Re: What have we learned..? Re: How fast can you cheat..?

Here's a proposal that I think will get you takers.

You won 8 out of 10 matches against gnubg. That makes you a 4-to-1 favorite.
So you should be happy to give 3-to-1 odds. That is, you play a series of
31-point matches against gnubg with Mersenne Twister. For every match you
win, you earn $1. (I say $1 for convenience; obviously we can multiply the
dollar figures by any base amount we agree on.) For every match you lose,
you lose $3. After ten matches, you should expect to be ahead $2.

The protocol involving the Mersenne Twister would be as follows. Your
opponent would secretly choose seeds, and send you the dice rolls one
at a time. After each match, your opponent would switch to a completely
different seed. The seed, however, would not be tampered with during
the course of a single 31-point match. After all the matches were over,
your opponent would send you the seeds so that you could verify that the
Mersenne Twister was indeed used.

Here's another proposal that might be even more attractive. I assume that
you can not only beat gnubg when it uses the Mersenne Twister, but you can
tell when the Mersenne Twister is being used. So you could agree ahead of
time to play, say, ten 31-point matches. Your opponent would secretly
decide to run five of them using the Mersenne Twister, and the other five
using some other generator, say Blum-Blum-Shub. You would then play the
matches as in the above scenario. After each match, you would state which
generator was used for that match. At the end, your opponent would tell
you which generator was used for which match, and would send you the seeds
to verify. Matches using the Mersenne Twister would pay off at 3-to-1 odds
as before, while matches using Blum-Blum-Shub would pay off at 1-to-1 odds
since you claim no advantage in that case. If you offer 3-to-1 odds for
your ability to peg the generator, then you would get $1 for each correct
guess and lose $3 for each incorrect guess.

In the latter scenario, say you win 4 out of 5 matches against the Mersenne
Twister, and 2 out of 5 matches against Blum-Blum-Shub. Say also that you
guess correctly which generator was used 9 out of 10 times. Then your net
gain would be 4*1 - 1*3 + 2*1 - 3*1 + 9*1 - 3*1 = 6 dollars, which is three
times as much as you would get in the first proposal.

At these odds I'm sure you'll find interested parties, with one catch: How
can you prove to your opponent that you'll pay up if you lose?
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.

Relevant Pages

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  • Re: Using /dev/random or /dev/urandom in C code
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    ... >The random number generator has a certain period after which it repeats. ... >Lookup Mersenne Twister. ... >Python uses the Mersenne Twister as the core generator. ... >Perl seems to be much faster than Python but Perl fails the DieHard test ...
    (sci.math)
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