internet game. If you only play with one deck at a time in any one game then it's the same as live. For it to be different you would need to play with a single deck of 1,000,000 cards each with a different face value. So no I don't understand.Yes you do understand, because in bold on the internet that is exactly what you do by the alignment of seat to card order,No I don't understand.What do you mean by "the alignment of seat to card order"How does this differ from live game.You are surely not suggesting that you play with a deck of 1,000,000 cards?And please, describe this in words don't try to use maths.
Well actually if there is 1,000,000 top cards there is 52,000,000 cards in total, If I asked you to pick any card from any position of any deck, I have asked you to choose a card of 52,000,000 cards.
If I tell you to choose a card from the top cards, you are choosing from 1,000,000 cards effectively playing a 1,000,000 card dec
But there are only 52 face values, so the probability of getting any given card is 1/52
I will put it this way, you are dealt a single hand using a single deck, or you pick a hand from 1,000,000 already made hands.Do you think this sounds like the same game?
Quote from: Thebox on 06/09/2015 08:16:36I will put it this way, you are dealt a single hand using a single deck, or you pick a hand from 1,000,000 already made hands.Do you think this sounds like the same game?Let me ask some questions so I can understand.1) In a live game the dealer uses a single deck which he shuffles after each hand.2) If instead he preshuffles 100 decks which he then lays out on the table and asks the first player to choose a deck at random. Is this the same probability as 1)? no3) if the dealer does as 1), but instead of dealing off the top of the deck he deals from the bottom has that affected the game?yesAgain words only please, no maths.