Four positions from the
historic
Hope and Anchor
versus Whine and Dine SEMI-FINAL
by Simon
Gasquoine
Hope and Anchor got stuffed 7-2 by Whine and Dine on
Friday night in Ryan’s back yard to the accompaniment of
a crescendo of head-banging music from the basement below.
We should’ve forced a draw by appealing for the light to
umpire Mike, but gamely continued in the semi-darkness.
A number of interesting positions were recorded by
Stefanie (to whom thanks) before it got too dark to see
dice, checkers or the players themselves. Brian has
already publicised the decision which Hope and Anchor got
horribly wrong. Here are four which everybody
managed to get right. I’ve pasted in the full
Snowie data at the end for those who are interested, but
there’s no need for the uninitiated to set out through
the quagmire.
Position 1
Should Black (Whine and Dine) double? Can Red (Hope and Anchor) take?
A simple pip count (60 : 63) gives Black (Whine and Dine)
only a 5% lead and if Red’s (Hope and Anchor’s)
checkers were distributed as neatly as White’s the
position would be nowhere near a double. But here
Red’s checkers aren’t likely to bear off as
efficiently as Black’s and we need to try to quantify
the necessary adjustments rather than just take a wild
guess. Penalties are required for (a) the gaps and
(b) the surplus checkers on the ace and deuce points.
The values for these suggested by Paul Lamford in Improve
Your Backgammon (pp 12-13) allow a very accurate estimate
of the winning chances:
● A gap on the
four-point is usually serious and should incur on average
4 penalty pips, but as one of the checkers in the outfield
may fill it, I thought 3 penalty pips should suffice.
● The gap on the
three-point would normally incur a 2 pip penalty, but here
it doesn’t much matter as when we roll threes we can use
surplus checkers from the six-point to fill it.
Therefore no pip penalty for this.
● The third checkers
on the ace- and deuce-points impair the efficiency of our
bear-off as we are liable to waste pips when we have to
use bigger numbers than ones and twos to bear these
checkers off. We add 2 pips for the third checker on
the ace point and 1 pip for the third checker on the deuce
point.
●The extra
crossover from the outer to inner board is average for the
race difference and requires no penalty.
So we have a total of 3+0+2+1+0 = 6 penalty points and the
adjusted pip counts are therefore 60 for Black and 69 for
Red, a lead of 15%. Clearly a big cube and equally
clearly a big pass. Snowie has the position in its
database and gives White 80% wins; Paul’s formula on
page 10 of Improve isn’t needed this time, but for the
record it gets the equity within 1%.
Cube
action equity
Database
Money
equity:
0.599
0.0%
0.0% 80.0% 20.0%
0.0% 0.0%
1.
Double,
pass
56.48%
2.
No
double
55.78%
(-0.71%)
3.
Double,
take
57.25%
(+0.77%)
Proper
cube action: Double,
pass
Position 2
Should Black double? Can Red take?
Black’s cube looks obvious. Only a very timid
player would delay cubing for a further roll, for by that
time the pass is liable to look beyond doubt. Red has two ways of winning. We can win the race, or –
far more likely – we can hit a shot and cash the game
with an untakeable recube. Shots are prone to get
left when bearing in against an anchor with a gappy
position like this one – but shots still have to be hit.
We passed (correctly), but weren’t at all sure this was
right.
So what are the benefits of hindsight? Unlike the
previous problem, this can’t be evaluated by any formula
known to man or beast. It’s the kind of board for
which a previously learned reference position is the best
guide. If we simplify by putting the seven-point
blot somewhere safe like the eight-point, Red turns out
to have a fairly clear pass (though it’s misevaluated as
a narrow take by Snowie 4). That’s the reference
position to remember. So: is the blot in Friday’s
position an asset or a liability for Black? Their
blot activates 2-1 and 3-2 as numbers which fill in the
five-point, an enormous gain in future safety. (Double
one makes the five-point in either version of the position.)
But there is a little bit more weighing on the debit side.
3-1 can’t make the five-point as that would leave leave
the blot exposed, as do double twos and threes, whilst
double fives exposes a blot on the six-point. So we
have some extra vig – but not enough to accept the cube.
The Snowie live cube figures in the chart below are more
reliable than the evaluation figures, Paul Lamford points
out, because Snowie discovers when it rolls the position
out that we get very little value for cube ownership: we
can use it only to cash games we’ve pretty much won
anyway.
Cube
action equity
Rollout
Money
equity:
0.587
0.0%
2.3% 78.7% 21.3%
1.0% 0.0%
95%
confidence interval:
- money cubeless eq.: 0.587 ±0.008,
- live cube no double: 56.98% ±0.17%,
- live cube double take: 57.81% ±0.17%.
Rollout settings:
Truncated rollout, depth 7,
128 games (equiv. 45838 games),
played 2-ply (precise), cube 3-ply,
random seed, with race database.
Evaluations
1.
Double,
pass
57.33%
2.
No
double
56.75%
(-0.57%)
3.
Double,
take
57.37%
(+0.05%)
Proper
cube action: Double,
pass
Live
cube
1.
Double,
pass
57.33%
2.
No
double
56.98%
(-0.35%)
3.
