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Here's a real one, but a bit tougher

Posted By: Daniel Murphy
Date: Saturday, 2 February 2008, at 3:55 a.m.

In Response To: Here's a real one, but a bit tougher (Chuck Bower)

DC has given us the clever general solution which applies here to Chuck's first question: determine how many losses there must be; that's how many matches must be played.

Of 91 players, 85 have lost three times, 5 prize winners (2nd-5th and the consolation winner) have lost twice, and the champion has lost either once or no times. So, either 266 or 265 matches will be played in the tournament.

With the original problem of 637 players and single elimination, I think my point was this:

an answer could be calculated for 637 players and calculated again for some other number of players. But why bother? Much more satisfying and useful is to find the solution that allows equivalent problems to be solved without calculation.

(One way to calculate for 637 players would be to realize that we need to eliminate 125 losers in a round full of byes so we can eliminate 512/2 + 256/2 + 128/2 + 64/2 + 32/2 + 16/2 + 8/2 + 4/2 + 2/2 in subsequent rounds. A clue immediately presented itself: how many matches were needed to eliminate 125 losers?)

Likewise, when playing backgammon, save the strain and time consumption of calculation for positions where calculation is appropriate. For the rest, look for the features that identify a position as one for which the solution can be more directly found by applying the appropriately thematic solution from our kit bag of experience-based references and guidelines. This will mean, often, that one need not be intent on finding the best move -- who has time? -- but a very good move for very good reasons.

In Michigan, don't lose in the last game of the winner's bracket! The loser of that game has a 1/16th chance of winning the tournament; the winner, 3/4ths.

As to Chuck's second question -- has anyone in Michi ever lost in the main flight semis, the loser flight quarterfinal, and gone on to play in the consolation final? Respect!

And don't lose in the first round of the main, either!

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