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Meta-MET Needed for Best 2 of 3 Matches

Posted By: Taper_Mike
Date: Thursday, 28 July 2011, at 10:17 p.m.

In Response To: Meta-MET Needed for Best 2 of 3 Matches (Michael Petch)

Thanks for the links. I followed the link to rec.games.backgammon where I found this very elegant mathematical proof.

Mike

Question:

On 12 Jun 2002 02:54:05 -0700, j...@chem.sdu.dk (jthyssen) wrote:

Does it change your doubling strategy when playing multiple matches? You will now have a MWC (current match winning chance), but also a TMWC (total match winning chance). I would most likely tend to use MWC for my doubling strategy, but wouldn't it be more correct to use TMWC? Of course, if the match is tied 1-1 best of 3, we have MWC = TMWC, but for all other scores MWC <> TMWC.

Answer:

Since

TMWC = MWC * P1 + (1-MWC) * P2 = P2 + (P1-P2) MWC

with P1 being TMWC after winning the current match, P2 being TMWC after losing this match, and (P1-P2) obviously positive, you maximize TMWC by maximizing MWC.

-- Nis Jorgensen Amsterdam

Source: https://groups.google.com/group/rec.games.backgammon/msg/41e719446a5cba80?hl=en

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