Double,
take
57.81%
(+0.48%)
Proper
cube action: Double,
pass
Position 3
Red to play 4-2.
Both sides have similar set-ups with 20-point anchors and
flexibility problems caused by outfield points stripped of
spare checkers. Points are going to have to be
demolished (unless friendly doubles pop from the dice
cups, enabling points to be moved homewards intact).
Direct shots will be left. But can be right to leave
a voluntary shot right now when we can still play safe –
and, if so, which voluntary shot should it be?
The safe but horribly unaesthetic play is to trash the
home board with 6/4 3/1, killing two checkers. But
we’ll never be to fix it up again and after this play
Black - who is nearly as stretched as we are - will
usually survive getting hit. It’s better by far
(worth 2% of match-winning chances, according to Snowie)
to leave a shot. We opted to play 7/3 6/4, making
one inner board point and slotting another. Snowie
gives this the nod, but likes 13/7 almost as much.
This leaves more immediate shots (sixteen compared to
eleven with our play) but, if Red isn’t hit, fewer
shots on the following roll and the likelihood then of
improving the home board. Not much in it.
#
Ply
Move
Equity
1
R
7/3
6/4
40.27%
0.3%
9.5% 42.6% 57.4% 14.9%
0.5%
Live
cube rollout: 40.28%
95%
confidence interval:
- money cubeless eq.: -0.205 ±0.015,
- live cube: 40.28% ±0.23%.
Rollout settings:
Truncated rollout, depth 5,
108 games (equiv. 32255 games),
played 2-ply (standard), cube 3-ply,
random seed, without race database.
2
R
13/7
40.18%
(-0.09%)
0.2%
7.3% 41.1% 58.9% 10.9%
0.3%
Live
cube rollout: 40.09%
95%
confidence interval:
- money cubeless eq.: -0.216 ±0.013,
- live cube: 40.09% ±0.14%.
Rollout settings:
Truncated rollout, depth 5,
108 games (equiv. 34261 games),
played 2-ply (standard), cube 3-ply,
random seed, without race database.
3
R
6/2
3/1
38.29%
(-1.98%)
0.1%
4.5% 37.2% 62.8% 13.6%
0.3%
Live
cube rollout: 38.46%
95%
confidence interval:
- money cubeless eq.: -0.348 ±0.013,
- live cube: 38.46% ±0.22%.
Rollout settings:
Truncated rollout, depth 5,
108 games (equiv. 28956 games),
played 2-ply (standard), cube 3-ply,
random seed, without race database.
Position 4
Red to play 6-3.
Once again, three choices:
(a) Hit with the three and play the six 13/7 (forced).
(b) Make a five point board with 13/4, leaving a direct
double shot.
(c) Dismantle the midpoint with 13/7 13/9.
The correct move, as played, is (c). It leaves us
with covers for the four-point, a spare to run around back
on the 20-point and good chances of later shots as Whine
and Dine clear their outfield points. The gonzo
hitting play (a) turns out to win fewer games and it has
gammon written all over it, or so it might seem, leaving
Black eight double hits from the bar (4-1, 4-2, 4-5, 4-6) and
ten single hits (4-3, 4-4, 5-1, 5-2, 5-5, 5-6). Only
5-3
re-enters and fails to hit. The gammon downside of
play (b), leaving only a single target blot, appears to be
much reduced.
But this is all a bit misleading, for with correct cube
handling by both sides, Red can make either play (b) or
(c) and never actually get gammoned at all – but these
plays always lose a single game. They are in fact
technically identical, for Black should cube after either
and Red has either a big pass, after play (b), or an
absolutely massive pass, after play (a). After (c),
Snowie thinks Whine and Dine have a marginal double, but
it changes its mind when it’s told to roll the position
out and approves of their restraint.
#
Ply
Move
Equity
1
R
13/7
13/10
37.40%
0.1%
2.8% 30.8% 69.2%
6.1% 0.2%
Live
cube rollout: 36.16%
95%
confidence interval:
- money cubeless eq.: -0.420 ±0.008,
- live cube: 36.16% ±0.21%.
Rollout settings:
Truncated rollout, depth 5,
162 games (equiv. 43332 games),
played 2-ply (standard), cube 3-ply,
random seed, without race database.
2
R
13/4
35.54%
(-1.86%)
0.1%
3.3% 23.2% 76.8% 17.7%
0.3%
Live
cube rollout: 35.54%
95%
confidence interval:
- money cubeless eq.: -0.682 ±0.020,
- live cube: 35.54% ±0.00%.
Rollout settings:
Truncated rollout, depth 5,
54 games (equiv. 10970 games),
played 2-ply (standard), cube 3-ply,
random seed, without race database.
3
R
20/17*
13/7
35.54%
(-1.86%)
0.2%
8.5% 28.5% 71.5% 41.6%
3.2%
Live
cube rollout: 35.54%
95%
confidence interval:
- money cubeless eq.: -0.791 ±0.030,
- live cube: 35.54% ±0.00%.
Rollout settings:
Truncated rollout, depth 5,
54 games (equiv. 8898 games),
played 2-ply (standard), cube 3-ply,
random seed, without race database.
Simon Gasquoine
17 June 2003
by Paul Lamford,
Simon Gasquoine
and Stefanie Rohan
