Probability Speaking

I often see mass confusion when it comes to probabilities—especially when it comes to systems. There are, in my mind, two probability numbers for each set of conditions. I feel it is necessary to explain this further to not only educate my visitors, like you, but to ensure that when you read my articles, you know what I am talking about.

As I stated in my introductions, there are two probabilities for every condition. To explain this, we are going to look at the classic coin flip. A coin has two sides—heads and tails. On any coin flip each side has a 50% probability of coming up. However, each flip also has another probability associated with it. This probability is constantly changing and is the probability of the opposite side showing up to bring the overall numbers to mathematical form.

Let’s say that I am going to flip the coin ten times. The first five flips are all tails. Now the following applies:

(1) Heads has a 50% probability of showing up on each flip, because this is the true probability of heads being selected.

(2) Heads has a 98.5% probability of being selected on the sixth flip, because the probability of tails being selected six times in a row, given the original 50% probability, is 1.5%.

Can tails come out again? Sure can—and for another 50 turns too. However, at some point the opposite will begin to occur to bring the numbers back to mathematical form. I wrote a simple program to perform coin flips and report the outcome. The program did ten sets of 1,000 coin flips each. At any point in time one side might have been selected consecutively for a term, but the opposite eventually got selected to bring the overall result back to mathematical form.

The Results

Set One: Heads (517) Tails (483)
Set Two: Heads (527) Tails (473)
Set Three: Heads (500) Tails (500)
Set Four: Heads (482) Tails (518)
Set Five: Heads (491) Tails (509)
Set Six: Heads (535) Tails (465)
Set Seven: Heads (483) Tails (517)
Set Eight: Heads (518) Tails (482)
Set Nine: Heads (497) Tails (503)
Set Ten: Heads (503) Tails (497)

In the end, Heads was selected 5053 times (50.5%) and Tails was selected 4947 (49.5%).

The main flaw of gambling systems that play on probability is sample size. As you saw in the above example, the numbers basically worked out. However, that was a pretty good sample size. If the sample size was only ten flips, the numbers could have easily been Heads 80% Tails 20%. This flaw coupled with a large progression chain can spell disaster.

As to playing streaks, I analyzed the test of 10,000 coin flips and found streaks in each set. Here they are:

Set One: 8, 11, 8, 8
Set Two: 9, 9
Set Three: 9, 13, 10
Set Four: 13, 8
Set Five: 9
Set Six: 8, 8
Set Seven: 10, 8, 8, 9
Set Eight: 8, 8, 8
Set Nine: 8, 9, 8, 9, 11, 9
Set Ten: 8, 8, 9

If you were playing a progression system that chases missing occurrences, and that chain was long, you would be killed in each set—especially set nine. It is important to remember that this was a coin flip that had two possible outcomes, each with a 50% probability. Streaks of say eight consecutive sixes in craps are less frequent, because the probability of rolling a six is 13.8% and not 50%.

In upcoming articles, I will tackle game specific tests.