# [FoRK] penny pitching or bit bashing?

Dave Long dl at silcom.com
Fri Mar 5 00:14:51 PST 2004

```
> > Say one knows for certain that a bet
> > will win with odds of 51%, but there
> > are parties offering even payouts.
>
> I think that game is compute-reducible to
> the traditonal matching pennies game.  If one
> has a pure strategy and the other has a mixed, I think
> I remember that one player can get a dominant strategy
> by pitching 7 Heads to 12 tails ...

Sorry I wasn't clear: the game is
betting on external events, say a
series of coin flips, not a matter
of guessing/matching strategies.

Perhaps I offer you a fair payoff on
50:50 odds, and you know that I flip
the coin starting with heads up, so
you should win with heads 51% of the
time.  What is your best play as an
arbitrageur?

On a completely unrelated topic, I'm
sure FoRKs are all aware of bit error
correction over noisy channels.  If
one has a channel that has a certain
probability (pulling a number out of
thin air: 49%) that it sends 1 where
we intended to send 0, or vice versa,
and we want to send a message which
is M bits long, by adding redundancy
we get a packet of M + Mr = Mec bits
that almost always behaves as if we
had sent the original M bits over a
perfectly reliable channel.

Now that Shannon is spinning in his
grave:

> > A) what is the optimal fraction of
> >    one's stake to bet per flip?
> > B) what is the expected return?

-Dave
```