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Here is the English translation:
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With 6 decks, you can play about 40 times. Let's assume we start recording from the first game until the last one.
Excluding ties, for example, with 40 games, there will be 40 outcomes (wins or losses) in a row. How many permutations and combinations can this long string of results produce? This definitely requires the help of a computer, as it exceeds our calculation capabilities.
If we encounter "10 consecutive banker wins" from the first game, then each person would force themselves to believe that there is a higher chance of "player" winning in the subsequent games, or that it is highly unlikely for "banker" to win again in the 11th game.
Now, place the "10 consecutive banker wins" into the "astronomical permutations and combinations of 40 games," with the outcomes of the remaining 30 games unknown. With 10 + 30 games, how many combinations are possible? It's also an astronomical number that can only be calculated by a computer.
Starting with "10 consecutive banker wins" may seem daunting, but if you put it into one of the thousands of billions of combinations, what's there to be surprised about?
The combination numbers for baccarat with six and eight decks are astronomical. Using 6 decks, the number of combinations for "banker" and "player" is close to 8,000 trillion. And please note, this 8,000 trillion is just the "starting with 6 decks, one shoe of 312 cards, possible number of combinations" - we often run out of cards in the shoe and have to replace it with a new set of 6 decks, and then this 8,000 trillion comes out to cause trouble again. What trend is there?
"10 consecutive banker wins" is commonly referred to as a rare occurrence, as it has a probability of one in a thousand (1/1024) according to probability theory, and it seems highly unlikely to occur frequently.
However, if you place this one-in-a-thousand probability into the range of 8,000 trillion, this probability becomes meaningless!
Suppose you encounter "10 consecutive banker wins" (everyone knows this is not uncommon, just walk around the casino and you'll see). In terms of probability, it's 1/1024, which seems incredible at first glance, and is often considered a "rare occurrence." At this point, we usually think: it would take 1024 occurrences for this to happen once, so encountering it today is simply a miracle.
So, if "banker" appears again on the 11th game, that would be strange! Because the probability of "11 consecutive banker wins" becomes 1/2048, which is even more absurd. How could such a miraculous thing happen? The probability of 2048 occurrences for this is impossible for me to encounter. So many people tend to bet on "player" on the 11th game (even if there are a few who bet on "banker," they wouldn't dare to bet big).
Those who dared to bet on "banker" on the 11th game clearly retreated. Then, when the game started, it was indeed "player"! Everyone cheers, and at this point, we often think: indeed, the probability of 1/2048 is even less likely than 1/1024 to occur?
But, can anyone explain the difference between "11 consecutive banker wins" and "10 banker wins, 1 player win"?
That's right, the probability of "11 consecutive banker wins" is 1/2048, but isn't the probability of "10 banker wins, 1 player win" also 1/2048? In permutations and combinations, both of these arrangements are included in the 2048 combinations, with the only difference being in the 11th game, either banker or player wins.
Therefore, the 11th game is still very fair, with each having a 50% chance of winning. In other words, the probabilities of "11 consecutive banker wins" and "10 banker wins, 1 player win" are the same. |
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Post time 11-3-2024 09:23:56