A friend, “Tom,” and I were talking about the senior drawing at Silverton as it exists in August 2012. There is optimism that it will change soon. Memorizing how it currently works isn’t important. Seeing how to use the rules of the promotion to calculate how much it is worth is important.
The way it works is that you play between 6 a.m. and 6 p.m., with maximum entries earned at $2500 coin-in. There are three drawings, at 2 p.m.; 4 p.m.; and 6 p.m. You may win more than once, but it doesn’t happen very often. With the daily maximum set so low, it’s not possible to have a really good chance to get chosen the drawing.
Of the 20 winners at each drawing, 15 win $25 in free play; 4 win $100; and 1 wins $500. How much is this worth? For purposes of this article, I’m assuming that winning free play and cash are equivalent. The differences between them can be the subject of another article some other time.
The traditional way this is calculated is called Expected Value, which is form of weighted average. To figure this we multiply the number of winners by the prizes won, add up the total of the prizes won, and divide by the number of winners. In chart form:
This means the drawing is worth $63.75 in EV to each of the winners. Insofar as Tom is concerned, the drawing is only worth $25 because that’s how much is guaranteed. He sees the possibility of winning $100 or $500 in these drawings as essentially impossible for him because he’s an unlucky guy. Other people can win these prizes but not Tom. In fact, in the three previous times he’s entered this drawing he hasn’t won a damned thing! (Which proves nothing to me but everything to him.)
“Tell you what,” I told him. “If you get called I give you $30 before you draw and then I’ll take the result. Usually I’ll end up paying you an extra $5, but occasionally I’ll win either $70 or $470. But since you believe this is only worth $25, you’ll be getting a guaranteed bonus.”
“You’re taking advantage of me,” he complained. “You just said it’s worth more than $60. Why are you offering me only $30?”
“Think of it as insurance,” I told him. “You are interested in guarantees. I’m providing you with insurance against only winning the minimum. And the difference between what the gamble is worth and what I’m willing to pay for it is the insurance premium.”
Tom passed on my offer, appropriately. He may or may not have passed on it had I offered him $60. We’ll never know because I’m not interested in making him such a “fair” offer. My goal in making the offer of $30 wasn’t to make money off my friend. It was meant to educate him how the value of something is calculated.
In Tom’s mind, if I’m involved in the drawing somehow, I’m going to have a better-than-average chance of getting the $100 or $500 scores because I’m lucky. If he’s in the drawing, he’s going to get almost-guaranteed $25 because he’s unlucky. If I piggyback on his results (as would be the case if he accepted my guarantee) then somehow I was going to be lucky and he was going to be unlucky at the same time on the same result. Never mind how all that would take place.
While Tom and I were having this conversation, a mutual friend “Jerry” was playing next to Tom at the Silverton playing. I told them both that I’d check at the 2 p.m. drawing and call them to let them know whether or not they won. I was hoping one of them would volunteer to check at one or both of the other drawings and call me. It’s a nuisance to drive over there several times in a day, although if I knew I won I would make the drive. But whether they volunteered or not, I would call them shortly after 2 p.m. Fortunately Jerry volunteered to check later.
If Jerry hadn’t volunteered to call me, I would have passed on the final two drawings. With an EV of $63.75 IF I’m drawn, and perhaps a 1-in-4 chance of being drawing each time, this drawing is only worth $16 on average. That’s too small for me to make a special trip. But since I was already here and they had a $5 lunch buffet for seniors, it was a reasonable price to stick around for 20 minutes or so.
“Don’t bother calling me,” Tom told us. “I’m only playing $500 today to get a pull tab. Other people are playing $2500, so I don’t have a chance.”
This, of course, was absolute nonsense. Tom had a smaller chance of winning than Jerry or me, to be sure, but he still had a chance. Not like Shirley. Shirley doesn’t play at all there, and I’m not allowed to play on her card. Shirley had no chance to win. Tom had a small chance.
Perhaps his chance was too small to justify HIM coming back to the Silverton to check, but if a friend was already there checking anyway, why not have that friend also check for Tom?
At 2:05, I checked the list. None of our names were on it. Disappointing but not really surprising. I called Jerry first and told him. He asked if I was going to call Tom. “Absolutely,” I replied.
Then I called Tom. “Tell me again,” I said. “I’ve looked at the Silverton results. Are you positive you don’t want me to tell you?”
“Okay,” Tom said with a big sigh. “Tell me.”
“You didn’t win. I’ll see you tomorrow.” With a big smile, I hung up. Although I was laughing about it, I had actually given him valuable information. He didn’t see it that way. He already “knew” he hadn’t won.
Maybe I thought my call was more humorous than he did.