From: John Conover <john@email.johncon.com>
Subject: Re: CNET.com - News - E-Business - Latest dot-com bomb: TheMan.com
Date: 4 Nov 2000 02:34:24 -0000
And what should Gore do with a 22% chance of winning? What is his
optimal strategy?
He should use a Greedy algorithm, (which has characteristics of what
the mathematicians call a "Devils Stair Case",) over the next four
days, which means he bets half of 47 - 43 = 6 / 2, or 3% of his
tracking poll, every day, until he is in the lead.
This means Gore should risk PO'ing 3% of his constituents for a chance
at gaining 3% of Bush's constituents, every day until the end of the
election, or until he is ahead of Bush, (i.e., sling some mud.)
And what would Gore's probability of winning be?
let r = (1 - p) / p = (1 - (0.43 / 3)) / (0.43 / 3) = 5.98
P = (r^0.43 - 1) / (r^0.47 - 1) = 0.89
remarkably, almost 90%!
That is, unless G. W. Bush does the same thing, in which case it moves
Gore's chances back to a 22%.
Bottom line, mud slinging is not only the way of politics-its optimal.
And, in the current state of affairs, Gore has absolutely nothing to
lose by slinging mud, (with only a 22% of winning if he doesn't.)
John
BTW, tsinvest does not use a Greedy algorithm, or Devils Stair Case.
If p < 0.5, it simply refuses to invest in the stock-and if no stocks
have p > 0.5, it will withdraw from the market, (although you can
override this if you are foolish-its the -D option.)
John Conover writes:
> That's about a 4 in 5 chance of winning. But it can be wrong 1 chance
> in 5, too. What this means is that you play this game many times, you
> will win 4 out of 5 times.
>
> So, you wouldn't want to bet your nest egg on it, (you stand a 20%
> chance of losing everything on the first game, if you do, and you
> can't play any longer.) But you have to bet something, otherwise you
> can't make anything, (another of mathematics most profound insights.)
>
> The optimum lies in between. And the magic optimum is when F = 2P - 1,
> where P is the probability of a win, (0.78 on Bush in this case,) and
> F is the fraction of your nest egg to wager, (or about 56% in this
> case.)
>
> Based only on the popular vote, of course-and I don't know any bookies
> that taking bets based only on the popular vote.
>
> John
>
> BTW, the -d option to tsinvest controls how the program does this
> methodology; the -d1 is what was outlined here.
>
> John Conover writes:
> >
> > So, Bush has a 0.84 * 0.93 chance of winning, or about 78%,
> > (considering only the popular vote,) based on the accuracy of the
> > tracking polls, and the ability of Gore to move them.
> >
>
--
John Conover, john@email.johncon.com, http://www.johncon.com/