Drawing Conclusions

Let’s say you had a good year at video poker in 2010 — and you made a lot. For some of you that means $1,000. For others, a lot more. In 2011, assume you lost a similar amount. You conclude from this that the games were tighter in 2011 than they were in 2010.

My question is: Is that a reasonable conclusion given the data?

The conclusion is absolutely false — but it’s hard to see why. A LOT of players (including me) believe that many machines were tighter in 2011 than 2010, so how can I now argue that the conclusion is false?

First of all, your annual score only partly reflects how tight the games are. A lot of your score deals with how many royals you hit. If you hit “slightly more” than average in 2010 and “slightly less” in 2011, that would explain your results even if the machines were the same.

Second, your final score is somewhat of an accident. Even if you played 2,000 hours (40 hours a week — 50 weeks a year), there will always be some variation in your results. Yes you are in the “long run,” however it is reasonably defined, but variance doesn’t disappear in the long run.

Let’s take an example. Let’s pretend 2010 happened 50 times. Each time you played the same games with the same skill level. Every time you start with K♥ Q♥ J♥ T♥ 4♣, you throw the 4 away and hope for the best. You hold three aces or three deuces (depending on the game) the correct number of times. But the number of times you connect varies. You enter the same drawings, but only one of the 50 times you won something big.

In our pretend example, you might have a low score of -$25,000, a high score of +$12,000, and the other scores are in the middle somewhere. Let’s say the average of those scores was -$5,000 — meaning you’re playing a losing game, not counting comps.

Of course you actually only played 2010 once. Your actual score (let’s say it was +$1,000) is a fairly random result over the 50 hypothetical tries. In this case, you actually got pretty lucky because your actual result was $6,000 better than your average result.

Let’s play 2011 the same 50 times. This time, let’s say the low score was -$18,000 and the high score was +32,000, with the average score at +$7,000. Clearly the combination of game selection and skill level was much better in 2011 than it was in 2010.

But since we only played 2011 once, let’s say our actual score was -$4,000. This is worse than average for the range, but it could easily happen. Any of the scores between -$18,000 and +$32,000 could have happened.

You never see these hypothetical 50 times, which is understandable because they don’t exist. But conceptually they are there. You never know how close you were to a big score or a small score. You only know that you didn’t hit a royal today or you were called first in the drawing.

I’m not saying the machines in 2011 were looser than they were in 2010. They weren’t. What I’m saying is that one person’s actual results can’t be used to make that determination.

If players were able to think this way they’d get away from such ridiculous statements as: “I know it was a terrible game to play, but I hit a royal flush and that makes it all okay.” If players knew they have to play the same game in 50 parallel universes they’d realize that whether you did good or bad in one particular universe wasn’t particularly important. It’s just one of 50. And the game is bad in all 50 whether you hit well in one universe or not.

Another point is that most machine tightening doesn’t affect you. When the Palms pulled out its 25¢ Full Pay Deuces Wild machines, it didn’t affect me in the slightest. I don’t play 25¢ machines and I thought the overall benefit package at the Palms was better if you played larger machines. Similarly, when another casino changed the pay schedules on its $25 machine, that affected only a few players.

Smart players have a number of places to play and they are competent at a number of different games. They KNOW there will be changes in games and slot clubs and promotions in 2012. They just can’t know what those changes will be until they happen. Often the changes will make success more difficult — but not always.

I’m not saying your annual score is meaningless. Over time, it paints a fairly accurate picture. But just because one year’s score was better than another doesn’t mean you can necessarily conclude that you played better. Or the machines were better.