Forum Archive :
3-away/4-away: what's the correct equity?
: Leader's drop point at 3-away, 5-away is quite sensitive
: to the match equity you assume for 3-away, 4-away.
: The higher the value of Trailer's equity at 3-away, 4-away,
: the more reluctant Leader will be to give up one point when
: the score is 3-away, 5-away.
: Kit Woolsey's table lists Trailer's 3-away, 4-away match
: equity at 41%. But there are other tables (e.g., Norman
: Zadeh's) which place the value for this score as high as 43%.
: Each one point increase in the assumed value of Trailer's
: equity at 3-away, 4-away produces a two or three point rise
: in Leader's drop point at 3-away, 5-away.
: So, as much as anything else, the position of Leader's drop
: point at 3-away, 5-away depends on which match equity table
: you use.
Kit Woolsey wrote:
> Good point, Tom. Let's see what this means if we use Zadeh's 43%. I
> don't know what his figure is for 1 away, 5 away Crawford, so let's
> assume it is the same as mine (85% for the leader). Now, let's look at
> the leader's drop point, assuming no gammons:
> Leader passes: He is ahead 4 away, 3 away for 57% equity.
> Leader takes and wins: He is ahead 1 away, 5 away for 85% equity.
> Leader takes and loses: He is even, for 50% equity.
> Thus he would be risking 7% to gain 28%, so he would be getting 4 to 1
> odds on his take. Therefore, he could take with 20% winning chances,
> ignoring possible recube vig.
> This just doesn't feel right, does it? All our intuition tells us that
> the leader should be more cautious in taking the cube than he should be
> in money (except possibly where the double puts him out exactly), but
> these figures say he can take positions which are clear money passes.
> To me, this indicates that Zadeh's 43% figure has to be off.
Maybe not. There is an "odd-even" effect on match scores that can
produce surprising results. Since points in backgammon often come
in twos and fours, the opponent's match-winning chances take a big
step forward when he goes from 5-away to 4-away. At 4-away he can
win the match with one doubled gammon or two 2-point games.
Because a one-point loss is so expensive when the opponent is 5-away,
and a two-point loss not that much worse, the leader is more willing
than usual to try turning the game around rather than give up exactly
> When I constructed my match equity table, one of the things I did was to
> introduce smoothing effects so anomalies such as the one above would be
> avoided. Thus I believe my table will lead to more practical results in
> one's match equity calculations.
Here's an interesting question: Which is better, leading a match at
at 3-away/4-away or leading at 4-away/5-away?
- 1-away/1-away: advice from Bernhard Kaiser (Darse Billings, July 1995)
- 1-away/1-away: advice from Stick (Stick+, Mar 2007)
- 1-away/1-away: and similar scores (Lou Poppler, Aug 1995)
- 2-away/3-away: playing for gammon (Tom Keith, Feb 1996)
- 2-away/4-away: Neil's rule of 80 (Neil Kazaross, June 2004)
- 2-away/4-away: cube strategy (Tom Keith, Dec 1996)
- 2-away/4-away: practical issues (Mark Damish, Jan 1996)
- 2-away/4-away: trailer's initial double (Kit Woolsey, Jan 1996)
- 3-away/4-away: opponent's recube (William C. Bitting+, Feb 1997)
- 3-away/4-away: racing cube (Bill Calton+, Nov 2012)
- 3-away/4-away: tricky cube decision (Kit Woolsey+, July 1994)
- 3-away/4-away: what's the correct equity? (Tom Keith, Sept 1997)
- 4-away/4-away: take/drop point (Gary Wong, Oct 1997)
- 5-away/11-away: redouble to 8 (Gavin Anderson, Oct 1998)
- 7-away/11-away: volatile recube decision (Kit Woolsey, May 1997)
- Both too good and not good enough to double (Paul Epstein+, Sept 2007)
- Comparing 2-away/3-away and 2-away/4-away (Douglas Zare, Mar 2002)
- Crawford rule (Chuck Bower, May 1998)
- Crawford rule (Kit Woolsey, Mar 1997)
- Crawford rule--Why just one game? (Walter Trice, Jan 2000)
- Crawford rule--history (Michael Strato, Jan 2001)
- Delayed mandatory double (tem_sat+, Oct 2010)
- Delayed mandatory double (Donald Kahn+, Dec 1997)
- Doubling when facing a gammon loss (Kit Woolsey, Jan 1999)
- Doubling when opponent is 2-away (David Montgomery, Dec 1997)
- Doubling when you're an underdog (Stein Kulseth, Dec 1997)
- Doubling window with gammons (Jason Lee+, Jan 2009)
- Free drop (Ian Shaw, May 1999)
- Free drop (Willis Elias+, Oct 1994)
- Gammonless takepoint formula (Adam Stocks, June 2002)
- Going for gammon when opp has free drop (Kit Woolsey, Jan 1998)
- Going for gammon when opp has free drop (Kit Woolsey, Apr 1995)
- Holland rule (Neil Kazaross, Apr 2010)
- Holland rule (Kit Woolsey, Dec 1994)
- Leading 2-away with good gammon chances (Douglas Zare, Feb 2004)
- Match play 101 (Max Urban+, Oct 2009)
- Matches to a set number of games (Tom Keith+, Oct 1998)
- Playing when opponent has free drop (Gilles Baudrillard+, Dec 1996)
- Post-crawford doubling (Scott Steiner+, Feb 2004)
- Post-crawford doubling (Maik Stiebler+, Dec 2002)
- Post-crawford doubling (Gus+, Sept 2002)
- Post-crawford mistakes (Rob Adams, Sept 2007)
- Post-crawford/2-away: too good to double (Robert-Jan Veldhuizen, July 2004)
- Slotting when opponent has free drop (onur alan+, Apr 2013)
- Take points (fiore+, Feb 2005)
- Tips to improve cube handling (Lucky Jim+, Jan 2010)
- When to free drop (Dan Pelton+, Oct 2006)
- When to free drop (Tom Keith+, July 2005)
- When to free drop (Gregg Cattanach, Dec 2004)
- When to free drop (Kit Woolsey, Feb 1998)
- When to free drop (Chuck Bower, Jan 1998)
- Which format most favors the favorite? (Daniel Murphy+, Jan 2006)