19 May 2008

It's a tax on stupidity -- but nobody's that stupid.

You win $1,500 by feeding slot only $3.75 million -- Paul Carpenter, from the (Allentown, Pennsylvania) Morning Call, via fark.com.

From that headline, it sounds like slot machines essentially never pay out, right?

Carpenter becomes suspicious that the machines are rigged because Flo Fabrizio, a "key backer" of legalized gambling in Pennsylvania, won $1500 on his first play of the machine. Now, I can understand this suspicion -- sure, it could happen randomly. But then Carpenter goes on to do some "math" which proves he really doesn't understand what he's talking about. The article basically debunks itself.

It states that slot machines in Pennsylvania have to pay back at least 85 percent of what they take in. So then Carpenter says:
If it takes a regular player 50 million three-second plays to get a big jackpot, it would take more than 11 years, playing 10 hours a day, every day. More important, if each play averages 50 cents, the player would have to put $25 million into the slot. The 85 percent payback would be $21,250,000. So, odds are, the cost of playing long enough to get a $1,500 jackpot would be $3,750,000.
That's true. (The "50 million" comes from the regulations that say that casinos can set up their slots so that the jackpot only pays one time out of every 50 million.) But somehow I doubt a $1500 jackpot would be that rare. And more importantly, while the player is making those fifty million plays, they'll make a lot of small bets back. This is like saying that poker's a losing game because you only get a royal flush once every several hundred thousand hands. Or saying that you must not be broke because you didn't buy a million-dollar house you couldn't afford, but ignoring all the little expenses that add up. (Try telling your credit card company that!) You can't cherry-pick the tail of the distribution like that!

Could there be corruption in the gambling industry? Sure. But this doesn't prove anything. Not to mention that these calculations seem to imply that slot machines basically never pay out. Casinos aren't stupid -- they know that if slots essentially never paid out then nobody would play! The whole trick is that if you have enough small gains, you won't realize that on average you're losing.

On the other hand, they say that gambling is a tax on stupidity. At least this man's stupidity will keep him out of the casinos.


Anonymous said...

I must be missing something. Can someone explain to me the math used to determine that "the cost of playing long enough to get a $1,500 jackpot would be $3,750,000"?

Michael Lugo said...


here's the "math" used there. The writer assumes that the $1,500 jackpot comes up one time in every 50 million, which is apparently the minimum allowed by Pennsylvania law. Then rather arbitrarily, he assumes that the average slot machine play is for 50 cents. (Given that the play which triggered the jackpot he mentions was a 75-cent play, I'm not sure where this number comes from!) So it takes fifty million plays at 50 cents each, or $25,000,000 put into the machine, to get the jackpot. But 85 percent of that, or $21,250,000, is expected to be paid back. The $3,750,000 is the difference, which is how much money you'd expect to lose while waiting for this rather paltry jackpot.

What's confusing, I think, is not the computation, but the fact that the author seems to think it means something.

Anonymous said...

Oh! I finally get it. So he's saying the $1,500 payoff is the big one, and the remaining $21,248,500 is won over the course of waiting for that payoff. And consequently, the cost of that big payoff is $3,750,000.

Now I think I understand your comment about his ignoring the little payoffs. That $3,750,000 cost is really the cost for all of the payoffs -- which is meaningless in terms of the big payoff, because the number and cumulative value of the little payoffs dominates (by several orders of magnitude) the big payoff. That cost is greatly amortized by the little payoffs, since each little payoff has a cost as well.

Sudipta Das said...
This comment has been removed by the author.
Sudipta Das said...

well friend corruption is everywhere, and it's human nature, we are greedy, and with our need we become corrupt with time.

thank you
sudipta das
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