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A few nights ago, in yet another desperate attempt to
improve my game, I sat down with a copy of Kit Woolsey's
Match Equity Table and high hopes of memorizing it. He must
be joking! That table is 15 columns by 15 columns of
numbers! Who does he think I am, Alfred Einstein?
Besides, suppose you happen to remember that your equity
at 11-away, 3-away is 10%. What do you do with that
priceless morsel of information? How do you estimate what
your chances of winning the game at hand are? Here's the
way Bill Robertie says to handle it (partial quote from
ADVANCED BACKGAMMON, Volume 1):
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Over-the-board, aside from guesswork and intuition, only a
case-by-case analysis offers any chance of lending some
insight to this position. Let's see how this might proceed.
Play (a):
White's replies to this play fall into three pretty clear
groups: rolls which hit back (14), rolls which enter one man
without hitting (13), and bad shots which enter at most one
man (9). When White hits back...(analysis)...I'll give
Black only 25% of these games, or 3.5 games out of 14.
White enters both men but doesn't hit...(analysis)...I'll
make Black 50% in this variation, giving him 6.5 games out
of 13. White rolls badly...(more analysis)...I'll give
Black 5 games out of 9. Totals for Play (a): Black gets 3.5
games in the first group, 6.5 in the second group, and 5 in
the last group, a total of 15 games out of 36.
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Once you've figured out Play (a), you do similar
calculations for Plays (b), (c), (d), and (e), total the
results, take the cube root, mulitiply by the distance from
the sun to Jupiter in parsecs, divide by the angle at the
tip of Madonna's bra in radians, and you come out with an
equity of 13%. You compare that to the match equity of...
ummm, ummm. Keep in mind that all this time your opponent,
back from his walk around the playing area, is tapping his
fingers and mumbling semi-intelligible comments about chess
clocks.
Maybe top players actually do those calculations during a
game and memorize all kinds of odds and tables. For those
of us mere mortals who actually have lives, however, I have
created an Equity/Action Table. This greatly simplified
table not only considers match equity, but also tells you
what to do in many real-life situations. It is a lot easier
to memorize than Kit's table, because it's smaller (if
you're 1-away, 13-away and don't know what to do, I don't
want to tell you), uses letters instead of numbers, and has
recognizable patterns. Here it is:
"Unrevised Equity/Action Table"
Opponent
1 2 3 4 5
1 TD DD DD DD DD
2 DS WD PC NT DM
Y
o 3 DS PC QE PC NT
u
4 DS NT PC QE PC
5 DS DM NT PC QE
TD - Tactical Double. Double. Your opponent might drop, or
he might get steamed. You have nothing to lose, unless you
dread getting flamed on r.g.b.
DD - Don't Double. Whatever you do, hold the cube. The
Tactical Double reasoning does not apply.
DS - Double, Stupid! If you have to refer to the chart in
these situations, I'd be interested in playing you for money
at your earliest opportunity.
WD - Woolsey double. Kit says you should double in this
situation as soon as you have an actual chance to roll. If
you believe him, double.
PC - Pretty close. If you think you're a better player than
your opponent, you have to pay more attention or get
luckier. If you're an underdog, just keep doing what you've
been doing.
NT - Not Too. The situation you're in is either not too bad
or not too good. Act accordingly.
DM - Desperate Maneuvers. If you are ahead, expect your
opponent to make maniacal plays and cube turns. If you're
behind, make maniacal plays and cube turns.
QE - Quite Even. Equity here is easy to evaluate. Also
applies at the beginning of matches.
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