There is a certain idea among gambling experts that comparing the “house advantage” in different games of chance helps you make informed decisions. The edge is a theoretical return for the casino, the complementary percentage for the theoretical return for the player. In other words, in any form of gambling there is only a 100% allocation of money. Gambling does not generate new wealth; all that gambling does is pool wealth between bettors and redistribute that wealth between bettors (and sometimes an intermediary).
In the 1:1 game of Blackjack, there are only 2 bettors in your game: you and the casino. The casino is willing to pay up to the full amount of your bet if you win. It is a game for the same amount of money, and that is what makes Blackjack so profitable for a casino. You risk less per round than, for example, in roulette or a slot machine game. But if you’ve read Blackjack tutorials, you should know by now that the house edge in Blackjack is lower than in other games, and therefore you have the best chance of winning in Blackjack.
In fact, the dealer has a better chance of coming out ahead because at a busy table the dealer plays several hands at once according to the most conservative rules. In other words, the casino takes less risk than the players in Blackjack per round, while at the same time multiplying its chances of winning.
Players make mistakes when they play Blackjack. Blackjack dealers don’t have to make tough decisions. In fact, since the dealer is always last to act, he often does not have to make any decisions at all. The players make most of the decisions in Blackjack. And yet Blackjack remains profitable for the casinos. The casinos profit from player mistakes.
The players make different types of mistakes. One of the most common mistakes is confusing the probability of winning with the theoretical return for the player. The probability of winning is limited to the next game round. The theoretical return to the player is an estimate of what all players in a game will receive in common during a given game (or an arbitrarily large number of rounds in the game).
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As a rule of thumb, the more rounds played for a given game, the more the actual results of that game will be on average close to the theoretical return for the player (or the house edge).
But what are the chances of drawing a natural blackjack on the next deal? What are the chances that the dealer will not beat you on the next deal? These are probabilities that can be calculated based on the cards remaining in the shoe, minus any cards that have already been played. These probabilities change as more cards are played, but they rarely, if ever, coincide with the theoretical return to the player.
The mistake players make is to assume that the house only has a 2.5% chance of winning the next round. The dealer’s chance of winning the next hand can be as high as 100% and as low as 0%. The house advantage is always irrelevant in relation to each and every hand played in any game of chance from Keno to slots to Blackjack to Baccarat.
When you play, it’s nice to know how much money the house is likely to hold over the next 30 days, but this will not help you predict how much you will win or lose in any of the next 10 game rounds.
Experienced players like to calculate probabilities, but probabilities do not predict the outcome of the next round. The Roulette wheel always has a chance of 1 in 37 or 1 in 38 to land on any number. The chance that the ball will land 100 times in a row on a number “7” remains 1 in 37 or 1 in 38, which never changes (and allows truly random spins, although the laws of physics dictate that spins will not be completely random).
On the other hand, what is the expected probability that a random spin of the Roulette wheel will result in “7” 100 times in a row? Here you multiply your individual spin probability (1/3x) by yourself the number of times in a row (in this case 100). The expected probability that the wheel will hit “7” 100 times in a row is 1.51296e-157 (a very, very small number). However, this small probability has no influence on the probability of the next spin.
This is the dichotomy of probability theory, where you are dealing with large sequences of independent events. The expected probability does not mean that you cannot or will not see the unlikely outcome. In this hypothetical example, we simply calculate how many possible outcomes there are and assume that the probability of achieving the same result 100 times in a row is equal to a certain percentage of those possible outcomes.
Unfortunately, (even semi-)random events have a way of defying the probabilities. However, if someone offers you 100-to-1 bets that a roulette wheel will land on “7” 100 times in a row, check their solvency and accept the bet. You lose if another result appears before the 100th spin.
The conclusion is simple: Don’t try to calculate like an expert. Chance will always prove the experts wrong in the end.