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A tedious verification of a banal comment

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Feb 10, 2024, 12:47:24 PMFeb 10
Tim posted a clip in another thread of Gus Hansen against Bob Koca.
Naturally, I watched the clip, heard the commentary and ordered the t-shirt.

The commentators (one of them) made a claim that in a gammonless
position at 3A 1A post-Crawford, the leader's take point is only 1%.

At time of writing, I haven't checked this. The purpose of this post is
to verify this in real time. (My real time anyway -- it won't be real time if
you're reading this later.)
Dropping gives a 2A 1A post-Crawford position. This free drop position
gives the leader 51.2% winning changces according to Rockwell-Kazaross.

Let x be the match-leader's game-winning probability and select x
so that the match-winning chances from dropping and taking are the same.
Such an x will be the take-point -- the point at which dropping and taking
are equally good.
Dropping leads to 51.2% but what does taking lead to?
Clearly, x will be part of the answer.
Taking leads to a match-winning-probability (for the match-leader)
of x + (1-x)/2. This is because the match winning possibilities are to
win immediately (x) or to lose and win the final game (1/x)/2.
So x + (1 - x)/2 = 51.2%.
(x + 1)/2 = 51.2%
x/2 = 1.2%
So x = 2.4%
This is absolutely miles away from the commentator's "one percent".
Bear in mind that these computations use a very low estimate for
the value of a free drop. So x might well be even larger.
The commentary was just major bullshit!
If Trump loses the presidential election, should we bring him in as a
backgammon commentator? He wouldn't be able to do any harm that
way, and if spreading bullshit is the main qualification, he might be
an ideal candidate.

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