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Vegas Finals – Akiko Yazawa vs. Kit Woolsey – Three Cube Decisions
Posted By: Igor
Date: Monday, 24 November 2014, at 3:52 p.m.
In Response To: Vegas Finals – Akiko Yazawa vs. Kit Woolsey – Three Cube Decisions (Taper_Mike)
I'll give it a shot to keep my EPC tools sharp and perhaps get a rare exercise with match equity computations.
1. Blue has a four roll position with 2 pips per checker average and since the number of checkers is odd, I'd adjust EPC to 29.5. White also has a four roll position with an average of 2.4 pips per checker and since the number of checkers is odd, I'd adjust EPC to 30. (I always round to 0.5.) According to Matussek's formula, white has about 25% here and even though I don't know the exact take point for white AtS on the 4 cube, it's clearly a lot lower than for money, definitely well below 20%, so it looks like a clear ND.
2. Blue has a three roll position with no adjustments necessary for 22 EPC. White has a three roll position, but I'd add 0.5 pips for possible misses if we roll two aces. It comes to 22.5 EPC. Now a pure 3 roll vs. 3 roll position wins 21% for the trailer. According to Matussek's formula each pip is worth about 6.5% on average for this race. Adjusting for concavity of the GWC curve, I'd guesstimate that extra 0.5 pips deficit reduce white winning chances to 18%. Now I wouldn't know the exact take points and hence doubling windows AtS, but I'd guess blue may be able to double now.
3. We can compute exact winning chances by brute force. For white to win, blue must roll a nondouble in every variation. Now white wins as follows:
66, 55, 44, 33 followed by any roll  4/36 wins
22 followed by any double  1/36*6/36 wins
65, 64, 63, 62, 61, 54, 53, 52, 51, 43, 42, 41, 32, 31, 11 followed by any double but 11  29/36*5/36
21 followed by 66, 55, 44, 33  2/36*4/36Let's tally up: we have
4/36 + 1/36*6/36 + 29/36*5/36 + 2/36*4/36
for simplicity of mental calculation I'd replace the last three terms with 32/36*5/36. We then have
4/36*36/36 + 32/36*5/36 = 144/1296 + 160/1296 = 304/1296
Now this gets multiplied by 5/6 (blue must not roll a double) for a total of
1520/7776 (it helps to remember all multiples of 1296 due to countless rollouts performed)
The latter quotient is just a tad below 1/5, so white has just under 20% winning chance.
For the next step I cheated by looking up some MET values.
ND and win gets us to 75 for 37% MWC
ND and lose gets us to 111C for 3% MWC
D and win gets us to 35 for 65% MWC
D and lose gets us to 0% MWCSo, we risk 3% to gain 28%, and hence our doubling window opens at about 10%. Since we have 20%, it might be correct to redouble in this last roll position, but I'm not sure.
***
OK, it just occurred to me to try this approach:
ND means our MWC are 1/5*37% + 4/5*3% or about 10%
D means our MWC are 1/5*65% or 13%
so it looks like we gain 3% MWC by redoubling!

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