Barstow’s Controversial Theories on Craps
Casino games of so-called "independent trials" such as craps, baccarat and single-zero roulette, can be beaten long range, as well as short range. This statement is predicated not only on personal experience and observation, but also on one highly unorthodox theory. I believe that, notwithstanding a small
minus expectancy -- the house edge -- there are certain times when true probability actually favors the bettor. I'll try to explain.
Mathematicians and physicists agree that as the number of trials increases, and substantial percentage deviation from the norm must tend to decrease. When dealing with a 50-50 proposition such as heads/tails or pass/don't pass, they agree there is a 90% probability that the variation will not equal of exceed the square root of the number of trials. This means, for example, that in 16 trials there is less than a 10% chance of one side winning as few as four times, while the other wins 12 times.
Thus, when very wide percentage variations from norm occur, as the often do in a small number of trials, the equalizing process is likely to be close at hand, and at least one new factor has begun to tip the scales of probability. If at the start of a new series we've seen 6 or 7 repeats of anything, we've already reached or surpassed the normal variation quota for 100 trials.
Why shouldn't the trend change? Of course there's no law that says it must change, but I contend that we're no longer dealing with strictly even chances. I contend that is we now bet on the weak side using a 3-bet, or 4-bet Martingale series, the probabilities in our favor will generally be strong enough too fully off-set a small mathematical disadvantage of say, one to three percent.
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Suppose we've seen 5 successive passes at our table or at 5 different tables; it really doesn't matter which. The odds were 31 to 1 against the sequence - and any conventionally trained professor will tell you that there is still 1 chance in 32 that the next 5 decisions you see will also be passes.
If you question that, the explanation you'll get sounds plausible enough: "The dice don't know what they have just finished doing; they don't have memories - so if there was a 50% chance one way or the other to begin with, that percentage cannot vary as long as the dice are thrown randomly."
You protest that one sees 5 passes or 5 misses quite often, but runs of 8 or 10, hardly ever. Again the explanation seems plausible: "Odds against 10 repeats of a specific even chance are better than 1000 to 1."
You ask whether there might not be factors other than arithmetic alone that cause dice or tossed coins to behave as they do; for example, cycles, the theories action and reaction, or permutations and combinations. You observe that there are different numbers of spots on each side of the dice, different shooters throwing them, etc. Mightn't one or more of these factors influence the outcome of those so-called independent trials? "Actually," you ask, "is there really any such thing as a completely independent trial?"
When your questions are scornfully dismissed, you remind your instructor that Emile Borel, one of the more prominent founders and exponents of the modern theory
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Eddessa_Knight with Lucky LIGHT
Nota Bene:
The odds will deceive you >>>>>