Well, as applied to gambling, the situation for me is the following.

First of all, Bahá'í law forbids gambling, so that's it (for me; of course, this doesn't apply to you, although some other religions also speak out against gambling).

(Anyway, I still find the calculations involved fascinating!)

Second, the mathematical part isn't really complicated at all, to figure out: the house calculates its probabilities so that, in the long run, they win. Therefore, in the long run, the clients lose. It is as simple as that!

>Hi Hilmar,
>
>I think the calculation you provided regarding the odds of hitting four heads in a row is correct. If I understand it correctly, it would be based on 16 tests where the dice were rolled 4 times per test. Thus, the probability of finding a steak of 4 head or four tails would be 1/16 or once every 16 tests, or 4/64, since the dice would actually be rolled 64 times.
>
>However, if a number of test were conducted where the coin was tossed 64 time and the results examine to see if there were a streak of four heads or four tails, it would be conincidential to find such a streak. The steaks seem to occur ramdomly. Also, there is the difficulty of defining what is a streak. For example there could be a streak where heads came of twice for each tails and the steak could have a frequency of maybe 20 time in a row.
>
>Now, if the test was over a billion occurrence, and the results examimed for the occurrence of streaks of four heads or four tails, I would expect the result to come close to you probabilty of 1/16. The results could be expressed as:
>
>1 billion files of a coin/64 = number of the occurrence of steaks of four heads or four tails in a row.
>
>Therefore your calculation would only be valid within the context of "The Theory of Large Numbers" where relavent occurrences of tossing the coin were very large.
>
>For me to go to Los Vages armed with the knowledge that certain odds existed in the game of Black Jack would be incorrect, especially if I planned to only play 100 games at tops. The trend would be towards my outcome following the calculated odds, but it could vary anywhere from a little to greatly. This would be because my relative occurrences would be so small.
>
>Now the House would get the benefit of "The Theory of Large Numbers", because its number of occurrence of interest would be very large and measure yearly via it Financial Statements. Actually the relavent number of occurrence for the house would be from its inception to its present time.
>
>This is a facinating topic, but one for which there is no definitive anwser, because there are several theories regarding the subject, and nobady has been able to provide the proofs necessary to explain how to predict steaks, etc.
>
>I still think I could win a predetermined amount of money by setting my objective to a predetermined amount to win, have the house agree to remove any limit, bet (losses + objective to win) infinitely until I won my first hand.
>
>Regards,
>
>LelandJ