Would you believe?

Jan 2, 2006 11:43 PM

The other day I was playing video poker next to this young blonde woman. All of a sudden, the video poker machine lifted off the ground as if defying gravity. The next thing I know, she blinked her eyes (with her arms crossed) and the video poker machine changed to a slot machine. Then she wiggled her nose and it changed back to a video poker machine. It slowly lowered itself to the ground.

You don’t believe me? Just because the machine violated several laws of science, including gravity, my story is not believable?

Yet, if someone were to try and tell you that the video poker machine didn’t abide by the basic laws of mathematics and probability, you might just listen. These laws are just as unchangeable as the laws of gravity.

A video poker machine will not float in midair, and it will NOT (barring malfunctioning) EVER violate the laws of probability. Most people don’t understand the laws of gravity (I’ll admit that I don’t fully understand how it works), but can deal with the basic idea that objects fall to the ground. The laws of probability are far more complex, and thus it is easy for those who don’t understand them to decide that they simply may not apply to all situations.

What if I had told you a different story? The other day I was playing a three-play video poker machine. I was dealt a 4-card flush and when drawing for the fifth card, I was dealt the EXACT same card on each of the three hands.

Something must have been wrong with the machine. It must have malfunctioned. Clearly this is proof that the laws of probability don’t apply because the odds of this happening must be astronomical!

Well”¦.not exactly. The odds that any ONE card occurs in all three draws (let’s say to complete an inside straight flush) are 1 in 103,823. The odds that the same card shows up in all three draws are only 1 in 2209. About 1 in 15 hands will have you drawing only 1 card. This means that about 1 in 33,000 hands that you play will wind up with this astronomical outcome. While this hardly is a common occurrence, astronomical would be overstating it a bit.

So, what do you do with this information? Knowing how often the same card will show up in this circumstance could clearly be classified as useless trivia. The lesson that can be learned from it is that what we often believe to be an unbelievable occurrence is in actuality the normal expected results from a video poker machine behaving randomly. It is this knowledge that allows us to show that expert strategy, a strategy based on sound mathematical principles is not just something for the long run, but is the proper strategy for the short run, as well.

Is there ever a time you would want to deviate from expert strategy? Sure. Certain types of tournaments may warrant playing a more volatile strategy. If you are playing with a short bankroll and are trying to stretch that bankroll to last as long as possible, it may be worthwhile to slightly alter the strategy.

But for anyone who is playing over the course of years (whether you play 10 hours a year or 100 hours a year), the best strategy to maximize your chances of winning or minimize the amount you will lose, is a strategy that maximizes the expected value of each hand.