Re: Heuristic probability quickie.

quasi <quasi@xxxxxxxx> writes:
On 16 Oct 2007 17:02:39 +0300, Phil Carmody
<thefatphil_demunged@xxxxxxxxxxx> wrote:

Imagine a game of skill, something like go would fit.

Imagine 3 experienced players of this game, A, B, and C say,
such that over their game histories A beats B about 60% of
the time, and B beats C about 60% of the time.

What proportion of the time would you expect A to beat C?

Let's model the strength of the players by using biased coins. Assume
Heads beats Tails. Thus the stronger player will have a coin more
biased towards Heads than that of a weaker player.

When 2 players play a single game, they flip their coins
simultaneously, repeating until there is a mismatch. A mismatch ends
the game, with Heads beating Tails.
....
Hence, if x = 3/5 and y = 3/5, then z = 9/13

Wow - another derivation which returns the same 'relativistic
velocity addition' answer. Of course, it's using the same
assumptions, just worded differently. I find this particular
model the one whose wording of the premises I find the easiest
to reject.

Phil
--
Dear aunt, let's set so double the killer delete select all.
-- Microsoft voice recognition live demonstration
.

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