Comments by "EebstertheGreat" (@EebstertheGreat) on "Wendover Productions"
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@taoliu3949 "With a CSM, that would mean that the face cards would never come out (there is no 'top' of the deck/shoe)."
No it doesn't. If low cards get put higher up than high cards on average, you will still get some high cards and some low cards, just more high than low.
Your claim that people are more likely to bust if the deck is full of higher cards is false. If you start out getting dealt J9, you will stand. If you start getting dealt 37, you will hit. If you then get a 5, you will hit again. If you then get a 7, you bust. The probability of busting on a given hit is higher if the deck is full of high cards. The overall probability is higher if it is full of low cards.
But for like the tenth time, you continue to ignore the fundamental problem with your analysis: this analysis has already been done. And even when a player knows that the remaining cards in the deck are low, they still suffer a significant disadvantage, more than normal. How do you account for this?
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OK, I've come up with another way of explaining this. We both have conflicting claims, so we will perform an experiment to distinguish between them.
Your claim: When low cards are more likely to get dealt in a game of blackjack, the player has better odds than when high cards are more likely to be dealt.
My claim: the opposite.
To test our claims, we need to actually set up situations where more low cards or more high cards are dealt measure the winnings in each situation. After many trials, if the low-card group wins more, then your claim is supported, and if the high-card group wins more, then my claim is supported.
It turns out that this experiment has already been performed many, many times. If a shoe has more low cards than high cards remaining, then they are more likely to be dealt, just like if you were playing with a rigged shuffler. This happens precisely when the count is low. ALternatively, if the shoe has more high cards than low cards (i.e. when the count is high), then high cards are more likely to be dealt. So we compare the winnings in these two cases.
And what do you know, players win more when the count is high than when the count is low. That's why they bet more on high counts. That's the whole point of the system. From this we can conclude that when low cards are more likely to be dealt in a game of blackjack, the player has worse odds as a result.
Note that it doesn't matter why low cards show up more often, just that they do. This could be because there are more low cards remaining in a conventional shoe, or it could be because a continuous shuffling machine has been rigged. Either way, the result is the same.
What about this explanation do you disagree with?
(And incidentally, it is not true that cards just dealt are equally likely to come up next in order. For one thing, dealers do not usually put cards in after every deal but after a few. More importantly, most machines are actually not very effective at randomizing the deck, and in particular, cards just put in do not tend to go to the top. Some machines with small buffers have actually been exploited by card counters in the past with more success than against a conventional shoe. Some machines do not suffer from this problem, but none are perfect. But none of this is relevant to the rest of the thread.)
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@neumo5005 There is more than one way to define multiplication by infinity. On the extended real line for instance, which is the union of the set of real numbers with ∞ and -∞, 0×∞, ∞×0, 0×(-∞), and -∞×0 are all left undefined. Similarly, 0/0, ∞/∞, (-∞)/∞, ∞/(-∞), and (-∞)/(-∞) are all undefined, as are ∞-∞, ∞+(-∞), (-∞)+∞, (-∞)-(-∞), 1^∞, (-1)^∞ and 0^0. This reflects the fact that these are all indeterminate forms in calculus. That is to say, if we have functions f and g with lim f(x) = ∞ and lim g(x) = 0, the product f(x)g(x) may have no limit, or it may have any limit. We get similar results on the projective real line, which has only a single point at "unsigned" infinity. A very different notion of infinite numbers comes from Georg Cantor, where they are used either to compare the size of infinite sets or to label infinite lists. In these cases, any number (even an infinite one) multiplied by zero equals zero, by definition.
The confusion comes from the fact that the idea of "zero times infinity" is underspecified. "Infinity" is too vague in this context. If we want to know how many elements are in an infinite product of empty sets, the answer is zero. It doesn't matter how many times you combine these empty sets, there will never be anything in any of them. But if we want to find the area of a shape by cutting it into infinitesimally thin slices, we are effectively calculating a sort of "zero times infinity" that clearly must have a positive result, since the shape has some positive area. And indeed it could have any area. Or you could try to calculate the area of the whole plane and get infinity. And there are even more pathological examples where you can't reach any answer at all. So it really depends on context.
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@EEVblog I assume you mean the most isolated major city. There are some extremely isolated cities in the world, such as Hanga Roa, Easter Island; Iqaluit, Nunavut; and Ittoqqortoormiit, Greenland. These blow Perth out of the water, but they are also comparatively tiny. Even among "major" cities (depending on the cutoff), there is a lot of competition from Yakutsk, Russia, which is extraordinarily isolated in Siberia. Note that most of these are also capital cities, like Perth.
As an honorable mention, Barrow, AK is inaccessible to virtually everyone by land, but it is another tiny city, it is not a capital, and it is not as inaccessible as Easter Island or Iqaluit.
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Driving in the USVI is a nightmare. The main issues of course are structural, with poor road conditions (narrow lanes, markings inadequate or completely absent, missing fences or grates allowing cattle and chickens to block traffic, etc.), but driving on the left is also a problem. Virtually all of the cars in the USVI are American imports with the steering wheel on the left, so you have to look all the way across the car to see oncoming traffic. And the majority of tourists are American, too. Imagine how many tourists get confused when, while driving in their own country in a car with the wheel on the left and no lane markings, they suddenly discover a van careening straight towards them in the same lane at a clearly unsafe speed?
And to be honest, the BVI basically have all the same problems, but at least then more tourists are British and there is a measure of consistency.
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Gary Baldi All right, think this through. Your position is that if flight cost ten times as much as its current rate, nobody would fly, because nobody is that rich. However, you are the one who pointed out that 45 years ago, flights did cost ten times as much as they do now. So, um, kinda shooting yourself in the foot there.
The airline industry is doing fine. New airlines continue to open and succeed. New planes continue to be made. Yes, a lot of individual airlines struggle; that's always been the case. But your reasoning would also seem to imply that, say, restaurants are going to go away because so many restaurants go out of business. If current prices are unsustainable, then prices will go up, or government subsidies will increase. But they aren't just going to scrap all their planes and close up shop. You have zero evidence for what you seem to consider a self-evident truth.
And you can't just say "something better will come along" than airplanes. Has something better than ships ever come along? We've had those for thousands of years, yet we keep making them. You can't even come up with a plausible replacement for planes, because there isn't one, let alone one in the foreseeable future.
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