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Re: -2/-5 race cube question

Posted By: Daniel Murphy
Date: Tuesday, 22 May 2007, at 6:53 a.m.

In Response To: Re: -2/-5 race cube question (Chase)

Chase wrote: White's take point at 5a2a is a bit higher than for money

Now I follow Chase's meaning. 5-away's takepoint with G11 MET is 22.82%. That is a 'bit higher' than for money.

G11 Match Equity Table

-1-2-3-4-5
-150.000068.145075.077081.768084.4510
-231.855050.000059.964067.184074.5240
-324.923040.036050.000057.373065.0260
-418.232032.816042.627050.000057.7450
-515.549025.476034.974042.255050.0000

2-away's doubling window in a last roll position:

Win % Correct Cube Action
0%-69.4%No Double, Take
69.4%-77.2%Double, Take
77.2%-100%Double, Pass

2-away's doubling window if 5-away can redouble:

Win %Correct Cube Action
0%-69.4%No Double, Take
69.4%-77.2%Double, Take
77.2%-100%Double, Pass

If, as DC-Ohio suggests, Leader is 300 rating points better than opponent, Leader's MET is about this (Jacobs/Trice +300 MET, rounded):

-1-2-3-4-5
-15676808889
-23959728186
-33250637279
-42542566674
-52235485867

And opponent's this:

-1-2-3-4-5
-14461687578
-22441505865
-32028374452
-41219283442
-51114212633

Opponent's take point when you lead 2-away 5-away and opponent can redouble:

P->5-away 1-away11%
T win->1-away 2-away 61%
T lose->5-away 0-away0%
T risks11%
to gain50%
R(R+G)->11/(11+50)= 11/61 = 18.03%

The bottom of your last roll doubling window when you lead 2-away 5-away and opponent can redouble:

ND win->1-away 5-away89%
D win->0-away 5-away100%
ND lose->2-away 4-away81%
D lose->2-away 1-away39%
D risks42%
to gain11%
R/(R+G)->42/(42+11)= 42/53= 79.2%

Your doubling window when you lead 2-away 5-away and opponent can redouble:

Win % Correct Cube Action
0%-79.2%No Double, Take
79.2%-81.9%Double, Take
81.%-100%Double, Pass

You've hardly any doubling window at all.

If there's a 50% chance this opponent will pass, and your GWC is 74%, then

Your Doubling/(half-take and half- pass) equity is (.50 * .89) + (.50 * .74 * 1.00) + (.50 * .26 * 0.39)

= 0.4450 + 0.3700 + 0.0507 = 86.57%

and your No Double equity is

(.74 * .89) + (.26 * .81) =

= 0.6586 + 0.2106 = 86.92%

So, you may be slightly better off not doubling (with these match equities, and no math errors by yours truly).

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