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BGonline.org Forums
Stick v. Keene - Cubage
Posted By: Chuck Bower In Response To: Stick v. Keene - Cubage (Stick)
Date: Friday, 7 March 2008, at 8:20 p.m.
Full MEC, anyone? Start at the top and work back. 4-->8 has a takepoint of 15.5%. 2-->4: pass for 35%; take and lose for 15.5%, take and win for 84.5%. Worthless cube takepoint is thus (35% - 15.5%)/(84.5% - 15.5%) = 19.5/69 = 39/138 = 39*(8/11) = 312/11 = 28.4% = 2/7. Full cube efficiency is (2/7)*84.5% = 169/7 = 24%. 70% cube efficiency is just over a bit over 25%. So now for 1-->2, pass for 43%, take and win giving 65% (above), take and lose simple for 35%, take and lose G for 15.5%. Not many G's so let's call it 34% prorated before accounting for the cube. Perfect cube efficiency means takepoint is 75% of 34% or ~25%. 70% cube efficiency is 28%. (If you haven't followed this, 28% is White's takepoint [in cubeless game winning chances]. Now push the easy button.
Blue leads the race by a bunch (effectively). Does the contact really favor White? I think that part is a tossup at best (from White's PoV).
Racewise (alone) I think White wins ~12%. Let's say someone leaves a blot in 60% of games. 30% of those are White's. So White wins 0.3*p(hit)*0.9 + 0.3*p(!hit)*0.12 + 0.4*0.12 + 0.3*p(hit)*0.05 + 0.4*p(!hit)*0.12 (order is White hits a shot, White misses a shot, no one gets a shot, blue hits a shot, blue gets a shot but misses). [Note that I'm assuming the probability of hitting a shot is the same regardless of which side gets it.] Then for White to have a take the sum of these five terms must be >= 0.28. 0.27p + 0.036*(1-p) + 0.048 + 0.015p + 0.048(1-p) >= 0.28. (0.27 - 0.036 + 0.015 - 0.048)p >= 0.28 - 0.036 - 0.048 - 0.048 ==> 0.20p >= 0.148. So under these assumptions White needs to have a 75% chance of hitting a shot in order to take. That's one triple shot or nearly two double shots. I don't think he can get that.
Could my calculations be wrong? Yes, but they'd have to be pretty far wrong. Could my assumptions be far off? Yes, but they'd have to be just that -- far off. I think most would consider a sure single shot for White about right. The GWC for races is likely controversial but I'm sticking with that My adjusted pipcounts were 79::97, a subsequent Kleinman Count of 484/172 which is close to 88::12 (Blue::White).
D+P.
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