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Problem for cube theory specialists

Posted By: John O'Hagan
Date: Thursday, 20 March 2014, at 5:29 p.m.

In Response To: Problem for cube theory specialists (__1ERROR1__)

Compare the gain vs. the risk from redoubling. First the risk. In order to answer this, you need to see if Black should redouble to 16 if he gets a chance to roll. If Black doesn't redouble to 16 and loses this game, he's down 0-10 with about 7% MWC; does redouble and loses loses the match so redoubling risks 7%. If Black doesn't redouble to 16 and wins this game, he's up 8-2 with ~80% MWC; does redouble and win wins the match. So redoubling risks 7 to gain 20. r/r+g = 7/27. He wins 14/36 so it's a clear recube.

If you don't redouble and lose this game, you will trail 2-4 with about 40% MWC, do redouble and lose and you lose the match. So the risk from redoubling is 40%.

Now for the gain. Don't redouble and win the game gives you a 6-0 lead with ~77% MWC. If you do redouble and win you're either ahead 10-0 with ~93% MWC or you win the match. About a quarter of your wins are when you roll an immediate double (6/36 vs. 30/36 x 22/36). So, using a weighted average, your MWC when you win are 75% of the way from 93% to 100% which is 98.25%. Your gain from redoubling is then 21.25%.

So redoubling risks 40 to gain 21.25. r/r+g = less than 2/3. Oppt wins 30/36 x 14/36 = 420/1296 which is < 1/3 which means you win over 2/3.

Recubing is therefore correct assuming equal players.

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