VIDEO POKER

The Wrong Side of Random

Let's say we have 100 strong players with identical, strong, video poker playing skills, all of whom play the same promotions. (This is definitely hypothetical. No two players have exactly the same skills. Also, there are large numbers of profitable video poker opportunities out there so it's rare that five players play the same promotions, let alone 100.) Assume further that these players play 1,000 hours a year and have an expected win of $20,000 over that year.

Even though we have specified that on average these players earn $20,000, that isn't saying that everyone earns exactly that much. Perhaps two-thirds of the players will earn between $15,000 and $25,000. There will be a few players losing money that year and there will be a few ahead $50,000 or more.

This is an important concept. An expectation isn't a guarantee. It means you have average luck to go along with your skill set and the games you're playing. If all 100 of these players entered the same drawing for a new $25,000 car, and each of them had 2,000 tickets in the barrel, there will be at least 99 losers that night and at most one winner. (I'm assuming that there are other players in the drawing as well.) And we can't tell up front which of the 100 players, if any, will be the winner.

With 1,000 hours of play, each player "should" get about one dealt royal that year --- which comes around approximately once every 650,000 hands. If you're playing on a single line game, a dealt royal is no different from any other royal. If you're playing on a Ten Play game, this is ten royals all at once.

Also, we'll assume these players sometimes play 25¢ games, sometimes $1, and sometimes $2. Even if they all get the same number of royal flushes over the year, the ones who get more than their share on the $2 games will have highly profitable years. Those who are over-royaled on the 25¢ games and under-royaled on the higher denominations will not have such profitable years.

In addition, over a time period as short as a year, some players will be plain unlucky. It's 46-to-1 (sometimes written as 1-in-47) against filling in a 4-card royal. Assume these players get 4,700 chances over this year. One hundred royals will be average number, but some players will only receive 90 and others will stumble onto 110. The difference in these numbers is totally due to luck.

The existence of the distribution of results shouldn't be a big shock to you. Yes skill is important, but even with identical skill there will be random elements at work that will hit different players differently.

Now let's look at one of the players who lost $5,000 in 2008. "Sam" earned $20,000 in 2006, $15,000 in 2007, but he took it on the chin in 2008. (We couldn't know which of the 100 players this was going to happen to, but we knew it was going to happen to somebody.)

From Sam's point of view, something is going wrong. He's likely to become convinced that somehow the casino has changed the fairness of the game. He used to get positive results and he isn't now. That "proves" that the casino has changed things. He might have a theory on how the casino is doing this. Perhaps he believes that ticket-in-ticket-out is the culprit. Or perhaps the newer IGT machines with the wider screens. Or perhaps it's something else.

What he's unlikely to conclude is that he was on the wrong side of random last year. It doesn't mean he was a worse player in 2008 than he was in 2006 or 2007 (although it's possible that he was.) It doesn't mean that casinos are pulling a fast one. All it means is that Sam was unluckier in 2008 than he was in 2006 and 2007.

This isn't a satisfactory conclusion to most players. We're wired to believe that if our profits go up we doing something right and if our profits go down we are doing something wrong. That doesn't necessarily have to be the case.