I was showing a friend how to play a particular Video Poker game the other day and, after just a few minutes into our session, I hit a four-of-a-kind which, as you know, makes this endeavor a lot more fun. We were at a casino where you can keep track of the number of hands you're playing by tracking the slot club points and I had received my 4K at about hand # 50. My friend wanted one also, but I pointed out that while one could expect to get a 4k about every 444 hands, on average ( we were playing quarter All American), the reality was that she might get one on the next hand, or may not get one until hand number 500 or 600 or even later. "Gosh, she said at that, "if it takes five or six hundred hands to get a four-of-a-kind, I'll begin to think that the Video Poker gods hate me".

I explained to her that religion has nothing to do with VP and everything to do with statistics. As her eyes glazed over, my voice trailed off and I dropped it. A little while later, I hit another 4K and two hands after that, another one.

"Hey", she said, "aren't one of those mine?"

I just looked at her, shrugged my shoulders and mumbled something about it 'being one of those types of games'. I'm not sure what that means, but she got the gist of it and I'm sure you do, too. We played for about three hours and neither of us ever saw another 4K and when we went to dinner, she was convinced that some deity or another was upset with her.

Well, don't worry, Dear Reader, that's not it; it's something a lot tougher: probability. No entreaties, no prayers, no pleading will change the immutable odds of mathematics. But look at it this way: If someone up there really does hate you, it's still mathematics that will rule, so - eventually - probability will come through. So, how bad is "bad"? Let's take a quick look.

As I mentioned earlier, a hand of four-of-a-kind will show up in All American once every 444 hands on average, if you are using the proper playing strategy. If you've played Video Poker for any length of time, you know that such events don't happen with precision; there have been many times that I've received a 4K and then 20 or 30 hands later, gotten another one. There have also been times when I couldn't get one to save my butt (and, it usually was needed to save my butt - from a financial point of view, anyway). We've discussed this concept before. It's called standard deviation and that's a mathematical way to explain why something which should happen every 444 hands doesn't.

I get a lot of e-mails from readers who have ventured a buck or two at online casinos and they're often convinced that the casino is cheating because, "I got 11 Blacks in a row at Roulette and I've never seen that at a 'real' casino." Remember, just because you've never seen something, it doesn't mean it can't happen. Most of the cries that go up about cheating at online casinos are really just the laws of mathematics in action, combined with a natural skepticism about these places. I'm all for being skeptical, but just because I lose, it doesn't automatically mean I was cheated. My friend, who never got a 4K, didn't feel cheated; she just thought that fate was against her. It reminds me of what Einstein said, "God didn't play craps with the universe." In other words, it can all be explained.

My friend played about 2000 hands of Video Poker and never saw a 4K. How unusual is that? She should have gotten four of them, maybe five, but what happened is entirely possible. At a rate of one every 444 hands, the 'expectation' is to get 2000 divided by 444 = 4.5, but you cannot, of course, get half of a 4K. But, let's use that number for accuracy's sake. The probability of a 4K is expressed as a decimal which we calculate by dividing that into 1. So, 1 divided by 444= 0.0022522. We also need to know the square root of the number of hands played, and that's 44.72. The square root of the probability (0.0022522) = 0.0474573 and if we multiply both of those numbers, we get 2.12. That's what we call the standard deviation. Expectation is 4.5 and the actual result was zero. That's just a bit more than 2 standard deviations and, since two SD covers 95% of all the results we can expect, my friend's experience was about a 1 in 30 event. In other words, there was about a 3% chance of that happening. A slim chance, admittedly, but still a very possible result. If she had played 4000 hands, the SD would be 63.24 (the square root of 4000) X 0.0474573 = 3.00. Expectation for 4000 hands is to get about nine 4Ks, so getting none would be an event which will happen only 0.3% of the time; an extremely rare event.

But think about it: if something like that happened to you, it's likely that you'd feel cheated, but that may not be the case. As I told my friend, it was just the math that got her; play a game long enough and you'll eventually see everything. The real key to success isn't prayer; it's skill, discipline and a large bankroll.

See you here next time.