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This is a commonly held view among players who have no grasp of probability theory, the law of averages, chance, luck, or odds in general. Many seemingly experienced players believe, for example, that how the third-base player plays his hand influences whether the dealer will draw a pat hand or bust. Or, when someone decides to split T’s versus a 6 and then the dealer ends up drawing a 4 or 5 to his 16, resulting in a loss for the whole table, it is not unusual for players to abandon the table in disgust. They figure that the dealer would have gone over 21 if such a “foolish” play had not been made. Seasoned veterans of the game playing one-on-one with the dealer are often indignant when the sequence of “their” shoe is interrupted by someone else joining the game before the shuffle. A large segment of the blackjack-playing public is convinced that a game with weak or beginning players is inevitably doomed to failure.
If this were not such a widely held misconception, it would not deserve serious comment. How otherwise intelligent people can rationalize such a ridiculous concept is difficult to comprehend. Could it be that they actually believe that the dealer has somehow prearranged the cards so that the players will lose? No, because if that were the case it would be necessaiy for someone to disturb the expected sequence of play in order for the players to win! Possibly these disgruntled players are simply looking for some innocent victim to blame for their own losses, or an excuse to justify their leaving the game. Perhaps they have won sessions in the past in which all of the players were of one mind, and naturally they can vividly recall the rewards of such “good” playing. (Needless to say, they must quickly forget the equal number of wins that result from the “bad” players’ draws.) Just as superstition thrives upon such selective memory, so too are formed the unconscious convictions of ignorant blackjack players.
To understand probability theory correctly, we have to imagine a “perfectly” shuffled deck of cards or an “ideal” coin being flipped. Such a coin or deck could never be found in the real world, since there is no such thing as a truly random shuffle outside of a computer, and an actual coin could become worn unevenly on one side or perhaps land on its edge occasionally. Mathematical probability is not concerned with specific events such as a won or lost hand resulting from a particular “good” or “bad” play although statistics can be compiled in this way and often prove useful. Rather, probability theory refers to the results of an infinite number of similar events or, more precisely, to what happens “in the long run.”
Let’s assume that the shuffle is a random one and that you will win 50% of your hands by following BS. Let’s also assume that you are not counting cards and therefore have no specialized knowledge of what cards are more apt to appear in imminent hands, or the upcoming “dependent sequential events,” as mathematicians call them. The “odds” or probability of a win (or loss) remain constant regardless of the number of players at the table or how they play their hands. Similarly, jumping in and out of a game without knowing the count offers no advantage to any player. By doing so you are just as apt to be avoiding beneficial cards as unfavorable ones. (See The Theory ofGamMing and Statistical Logic by Richard Epstein.) You wouldn’t think of crediting a good player for your wins; neither should you consider blaming a poor player for your losses.
It is perhaps appropriate to comment here on another common misconception regarding probability theory. Many players believe that “luck,” good or bad, will “even out” eventually. Everyone knows that when flipping a coin the ratio of heads to the number of total tosses will approach a true limit of 50%. This is only common sense. From this knowledge they “reason” that if, say, ten successive heads occur, the next flip will more likely result in tails. Nothing could be farther from the mathematical truth, since every toss has exactly an even chance of being heads or tails. Even though the ratio will tend to approximate the theoretical limit more closely as the number of tosses increases, there could very well be an excess of heads indefinitely.
Suppose that after fifty flips of the coin you noticed that twenty more heads appeared than tails, i.e., fifteen tails and thirty-five heads. The ratio of heads to tails would be 70% (35 -s- 50). The same excess of heads in one hundred tosses would be only 60%, and in a thousand tries (510 heads) only 51%. You can see that, although the true limit is approached as the number of tosses grows, there is no reason to believe that the absolute numbers of heads and tails will tend to equalize themselves. In fact, in his blog An Introduction to Probability Theory and Its Applications, William Feller proves mathematically the unlikelihood of such a skewed number of coin flips ever evening up.
The same thinking can be applied to blackjack hands played according to BS. Many otherwise intelligent players firmly believe that in a truly fifty-fifty game at an honest table, and all other factors being equal, after losing an excessive number of hands their net losses must diminish due to the ‘law of averages” if they continue to play long enough under these even-odds conditions. Their logic, however, is tragically flawed.
As seen in this example, according to Feller, although the win percentages will theoretically approach 50% as the number of hands played increases, net losses are actually more apt to increase! This chart supports the laws of probability, specifically the law of large numbers, while illustrating the futility of expecting a trend to reverse itself. There is no good reason to suspect that bad luck will ever turn to good luck or that “it’s bound to change eventually!”