What’s a mere million or two?

Jul 17, 2006 5:42 AM

One of the most misused phrases has got to be "one in a million." I honestly think that people don’t know what that phrase really means. Perhaps a husband will turn to his wife and say that she’s one in a million. How romantic. Of course, with 5 billion people on the planet, he really just told her that there are 4,999 others just like her.

Usually the misuse, however, is not of the under exaggerating type, but of the over exaggerating type. For example, let’s say you flip a coin 10 times, and amazingly enough, it comes up tails ALL 10 times.

My goodness this must be a one in a million event! Not even close — it’s more like a one in 1,000 event (1,024 to be exact). What if you flip a coin 20 times? What are the odds that they will be ALL heads or ALL tails. Well, the probability of either one separately IS in fact one in a million (1,048,576). But since the question was worded that it could be either heads OR tails (but all 20 had to be one or the other), the actual odds are more like 524,288 to 1. This is still not one in a million.

I recently came across this situation. I was given seven scratch-off tickets as part of a contest. There was a 66.6% chance that any one ticket was a winning one.

I guess I was having a bad day, because ALL seven were losing tickets. The person handing out the tickets made a comment to the effect that the odds must be around a million-to-1 of losing all seven.

In reality, the odds are just over 2000-to-1 (2,187-to-1 to be exact). My wife was having a much better day. She won on one ticket. The odds of doing exactly this were about 156-to-1. Even together, we were not at a million-to-1, yet along separately.

How many times have you heard the story of someone playing multi-play video poker and they hold four cards and get dealt the exact same fifth card on each of three hands. Clearly the machine must be broken.

Well, the odds of getting any one card all three times is just over 100,000-to-1. The odds of ANY card in all three hands is a "mere" 2209-to-1, as it can be any of the remaining 47 cards.

I’ve heard of people having this situation occur in Triple Play machines, but I’ve not heard any cases of it in 5-play video poker. Here the odds are well over a million-to-1.

It is a nearly 5 million-to-one that someone will be dealt the same card in all five hands when drawing a single card. Yet, I’m quite sure it has happened, and happened many, many times.

A little over 10% of all hands (in jacks or better) will require that the player draw a single card. So, a player would have to play 50 million hands (give or take a million) to see this situation occur. While it’s unlikely any one person will ever play that many hands, across all the video poker machines in all the casinos in the United States, this is really not that many hands.

So, what’s my point? Well, believing that certain events are far more rare than they really are can tend to do two things. The first is to get discouraged and to stop believing in the math behind the game. This leads players to abandon sound mathematical strategy. The end result to this is a stronger likelihood of losing or losing faster.

The second is that players begin to believe that the games are either rigged or broken. As I have stated many times before, I don’t believe games in the major casinos are rigged, and I can’t for life of me figure out why anyone would play a game that they believe is rigged. As a computer programmer, I can tell you with 100% certainty that if I wanted to rig a video poker machine so that you don’t have a chance of winning, yet you will never know what is going on, I could do so with very little effort.

If you believe the games are rigged, you need to find a new hobby. As for games being broken, they do break down once in a while, but these are the exceptions not the rule.

The important things to remember is that most things are not nearly as rare as you perceive them to be, and even when they are, they still fall within the realm of the mathematical probabilities.

The games are designed and built with the math in mind. You can either deny this fact or you can use it to your advantage. I prefer the latter.