Cube Handling

Forum Archive : Cube Handling

How does rake affect cube actions?

From:   Paul Epstein
Date:   12 September 2005
Subject:   Examples of rakes affecting cube actions in no-limits play.

Suppose it's a bearoff position where both players have one man on the
5 point and one on the 2 point (010010 vs 010010) and that the on-roll
player has access to the cube.

In the face-to-face money game it's a double/take.  The double is
completely obvious.  The take is also quite easy to demonstrate because
the underdog has enough equity regardless of whether the taker plans to
redouble if the on-roll player rolls 21.  (And that is the only
non-obvious cubing decision that can be faced by the underdog other
than the initial pass/take decision.).  Suppose the on-roll player rolls
a 21.  Then the position becomes redouble/take for his opponent.

Now, let's look at the online game with rakes of 2.5% per player per
point with winner paying both rakes.  Both the above actions are
different!  Now, the underdog should pass a double in the original
position.  Furthermore, if the underdog errs and takes, and if the
favourite rolls the anti-joker 21, then there is no redouble.

I don't have the time to post these calculations but I did check them
carefully.  Others are welcome to post the details.

Paul Epstein

Tom Keith  writes:

I agree with you that cube actions in raked play are not exactly the
same is in unraked money play.  Here is an illustration using your
example of 2.5% rake per point per player.

Suppose I accept an invitation to play for $100 a point.  Basically this
means both players put $100 into the pot, and $2.50 from each player is
immediately raked away, so we each have $97.50 at stake.

At some point my opponent doubles to 2.  If I drop, I lose my $97.50.
If I take, I have to contribute an additional $100, and $2.50 of that
gets raked away.  Should I take or drop?  Let's assume no gammons and no

Raked Play: If I accept and win, I collect $195 from my opponent, but I
only get back $97.50 of the extra $100 I put in.  So my true gain is
+192.50.  If I accept and lose, I give up the $97.50 already at stake
plus an addtional $100, for a net loss of -197.50. If my winning chances
are exactly 25%.  Here's how the equities break down:

    double/drop                          -97.50

    double/take/win    +192.50 x .25 =  +48.125
    double/take/lose   -197.50 x .75 = -148.125
    double/take                        -100.000

So I am better off dropping than taking because I lose $97.50 instead of
an expected $100.  This is not the same as in unraked money play where
my expected loss is the same whether I take or drop.

Unraked Play:

    double/drop                        -100.00

    double/take/win    +200.00 x .25 =  +50.00
    double/take/lose   -200.00 x .75 = -150.00
    double/take                        -100.00


Question: Suppose the rake is x% per point per player.  What are the
minimum winning chances you need to take a double (assuming no gammons
and no recubes)?


Raccoon  writes:

Yes, the rake affects cube decisions, as Paul and Tom's examples show.
Thank you both for those examples.

If there is no rake, you can obviously profitably double in a last-roll
position with 50% or more winning chances and opponent can take if your
winning chances are no greater than 75%. Thus your doubling window is
50%-75% and opponent's take point is 25%.

When there is a rake, it affects both the TOP and the BOTTOM of the
doubling window. As the rake rises, the doubling window narrows, the
bottom rising and the top descending, until the doubling window
disappears entirely when the rake reaches 25% per player.

So, assuming no gammons and recubes, the bottom of the doubling window
equals the win percentage you must attain in order to overcome the rake
and break even. You can calculate that as 1/(2-2r) where r=rake per
person. You can calculate the take point as 1/(4-4r) and the cash point
as 1-(1/(4-4r)).

        Doubing Window
Rake | Doubling   Cash   | Take
     | Point      Point  | Point
 0%  |  50%       75%    | 25%
 1%  |  50.50%    74.74% | 25.26%
 2%  |  51.02%    74.49% | 25.51%
 3%  |  51.55%    74.23% | 25.77%
 4%  |  52.08%    73.96% | 26.04%
 5%  |  52.63%    73.68% | 26.32%
 6%  |  53.19%    73.40% | 26.60%
 8%  |  54.34%    72.82% | 27.12%
10%  |  55.55%    72.22% | 27.78%
12%  |  56.82%    71.59% | 28.41%
18%  |  60.975%   69.51% | 30.49%
20%  |  62.25%    68.75% | 31.25%
25%  |  66.67%    66.67% | 33.33%
Did you find the information in this article useful?          

Do you have any comments you'd like to add?     


Cube Handling

Against a weaker opponent  (Kit Woolsey, July 1994) 
Closed board cube decisions  (Dan Pelton+, Jan 2009) 
Cube concepts  (Peter Bell, Aug 1995)  [Long message]
Early game blitzes  (kruidenbuiltje, Jan 2011) 
Early-late ratio  (Tom Keith, Sept 2003) 
Endgame close out: Michael's 432 rule  (Michael Bo Hansen+, Feb 1998)  [Recommended reading]
Endgame close out: Spleischft formula  (Simon Larsen, Sept 1999) 
Endgame closeout: win percentages  (David Rubin+, Oct 2010) 
Evaluating the position  (Daniel Murphy, Feb 2001) 
Evaluating the position  (Daniel Murphy, Mar 2000) 
How does rake affect cube actions?  (Paul Epstein+, Sept 2005) 
How to use the doubling cube  (Michael J. Zehr, Nov 1993) 
Liveliness of the cube  (Kit Woolsey, Apr 1997) 
PRAT--Position, Race, and Threats  (Alan Webb, Feb 2001) 
Playing your opponent  (Morris Pearl+, Jan 2002)  [GammOnLine forum]
References  (Chuck Bower, Nov 1997) 
Robertie's rule  (Chuck Bower, Sept 2006)  [GammOnLine forum]
Rough guidelines  (Michael J. Zehr, Dec 1993) 
Tells  (Tad Bright+, Nov 2003)  [GammOnLine forum]
The take/pass decision  (Otis+, Aug 2007) 
Too good to double  (Michael J. Zehr, May 1997) 
Too good to double--Janowski's formula  (Chuck Bower, Jan 1997) 
Value of an ace-point game  (Raccoon+, June 2006)  [GammOnLine forum]
Value of an ace-point game  (Øystein Johansen, Aug 2000) 
Volatility  (Chuck Bower, Oct 1998)  [Long message]
Volatility  (Kit Woolsey, Sept 1996) 
When to accept a double  (Daniel Murphy+, Feb 2001) 
When to beaver  (Walter Trice, Aug 1999) 
When to double  (Kit Woolsey, Nov 1994) 
With the Jacoby rule  (KL Gerber+, Nov 2002) 
With the Jacoby rule  (Gary Wong, Dec 1997) 
Woolsey's law  (PersianLord+, Mar 2008) 
Woolsey's law  (Kit Woolsey, Sept 1996) 
Words of wisdom  (Chris C., Dec 2003) 

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