Forum Archive :
Terminology
> Can someone please explain equity to me and how it is calculated?
I'll try to answer this question in steps. Hopefully I will neither
insult the reader (by explaining something already known) nor lose you (by
making things too complicated and using "jargon"). Here goes:
1) in general, "equity" is "value". The word is common in financial
circles, especially in accounting.
2) in backgammon, "equity" is equivalent to "expectation"a term used
by mathematicians, especially statisticians.
3) There are two kinds of equity in backgammon: "Cubeless", and "Cubeful".
Cubeless equity is the "value" of a position if THERE IS NO DOUBLING CUBE
around, so that the game will be played to completion, and six outcomes are
possible: either side can win a simple game, a gammon, or a backgammon.
So, if we define:
W = player on roll's chances of winning a simple game,
G = player on roll's chances of winning a gammon,
B = player on roll's chances of winning a backgammon,
w = player NOT on roll's chances of winning a simple game,
g = player NOT on roll's chances of winning a gammon,
b = player NOT on roll's chances of winning a backgammon,
then we can define player on roll's equity as:
W + 2*G + 3*B  w  2*g  3*b.
(* is multiplication sign).
Some things worth noting:
a) W + G + B + w + g + b = 1. That is becuase SOMETHING MUST HAPPEN!
b) The equity for the player NOT on roll is just (1) times the equity of
the player on roll. Another way of saying this is that if we add the
equity for the player on roll to that of his/her opponent, the sum is ZERO.
c) cubeless equity will be somewhere in the range 3 to 3.
Now, what about "cubeful" equity? This is a slightly more complicated
case. Two things must now be included. If we asume the same (cubeless)
definitions above, then
a) multiply the current value of the doubling cube times the above
"cubeless" numbers to get equity. (Cubeless equity can be bigger than 3 or
less than 3).
b) ownership of the doubling cube now plays a role, so some adjustment must
be made for that. Typically +510% is added to the equity of the player on
roll (and equivalently subtracted from the player NOT on roll)
to account for cube ownership in money games. There are more complicated
ways to figure it, but this message is ALREADY GETTING LONG! At matches,
there may or may not be cube ownership equity, depending on where you are
in the match. That, too, can be quantified.
WARNING #1: With the doubling cube in play, the cubeless quantities (W, G,
etc.) are NOT each players true winning/losing chances. That is because
the cube can (and often will) be used to end games prematurely AND convert
some losses into wins. That is why the adjustment [b) above] was made. It
is also why you need to find out if rollout results (human or robot) were
performed with a doubling cube in play.
WARNING #2: For anyone familiar with Jellyfish evaluation and rollouts,
note that the numbers in the JF results windows are NOT the values I
defined above. Here is how JF defines things:
Wj = player 1's chances of winning a this game (any flavor),
Gj = player 1's chances of winning a gammon or backgammon,
Bj = player 1's chances of winning a backgammon,
wj = player 2's chances of winning a this game,
gj = player 2's chances of winning a gammon or backgammon,
bj = player 2's chances of winning a backgammon,
NOW, equity for player 1 is: Wj + Gj + Bj  wj  gj  bj.
Also, Wj + wj = 1, but the sum of all six values is not, in general.
Method is equivalent, just using "oranges" instead of "apples". Be
careful not to interchange the fruit, though...
Chuck
bower@bigbang.astro.indiana.edu




Terminology
 Alphabet soup (Tom Keith, Apr 2004)
 "Anchor and guard" position (Chase+, Apr 2010)
 "Back game" (Marty Storer, Jan 2004)
 "Baffle box" (garyo+, Mar 2005)
 "Bagai position" (Timothy Chow, Dec 2012)
 "Banana split" (Rich Munitz+, June 2011)
 "Banana split" (Adam Stocks+, Sept 2004)
 "Beavers" (Sander van Rijnswou, May 1999)
 "Beavers" (Shuman Lloyd Lee, Aug 1991)
 "Blunder", "whopper" (Raccoon+, July 2005)
 "Bot" (Pit Bull+, Mar 2004)
 "Bronstein" clock setting (rew+, Sept 2012)
 "Calcutta auction" (Roland Scheicher+, Dec 2001)
 "Chouette" (Roland Scheicher+, Mar 2002)
 "Cube provocation play" (Chuck Bower+, Apr 2007)
 "Dance" (William R. Tallmadge, May 1998)
 "Dropper" (Robert D. Johnson, Sept 1996)
 "Duplication" and "diversification" (Simon Woodhead, Nov 1991)
 "Equity" (Gregg Cattanach, Aug 2000)
 "Equity" (Gary Wong, Dec 1998)
 "Equity" (Chuck Bower, Oct 1996)
 "Equity" (Michael J. Zehr, Mar 1996)
 "Equity", "volatility", "claim", "market" (Erik Gravgaard, June 1995)
 "Freeroll" (montygram, Nov 2005)
 "Gammon price" (Ron Karr, Aug 1996)
 "Gammon rate", "gammon price" (David Montgomery, June 1995)
 "Gammongo" (GG) and "gammonsave" (GS) (Mary Hickey, Feb 2004)
 "Gammongo" (GG) and "gammonsave" (GS) (Marty Storer, Oct 2002)
 "Gammongo" (GG) (Chuck Bower, Jan 2004)
 "Golden point" (Daniel Murphy, Dec 2004)
 "Holding game" (Alan Webb+, Dec 1998)
 "In the box" (Ken Bame+, Sept 2012)
 International phrase dictionary (David Allen Sorensen, Sept 1997)
 "Joker" (Richard Divdesman, Sept 1998)
 "Kamikaze play" (Bill Patterson+, June 2011)
 "Kauder paradox" (Carl Tait+, Nov 1995)
 "Latto paradox" (JeanPierre Seiman+, July 2004)
 "Lose your market" (Shuman Lloyd Lee+, Aug 1991)
 "MCV" (Mislav Radica+, Oct 2009)
 "PRaT" (Raccoon+, Jan 2007)
 "Phantom double hit" (Marty Storer, May 2010)
 "Polish prime" (Jason Lee+, Jan 2006)
 "Pure play" (Daniel Murphy, Nov 2000)
 "Pure play" (Casey Forrest+, Feb 1996)
 "Raccoon" (Steven Keats, Feb 2011)
 "Root number" (Ken Bame, June 2004)
 "Russian Bridges" (leobueno+, Mar 2013)
 "Short play" (AJ+, July 2012)
 "Speed board" (Gregg Cattanach, June 2004)
 "Splot" (mamabear, Apr 2007)
 "Squeeze", "trap play" (Philippe Michel+, Feb 1997)
 "Suicide play" (Brian Sheppard, Aug 1997)
 "Swing tournament" (Carlo Melzi+, Mar 2006)
 "Table stakes" (Carlo Melzi, Sept 2002)
 "Technical play" (Adam Stocks+, July 2002)
 "Thematic" (Beauregard+, Aug 2009)
 "Thorp count" (Stephen Turner, June 1996)
 "Time," "timing," "checker," "dancing" (Marty Storer, Apr 1992)
 Turkish names for rolls (Lars Soezueer, Mar 1997)
 "Vigorish" (Anthony R Wuersch, Feb 1995)
 "Volatility" (Michael J. Zehr, June 1998)
 "Wash" (Hardy Hübener+, Sept 2004)
 "Wash" (Brian Sheppard, July 1997)
 "Weaver" (Alan Webb+, May 2000)
 "Zone" of attack (Matt Reklaitis+, Dec 2007)
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