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It Doesn't Seem Fair

While waiting for my takeout food order from Ping Pang Pong at the Gold Coast I was playing $2 NSU. I saw a friend of mine, Linda, who was quite upset. I asked her why. She told me she had been at a Palms Casino drawing across the street. She had more tickets than the people who actually won. She felt it was unfair.

"You can feel bad if it will make you feel better," I told her, quoting an old Patty Loveless song, "but that would be the typical result even if the drawing were 100 percent fair, and I have no reason to believe the drawing wasn't fair."

"How can that be? I had more tickets. I should have won." She didn't really want to be lectured so she took off.

Let's take a simplified look at the drawing. Let's say there were 20 tickets in the drum and they were going to draw one name. Linda had eight of these tickets, and a four people (Abe, Ben, Carl, and David) had two tickets each and four additional people (Emma, Frances, Grace, and Helen) had one ticket each.

Linda's chances are good in this example. Eight out of 20 is 40 percent. She's still a small underdog to be drawn but her chances are far better than anyone else's.

Let's also assume that she didn't win this time, but rather Abe won. While Abe only had a 10 percent chance of winning, there were three other players with a 10 percent chance, along with four players with a 5 percent chance each. Their total was 60 percent, which was greater than Linda's 40 percent.

Linda is comparing her eight entries to Abe's two entries and is feeling gypped. That's not the relevant comparison. She should be looking at her total entries (eight) versus the total number of entries (20). This is tough to do, however, because usually the casino doesn't announce the number of entries in the drum.

Linda's chances before the drawing were four times as great as Abe's. But the chances of (Abe + Ben + Carl + David + Emma + Frances + Grace + Helen) combined were 50 percent greater than Linda's. Looking at (Linda versus Abe) leads to misleading conclusions. Looking at (Linda versus not-Linda) leads to the correct conclusions.

You sometimes hear that someone with only one ticket in the barrel won a big drawing while somebody with thousands of tickets was shut out. What you don't hear is that there are HUNDREDS of people out there each time with only one ticket, and usually none of them wins. If figures that sometimes one of these people win and when that happens it's remarkable enough that everybody talks about it. So most people have heard of people with one ticket winning a drawing even though it rarely happens.

If Linda continues to earn more tickets than most other players she will continue to win much of the time. (And trust me, the players who see her win "all of the time" will get very annoyed.) But even though it looks to others like she wins "too much," she won't win all the time, or even most of the time. And usually when she doesn't win, whoever does win will have fewer tickets than she does. That doesn't mean she's being cheated. That just means that there are LOTS of people with fewer tickets than she has and when you add up all of their tickets, they have more than Linda does.

I showed this article in draft form to Linda and a mutual friend. The friend thought it was right on and Linda didn't want to talk about it. The following week there was a similar drawing and Linda actually won.

"You need to rewrite your article," she told me.

Not really. My point wasn't that she would never win. My point was that the person who has the most tickets doesn't always win. And shouldn't always win. And that analyzing only what is readily apparent isn't nearly as important as analyzing what is not so apparent.