[Beowulf] OT: public random numbers?

[Andrew Piskorski]

On Fri, Aug 26, 2011 at 08:17:46PM +0200, Vincent Diepeveen wrote:
> On Aug 26, 2011, at 10:43 AM, Shawn Hood wrote:

>> A betting system will not improve the negative mathematical  
>> expectation of a casino game.

Right.

> Except that this system doesn't have a negative expectation. it has a  
> positive expectation.
> 
> There is no other system in roulette that has a positive expectation,  
> other than the doubling system.

Vincent, are you shitting us?  Or am I misremembering the tortured
history of this thread, and by "doubling system" you do NOT mean the
trivial martingale betting system that's been used (disastrously) and
analyzed for over 200 years?

Actually it doesn't matter; as Shawn Hood pointed out above, your
assertion is still wrong even if you actually meant some other
non-martingale betting system.  You insisting that *martingale*
betting gives you a positive expectation at roulette just makes it
much funnier!

There are ways to gain positive expectation in roulette (other than
the obvious fraud and collusion).  They involve finding a poorly
installed roulette table and using a wearable computer and physics to
predict where the ball will land.  Look up Thorp and Shannon's
research on the subject; they actually used it in casinos c. 1961.

None of those ways are due to some special method of betting.  The
point of betting systems is to optimize your small edge, but you have
to HAVE that edge in the first place.  Money management is important
because tells you how to properly size your risk, but it can't give
you alpha.

Now yes, if you have a very volatile "roulette" game and a 0% edge (no
advantage to either you or the house), with some luck you could get
rich by playing it for a limited period of time and quitting while
you're ahead.  But you still have a 0% expectation game; look up the
mathematical definition of "expectation".

Also, I don't remember for sure, but I believe martingale betting is
(always) more aggressive than Kelly.  If so, then it is inherently
stupid.  Kelly defines the MAXIMUM size bet that it is rational to
make, assuming your goal is maximum compounded wealth AND you have a
quantifiable edge (however small) in the game.  It can make sense to
bet less than Kelly, and if you believe you have no edge the rational
bet is zero.  It is never rational to bet more than Kelly.

In practice, even when you are sure you have a real edge, you want to
bet less than Kelly, often much less.  There are several reasons for
that; one is that calculating Kelly depends on your estimate of how
big your edge is, and it is easy to overestimate your edge such that
in truth you are massively overbetting (taking way too much risk) at
2x Kelly or even more.

But optimizing the way you bet doesn't turn an inherently losing game
into a winner.  If the edge is with the house - as it certainly is
with a fair roulette table - the rational bet is not to make one.

This news article is probably more interesting:

  http://www.theonion.com/articles/casino-has-great-night,1506/
  Casino Has Great Night; May 28, 2003

-- 
Andrew Piskorski <atp at piskorski.com>