Thanks for posting such an interesting set.
Number 1
I don’t mind too much getting hit, but not from White’s spares on the midpoint. So the 6 goes down to the 10pt. Then, at least over the board, I would lift the blot on the 9pt with the 2, D (Down) = 16/10 9/7. The QF play, of course, is to leave it, D (Down) = 16/10 13/11. Number 2
It is way too early to hit. After hitting, it would be nearly impossible to contain the opponent’s checkers, and the three-anchor backgame might forever be reduced to two. Ideally, the hit(s) should come after the opponent has been forced to dismantle his offense. Play D (Down) = 13/7. Number 3
I believe it was Barclay Cooke, in one of his texts, who has a club mate saying, “Missing a double shot is the easiest thing in the world.” With Blue’s board still incomplete, I would take in a flash. Don’t get me wrong. It’s not that I want to be doubled. This just looks like an easy take. As Blue, I would not double here. Number 4
Now, this is more like it. Usually it is better to hit before cubing, but there are only 4 rolls that miss this quadruple shot. Doubling deserves serious consideration. Blue’s rolls look like this:
In summary:
After two checkers are hit, if they are closed out, White’s winning chances with 8 checkers off fall to about 9%. For simplicity, let’s assume that whenever Blue hits both checkers on the first try, he always contains them. When only one checker is hit, White will have only 2 or 3 immediate rolls in 36 that enter and safety the second checker. That’s the bad news. The good news is that given a chance to shoot at the second checker, Blue might not hit it on his first try. Of the 11 rolls where White enters immediately, let’s guess Blue can eventually pick up both of White’s checkers after at least 8 of them. That means we are guessing Blue will hit and contain both checkers in about 19 or 20 of the 22 games where Blue hits only one checker initially. To be cautious, and allow for other various ways that White might rebound, let’s round that down to 18. In the other 4 games, even when White’s single checker is closed out, his winning chances are between 48% and 52% depending whether Blue can get an optimal arrangement of spares. Suppose Blue misses the hit on his first try. Then he will get a second chance 16 times in 36. The other 20 times he will likely face a gammon loss. Here is the breakdown of White’s rolls (after a Blue miss). White will safety at least one of his checkers in all of them. First, the 16 shot-leaving numbers:
The other 20 rolls all play safely:
Of the 4 games where Blue misses his first shot, he will hit on his second try about (16/36)*(20/36) or 25% of the time. After that, if we grant him the closeout, he will win only half of those. To be generous, let’s guess Blue will win 1/2 game of the 4, lose 1/2 single game, and lose 3 gammons. Totalling our cross-section of 36 games: Blue hits and contains both checkers in 28 games. Let’s say Blue wins 25 of those, losing only a single game in the other 3. Of the other 4 games where Blue hits on his first try, he should be able to contain White in at least 3 of them. With a close out, he will win half of those, or 1.5 games, losing a single game in another 1.5. In the fourth, lets say White somehow wins a single game only. In reality, White will sometimes win a gammon, but those wins will be offset by the fact that White will probably not escape at that high rate we have assumed.
If all my guesses are accurate ;-) then this position is Double / Take. Number 5
I would not double this. Blue has awkward 3s, to say the least. Even the POH numbers like 31 and 32 leave White shooting at the blot on the 1pt. Were there no gap between White’s anchors and Blue’s forces, then I would double. Mike | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
