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The following is a copy of some recent correspondence
I've had on this subject. (As an anti-spam measure,
e-mail addresses have been deleted. If you want to
send me e-mail, delete "ferrari." from the address in
the header above.)
Gerry Tesauro
(Author of TD-Gammon)
=========================================================================
Date: 28 January 1997, 18:23:40 EST
From: Gerry Tesauro
To: Douglas Metcalf
Re: TD-Gammon
Ref: Your note of 28 JAN 97 07:10:39 CST
Thanks for your comments. If you can manage to get a copy
of OS/2 Warp 4, it includes an Applications Sampler CD
which contains the latest version of TD-Gammon, which
has among other features an option for Manual Dice Entry.
It's been pretty interesting to see people's feedback
about the dice rolls-- people are suspicious not only of
TD-Gammon, but basically all programs that are good enough
to wins lots of games. Apart from going into a dissertation
on statistics, what I can say is the following:
(1) I'll give you my personal word of honor that the dice
rolls are honest. The dice generator has no idea whose turn
it is or what the state of the board is when it rolls.
(2) There's an elegant proof that the dice rolls can't
depend on the state of the game, based on the fact that
the random number generator is seeded by the time of day.
What this means is that, if you start two copies of the
program at the same time, you will get the exact same
sequence of dice rolls on both copies. This will hold even
if you are playing on different levels and making completely
different moves, leading to radically different game states.
Best wishes,
-- Gerry Tesauro
=========================================================================
Date: 29 JAN 97 07:52:06 CST
Subject: re: TD-Gammon
To: Gerry Tesauro
Thank you for the reply. I have Warp 4, and have now installed the newer
TD-Gammon. I can hardly wait to get a pair of dice and see how Backgammon
is supposed to be played.
I'll bet your responses have been interesting. Although I have only played
one game (in Grandmaster mode) with the new program, I would like to relate
the following incident to you, although after reading your e-mail, I'm
quite sure it is just a coincidence/bad luck.
I was ready to get my men home, with only one roll that could cause me
trouble (6,2) and the only thing that would cause me trouble after my
rolling 6,2 was the program rolling any 2. Guess what. I rolled 6,2 and
the program followed with 2,2. I think the odds of that happening are
almost 60-1, certainly not in the realm of the impossible, but even after
only one game, it is a little suspicious. I sure hope that's just my bad
luck. But I will find out for sure when I input the rolls myself, and have
played more games to see if my luck is consistently bad.
Oh, and by the way, the changes to the program, ie, resignation, manual
dice, etc, make this one of the finest (backgammon) games available. (And
it only works on my favorite operating system - too bad for those MS
folks!) Thanks for the fine work, and if I'm convinced my luck is no good
after several weeks, I am going to attempt to document my 'bad luck' with
some statistical proof, which I will forward to you.
Thanks again,
Doug Metcalf
=========================================================================
Date: 30 JAN 97 06:53:37 CST
Subject: re: TD-Gammon
To: Gerry Tesauro
Mr. Tesauro,
My apologies. TD-Gammon wins even if it lets me roll the dice! The manual
entry convinced me! Of course, now I'm wondering why I play so badly.
Which, of course, makes me wonder if perhaps someday, TD-Gammon might tell
me when I'm making an obvious mistake... Users, huh? Never happy...
Oh, well. At least I can brag to my "Windows" friends that at least I have
a real Backgammon opponent whenever I want.
Thanks, and once again, my sincere apologies sorry for doubting your
program's integrity.
Doug Metcalf
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