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Money game 2-2 to play

Posted By: Nack Ballard
Date: Thursday, 28 January 2010, at 9:54 a.m.

In Response To: Money game 2-2 to play (Timothy Chow)

I agree with Stick that three 2s are obvious: 13/11(2) 24/22. And I chose the same fourth deuce he did: 13/11. However, I have a different slant on why 13/11 is better.

Normally, having the last checker up on the 20pt is better than being on the 22pt. The cost of Opp hitting where he wants to hit is outweighed by the value of simply escaping more often.

This position is an unusual exception because the numbers that White wants to hit with, 1s and 3s, are the very numbers that block her 15pt blot that is such a high priority to move. By coming up, Blue allows White to swing around the 15pt blot and create a new builder with a 6, 5 or 4, and hit with a 3 or 1 (and cover with a 2 if he hits). Because of this ideal diversity of White's numbers, coming up with 22/20 is probably quite close in strength with playing no 2 at all instead of the usual paradigm of simply being clearly (net) preferable to be up on the 20pt.

The reason I think 13/11 is a better fourth deuce is because it is of positive value (as opposed to the closer-to-neutral value that playing 22/20 is). The 11pt builder can be used to hit or make/cover the 10pt, or sometimes hit or make/cover the 9pt in later variations. With his 7pt already made, and Opp having anchored on the 20pt, the value of Blue's 11pt has risen dramatically compared to his midpoint. The spare is more valuable on the 11pt than the midpoint simply because Blue is more willing to break the midpoint than the 11pt.

The 11pt builder is useful. This can already be seen in immediate sequences of White pointing on the 3pt (54 53 43 33) and Blue is much worse off when he enters and hits with a 1 (or chooses not to because it would break his 10pt), whereas he much more willingly hits with a 3 from his midpoint even though he has to break it. Likewise, if White rolls 42 31 11 and leaves her 15pt blot where it is, Blue's 11pt spare can be put to instantly better use than his 13pt spare. Plus, as I stated, there may be later benefits of a similar nature.

In other words, if Blue is allowed to play only three 2s (24/20 13/11(2)), he definitely shouldn't; he should add 13/11 as a fourth deuce to gain the positive benefit outlined above. Conversely, if after playing only three 2s he has to choose between standing pat or adding 22/20 as a fourth deuce, it's a close choice (and that is only true because of the unfortunately, unusually efficient diversification of White's numbers mentioned earlier -- otherwise 22/20 would have definite positive benefit as 13/11 does).


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