Randomness in Video Poker Results

This past summer the whole country marveled at rejoiced at Michael Phelps' 8-for-8 swimming wins at the Beijing Olympics. He is unquestionably a gifted athlete who brought out his best on the world'sBob Dancer is one of the world's foremost video poker experts.  He is a regular columnist for Casino Player, Strictly Slots, and the Las Vegas Review-Journa land has written an autobiography and a novel about gambling.   He provides advice for tens of thousands of casino enthusiasts looking to play video poker.  Bob's website is www.bobdancer.com  biggest stage.

Also unquestionably, he was very lucky to pull it all off. One race was won by 0.01 seconds, where he was three feet behind with six feet to go. For him to win his gifted opponent had to glide the last 15 feet without taking any stroke. In the 4x100m relay, a teammate, Jason Lezak, had to come from behind against a Frenchman who won the 100m freestyle event a few nights later. Phelps' goggles malfunctioned in two separate races. The four-man relays went off without a hitch, which didn't happen four years ago in Athens, and twice didn't happen this time in track relays.

Slipping to "only" 5-out-of-8 or 6-out-of-8 wins (still very remarkable achievements) could easily have happened. If the same races were run a month later, the smart bet would be he would NOT win all eight races.

Still, he captured lightening in a bottle and will likely reap $50 million to $100 million in endorsements. Good for him!

Now to video poker. In any given year, let's take 2007 as an example, let's say a player named George ended up with exactly 12 royal flushes. Had George run that same year over and over again, playing the same amount of hands on the same machines with the same promotions, sometimes he'd end up with more royal flushes --- sometimes with less.

If you can imagine George hypothetically experiencing 2007 one thousand times, there would be a distribution of royal flushes. Perhaps one of those 1,000 times he'd end up with 26 royal flushes. Fourteen of those times he'd have between 20 and 25. Forty-seven times he'd have 19 royal flushes. 150 times he'd have 16 royal flushes and 149 times he have 15. At the bottom end of the distribution, one time he only had two royals and three times he only had three.

I made up those numbers -- as I had to because it is a "mind experiment." But if you can look at it that way, you'll see that the actual number of royal flushes George actually ended up with is a random number. In our example, he "should have" ended up with 15 or 16, so 2007 was an unlucky year for him. This doesn't mean he played badly (although it's possible). Rather than counting royal flushes, a better measure of your results is net dollars won or lost.

The amount you play and the skill level with which you select machines and play the hands end up giving you a range of results possible. Let's assume George is a better than average player and his worst 2007 score (out of 1,000 tries) was minus $9,000 and his best was plus $85,000 (but that time included winning a $25,000 drawing, which only happened once in 1,000 times.) His average (of the 1,000 times) is $33,000. A bad player, Henry, who plays about the same amount as George might have a range of minus $64,000 to plus $1,500.

Exactly where they end up in the one time they actually experienced 2007 had a large luck component. George probably had better results than Henry, but not necessarily. If it happened that George is at the unlucky end of his range while Henry is at the lucky end of his, Henry could actually outscore George -- even though George is clearly the superior player.

Winning players tend to be proud of their results. (I've had my own button-popping moments. I even wrote a book about my million-dollar success.) While there is no doubt that a large amount of skill is important in the winning process, whether George ended up with 19 royals or 12 in 2007 was largely a matter of blind luck.

If you tell a winning player that the reason she won was because she was lucky, she will be insulted. When players win five or ten years in a row, it tends to indicate a significant amount of skill is involved but it doesn't have to. When you have more than a million players out there, it is a 100% certainty that several of them will have luckier-than-average results ten years in a row.

Better-than-average luck does not necessarily mean you make money. Henry's average score might be losing $8,000 because he's really not a very good player. If he only lost $2,000 in 2007, that would be a luckier-than-average outcome but he still lost money.

Losing players are very willing to attribute their results to bad luck. It is easier on the ego to blame bad luck than bad skill. These players typically, but not always, underestimate the amount of skill required for good results. Still, over the millions of video poker players out there, it's also a 100% certainty that several of them will unluckier than average ten years in a row as well.

This column has been inspired by an excellent book I've recently read and highly recommend. It's called "The Black Swan" by Nassim Nicholas Taleb. Among many other topics, Taleb discusses how your actual results may or may not accurately reflect your skill level.

This column reflects a recent change in my thinking. In the past I argued that if you played more than a couple of hundred hours a year, your results were pretty much what you deserved. While this would undoubtedly be true if you could look at all 1,000 imaginary times you experienced the same year, when you only experience a year once you cannot know for sure.

That's the nature of gambling as well as most other things in life.