>Hi Hilmar,
>
>I like your thinking on streak probability. I decided to look into to it, so did some web browsing. I think the answer to steak winning can be found in the "Theory of Large Numbers".
>
>We know the probability in tossing a coin is 50:50 as there are only two possible outcome, and each has an equal chance of occurring. If a coin was tossed 100 times, I would expect the outcome to be close to 50 heads and 50 tail. The outcome would probably not be exactly 50:50, but would usually be close.

Exact formulae may be complicated, but it is my understanding that, roughly, the following will happen if you toss the coin more times:

The absolute deviation from 50:50 will tend to increase. The percentage deviation will decrease.

For instance, if you toss 100 times (and repeat this experiment several times), most of the times you will get, say, between 40 and 60 heads (numbers are my own, rough estimates). This is a deviation of 10 (absolute), or 10%.

With 10,000 tosses, most of the times you would get between 4900 and 5100 heads, that is, a deviation of 100 (absolute) or 1% (relative).

Although the numbers come from my own observations, I remember having read something in this sense.

The basic idea is that the absolute deviation tends to increase, more or less, proportional to the square root of the number of tosses, while the percentage deviation tends to decrease, also, proportional to the square root of the number of tosses. (In the examples, an increase by a factor of 100, in the number of tosses, caused the absolute deviation to increase by a factor of 10, and the percentage deviation to decrease by this same factor).

>I also know that as the coin is tossed more time the outcome of the occurrence will approach an exact 50:50 occurrence rate. This is essentially the "Theory of Large Numbers".

Yes, but see above: this is only if you consider percentages, not absolute numbers.

>I also know that as the coin is tossed more, the likelihood of streaks increases, so if the coin were tossed enough times, I would find somewhere in the distribution, a streak where heads was tossed 90 times in a row. If I examined the distribution further, I would also find a streak where tails was tossed 90 times, which would counter balance the streak of head tosses and bring the probability of all occurrence back to the 50:50 ratio.
>
>Over small occurrences the result can be very slanted. For example, if the streak of 90 heads occurred during the tossing of the coin 100 times, it could greatly exaggerate the result from expected, causing great wins or loses.

Yes, right. I was surprised myself to get a relative large deviation with 10,000 tosses of two dice - I thought the numbers were large enough, but apparently I was wrong.

>If the coin were tossed so many times that a line between the earth to the moon was required to hold the results, I could examine the results to determine the probability of streaks by counting the number of time a streak occurred relative to the total number of occurrence, so I'm sure streak probability could be measured mathematically, but I not sure exactly what the formula would look like. I do know that the "Theory of Large Numbers" can be very complex.
>
>If the coin was tossed an infinite number of times, there would be at least one occurrence of every possible streak with an offsetting steak. <bg>
>
>Here is a link, but there are many more links on the web.
>
>http://mathforum.org/library/drmath/view/52799.html
>
>Regards,
>
>LelandJ