The following advertisement appeared simultaneously in GROGGS, INFO.ADVERT.CURRENT, and JRP1.INFO.NEW (each of which managed to attract entrants).
In the interests of Science, I am carrying out an experiment similar to one performed by Douglas Hofstadter a few years ago in Scientific American.
The prize is 10 pounds, and any user may send me a MAIL message (for confidentiality) claiming a whole number of shares in this kitty. The one who names the largest number N will win 1000/N pence (with odd fractions rounded down). If more than one person names the same number N then they will share the loot.
For example, if the highest named number is 5 and two people name that number, they each receive 1 pound (i.e. 2 pounds shared between them), but those naming lower numbers get nothing.
The closing date for entries is March 31st, midnight. Nobody may enter more than once and so second and subsequent entries will be ignored.
Results will be published early in April.
Enter now - you can't lose.
N.B.
1. Only users of Phoenix are eligible -- no external entries
please!
2. This project IS authorised by the Computing Service.
The last two clauses were inserted to appease the Computing Service administration, who seemed slightly dubious about the whole affair.
It will be noted that the conditions were deliberately different from Hofstadter's lottery (where 1,000,000/N dollars were to be shared between all entrants, N being the TOTAL entry). This seems to have had the effect of deterring the sort of person who would submit 9!!!...!!! (with 9!!!!!!! factorial symbols) and other monstrosities. Or possibly the average user of the Cambridge University computer is more intelligent than the average Scientific American reader...
I myself did not send an entry to the original Scientific American lottery: not because of arguments to do with cooperation and defection (which I considered irrelevant in this instance as others were bound to defect), but because I calculated (correctly) that my expected winnings were less than the cost of sending an entry. In this latest version of the lottery, it cost nothing to enter!
Matters were complicated by the appearance of a counter- offer by P.J. Rodgers (PJR11), a few days later: "Since JRP1 seems to be testing the greed level of the public, the best way to retaliate is with moral blackmail." PJR11 undertook to bid 1 and to send anything he won to OXFAM. However by then it was too late to stop the trickle of entries, and the offer of 1, which duly came, did not win the kitty.
In fact I got 37 entries, distributed as follows:
Entry Frequency 0: 2 (The ingenious) 1: 5 (The optimistic) 2: 1 4: 1 5: 1 6: 2 9: 1 10: 1 11: 6 (The mode) 12: 1 19: 1 32: 1 38: 1 42: 2 44: 1 57: 1 83: 1 84: 2 111: 1 1000: 4 (The awkward) 1003: 1 Maximum Entry: 1003. Minimum: 0. Median (and Mode): 11. Quartiles: 5, 57.
I also had to disqualify entries of 0.000000001, 10.1, and "1 more than the highest number named or implied by anyone else".
Thus the distribution is approximately trimodal, with peaks at 1 (predictable), 1000 (also predictable) and 11 (presumably people expecting their rivals to bid 10).
I received a few general comments from entrants. One said that he didn't know I had become an experimental psychologist (I don't think I have!) Another compared the experiment to auctioning off a pound note, where the highest bidder gets the pound but the second highest bidder also has to pay up (and the players are unable to collude): the game reaches an interesting psychological stage when the bidding passes 50p (and the auctioneer is going to make a profit), then again at 1 pound, when each player is bidding so as not to lose money, ...
Another person smothered me in Hofstadterian self- reference, but did not actually offer a bid.
There were also various guesses at the likely distribution of bids, though nobody was particularly close. More interesting, perhaps, were the comments used to justify particular entries. A selection follows:
0: "I shall not hold you to the full sum if I win!"
"If this should turn out to win the prize, I will consider accepting your entire life savings in lieu of my entitlement."
"It maximises my expected gain."
[If 0 had won, my lawyers were going to argue that 1000/0 could be minus infinity as easily as it could be plus infinity...]
1: "You never know..."
"As an unreasonably hopeful gamble."
"Because I am a hopeless idealist."
"Because I said I would."
5: "It wouldn't be worth bothering with this for less than two pounds."
11: "Just in case EVERYONE is relatively sensible and doesn't go higher than ten."
32: "It was as near as I could get to the square root of 1000."
38: "I need the money."
42: "It may not be the best answer but it is the ultimate answer." [Justification by means of the original GROGGS package, which always produced the answer 42. The entrant claimed to have run it with OPT DEBUG, thus getting the most fundamental question printed out for him; he has unfortunately now forgotten what that question was.]
57: "Thought is useless, since other entrants are equally unpredictable. My magical number is therefore a random number between 1 and 100."
84: "42 is too obvious, so double it."
"It's the closest I can get to a Vendepac coffee!"
1000: "This is because I am an awkward sod. Is the object of the trial to demonstrate than any population always contains at least one awkward sod?"
"As I see it, the cost of entering is 0, so any sum won is infinite profit."
1003: "I hope this mucks up whatever approximation to a normal distribution you were trying to produce." [I would have been very surprised to get a Normal Distribution!]
I therefore declare J. Fisher (JF101) the winner, though other entrants will be consoled to know that they all won exactly as much as she did: nothing! The largest sensible entry was probably 111 (sensible in the sense that, if all higher ones were ignored, it would win a nonzero sum of money!)
Anyway, my thanks to all who entered, and raspberries to all who were too lazy!
Jonathan R. Partington
April 2nd 1987
P.S. Today's useless fact. Did you know that "Metamagical Themas", as well as being an anagram of "Mathematical Games", is also an anagram of "Chemist, eat amalgam", "Thematic lemma saga" and "Malice at Maths game"?
Last updated December 7th 2002