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cube at 9a-8a

Posted By: Daniel Murphy
Date: Friday, 21 June 2013, at 6:35 p.m.

In Response To: cube at 9a-8a (ah_clem)

Double/pass seems awfully pessimistic, from White's point of view. Might I argue you into a no double/take?

Blue on roll

White134

Blue125
Position ID: mLeDA0C2NYMBMA Match ID: cAkAABAAAAAE

I believe 18, not 17, of 36 rolls make the 5 point (the 14 threes plus 62 44 and 22).

But notice that only 7 of those 18 rolls allow Blue to cover and split. For as long as Blue is unable to split, White's little prime blocks fully 25% of Blue's numbers.

More important, 18 of 36 rolls don't cover the 5 point. What happens then? First, about 1/3 of the time (when White rolls any 5 or 41 (any 5 only if Blue has played 66) White enters on the five point, usually hitting. That's 1/2 * 1/3 = 6/36 very good sequences for White. Second, about 1/2 * 16/36 = 8/36 of time Blue doesn't cover and White doesn't enter, but after that Blue doesn't always cover, so White has to win some of these, also.

And even more important: whether or not Blue covers the 5 point on his next turn, White can simply enter on the ace point. If he does, Blue still has a lot of work to do.

Suppose Blue has covered the 5 point, say, with a 36 played 8/5 13/7. Look how White's aces play:

White on roll

White134

Blue116
Position ID: tm0FATCYt4MDQA Match ID: AQEAABAAAAAE

 11 bar/24 6/5(2) 13/12* 12 bar/24 6/4 13 bar/24 13/10 14 bar/24 8/4 15 bar/24 13/8 16 bar/18*

62 53 or 22? The same except 61 plays bar/24 13/7.

43, a nice cover and split number?

White on roll

White134

Blue118
Position ID: tm2CASGYt4MDQA Match ID: AQEAABAAAAAE

 11 bar/24 8/7 6/5*(2) 12 bar/24 6/4 13 bar/24 8/5* 14 bar/24 8/4 15 bar/24 13/8 16 bar/24 13/7

And what if Blue hasn't covered, say with a 51?

White on roll

White134

Blue119
Position ID: trUGATCYt4MDQA Match ID: AQEAABAAAAAE

Above, White has 16/36 excellent numbers, but who's the favorite if White merely enters with a 21?

To sum up -- White has a lot of ways to win. From strongest to weakest they are:

 Blue doesn't cover, White enters on the 5. Very strong for White. Blue doesn't cover, White enters on the ace. Strong for White. Blue covers, White enters on the ace. Not weak! And, if Blue has doubled, Blue covers and White fans. White still wins some of these.

Let's reconsider double versus no double in the original position:

(1) Blue covers but White enters on the ace without hitting. Will Blue have lost his market?

(2) Blue doesn't cover and White fans. Will Blue have lost his market?

(3) Blue doesn't cover and White enters with a hit (or on the 5 point without hitting). How badly will Blue wish he hadn't doubled? when he doesn't cover and White enters on the 5?

(4) How many sequences are really market losers for Blue, and how badly has he lost his market? I think only when Blue makes a five point boart and White fans has Blue lost his market, and these sequences aren't all winners for Blue if he has doubled.

If you can convince yourself that no-cover/fan and cover/enter are mostly not market losing sequences, you're left with comparing no-cover/enter (very good for White, about 1/2 * 1/3 = 6/36 of the time) and cover/fan (very good for Blue, about 1/2 * 2/3 = 8/36 of the time. Seen this way, I think it becomes clear that White has an easy take in the original position, and the question should be whether Blue has enough of a threat to double.

• cube at 9a-8a
onur alan -- Friday, 21 June 2013, at 9:16 a.m.
• cube at 9a-8a
ah_clem -- Friday, 21 June 2013, at 2:09 p.m.
• cube at 9a-8a
Daniel Murphy -- Friday, 21 June 2013, at 6:35 p.m.
• cube at 9a-8a
neilkaz -- Friday, 21 June 2013, at 6:53 p.m.
• RO
onur alan -- Sunday, 23 June 2013, at 8:19 a.m.

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