[ExI] alternative gambling game, plus epsilon

Gregory Jones spike66 at att.net
Wed Jun 30 16:03:08 UTC 2010

If you aren't following this thread but are mildly interested in psi, please read the last paragraph only thanks.

Oooooo ouch.  Did anyone here discover a fatal flaw in the design of my game?

--- On Wed, 6/30/10, Florent Berthet <florent.berthet at gmail.com> wrote:
>...I'll give it a try (it's kind of a repost from the other thread, sorry) : the higher the number of people who play, the more evenly distributed the choices are, then it's possible that even the less chosen number is chosen by too many people to make the game profitable for the state...

Ja, that is one of two problems with my game design.  I started deriving the closed form equation to describe the filthy lucre I would earn, then found that the profit actually goes down as the number of players goes up.  I want more profit with more customers.  The other problem is that any prole with 1000 bucks could buy one of each of the three digit numbers, assuring herself of winning 1100 bucks.  Such a deal!  Not.
If I would need to patch the game in two ways: make it so that it 1) automatically starts a new round when the number of tickets sold reaches 50,000 and 2) defeats the 1000-ticket buyers by some means, such as offering a computer generated random number, which is a buy-or-no-buy.
The second strategy offers the state an unlimited opportunity to cheat, by rigging the machines to hand out the same couple hundred numbers and seldom or never offering the winning one.  But there may be other ways to defeat the 1000 ticket buyers.
In any case, I ran the numbers over night, and found that with 50,000 tickets sold per round, randomly chosen, the state would need to pay off an average of 28.7 winners per round, at 1100 would cost about 31,600 per round, for a profit of about 18,400.  In 5000 games I simulated, I found a minimum of 18 winners and a maximum of 34 winners, with a standard deviation of 2.04 winners.
Now, here this the important point of all this.  There is a phenomenon in this game which might look exactly like psi, but really isn't.  Imagine you play the 1100 version of this game, with a non-cheating random number generator in the ticket sales machine as described above, to defeat the 1000 ticket buyers.  If you ran that game, the number of winners would mysteriously be slightly higher than the numbers I ran last night!  Why?  Becaaaaaauuussseee... (stop reading and think it over first if you wish, otherwise read on...)  because the ticket buyers at the machines would reject any duplications of ticket numbers they already hold or that their pool holds.  The effect wouldn't be large, but over time it would cause the average number of winners to go over 28.7, ja?


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