RadLonghammer

04-27-2013, 07:01 AM

I'm writing this because there's been a great deal of discussion regarding probabilities and odds in the forum lately. Because I have a suspicion that some people who read these boards are younger folks, and folks that might one day wander into a casino, I want to make sure that they're exposed to accurate info with regard to statistics.

The first thing to understand is that for the chance of something happening to be gleaned from observed instances, the sample size has to be HUGE. Not in the tens, hundreds, or even thousands.

Think of a coin flip. We all know that the chance of landing heads is 50% If we flipped a coin 1000 times, however, it's quite easy to get a result on the order of something like 550 heads and 450 tails.

Clearly, this hypothetical (but completely reasonable result does NOT mean that the coin has a 55% probability of turning up heads. We know better.

In fact, it would take hundreds of thousands, even millions of trials to overcome random chance, and get results that mirror the true probability of the event.

Secondly, understand that all random events are independent events. The result of the first trial in no way affects the result of the second trial. If your coin comes up tails seven times in a row, the next flip is still 50% likely to be heads. You are not "due" any result. The coin will do what the coin will do.

Finally, the idea that something is guaranteed to happen because you've tried it a certain number of times is completely inaccurate.

Suppose you were rolling a 10 sided die, and needed the number 7 in order to win. All other numbers lose. You know the probability of rolling a 7 is exactly 1 in 10, or 10%. It is completely wrong, however, to assume that if you get to roll the die 10 times, you will roll at least one seven. The odds of NOT rolling a 7 in 10 tries are actually much higher than you might believe.

To find the chances of NOT rolling a 7 in 10 successive tries, we must first find the chance of failure on a single try. The chance of failure is 1 minus the chance of success. In this case, 1 - .10 = .90 So, we have a 90% chance of failure on a single try. When we have 10 tries, we simply multiply the failure rate by itself 10 times.

In this case .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 = .3487 or 34.87%

That means that our 10 tries don't guarantee us a success at all. In fact we'll fail to hit that win 34.87% of the time when making 10 roll attempts!

So please, don't let anybody, no matter how well intentioned, convince you that trying something a certain number of times will guarantee success. That's just not how the math works.

The first thing to understand is that for the chance of something happening to be gleaned from observed instances, the sample size has to be HUGE. Not in the tens, hundreds, or even thousands.

Think of a coin flip. We all know that the chance of landing heads is 50% If we flipped a coin 1000 times, however, it's quite easy to get a result on the order of something like 550 heads and 450 tails.

Clearly, this hypothetical (but completely reasonable result does NOT mean that the coin has a 55% probability of turning up heads. We know better.

In fact, it would take hundreds of thousands, even millions of trials to overcome random chance, and get results that mirror the true probability of the event.

Secondly, understand that all random events are independent events. The result of the first trial in no way affects the result of the second trial. If your coin comes up tails seven times in a row, the next flip is still 50% likely to be heads. You are not "due" any result. The coin will do what the coin will do.

Finally, the idea that something is guaranteed to happen because you've tried it a certain number of times is completely inaccurate.

Suppose you were rolling a 10 sided die, and needed the number 7 in order to win. All other numbers lose. You know the probability of rolling a 7 is exactly 1 in 10, or 10%. It is completely wrong, however, to assume that if you get to roll the die 10 times, you will roll at least one seven. The odds of NOT rolling a 7 in 10 tries are actually much higher than you might believe.

To find the chances of NOT rolling a 7 in 10 successive tries, we must first find the chance of failure on a single try. The chance of failure is 1 minus the chance of success. In this case, 1 - .10 = .90 So, we have a 90% chance of failure on a single try. When we have 10 tries, we simply multiply the failure rate by itself 10 times.

In this case .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 = .3487 or 34.87%

That means that our 10 tries don't guarantee us a success at all. In fact we'll fail to hit that win 34.87% of the time when making 10 roll attempts!

So please, don't let anybody, no matter how well intentioned, convince you that trying something a certain number of times will guarantee success. That's just not how the math works.