4-2 backgame - hit 1, hit 2, don't hit?

[ah...Clem]

XGID=--b-bCCaDaA-aD---d-d------:1:-1:1:41:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O | +---+
| X O | | O | | 2 |
| X O | | O | +---+
| X O | | O |
| | | |
| |BAR| |
| | | |
| X | | |
| X | | X X |
| X | | X X O O |
| O X O X O | | X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 127 O: 191 X-O: 0-0
Cube: 2, O own cube
X to play 41

O has 64 pips of timing. Is that enough? Should X give her more? If so ,
how much more?

[Timothy Chow]

I'd hit two with 13/9* 8/7*. The first order of business when
playing against a backgame is to form a prime. X has no prime
to speak of, and 13/9* 8/7* gives him excellent chances of making
a five-prime. If he doesn't hit, O might make some of those points
in X's outfield, which will be thorns in X's side. As for timing,
X should have the opportunity to slot the 3pt and maybe the 1pt in
the next couple of rolls, which will regain timing if O is forced
to hit.

---
Tim Chow

[Stick Rice]

Not hitting isn't even an option. After eliminating that we can also eliminate hitting one (9*, 9) as an option as what we're trying to do is form a solid prime and destroy our opponent's timing. Hitting two, either two, does this in a much more efficient way than making the 9pt which only puts one on the bar and steals some of the opponent's flexibility/timing and leaves the bar point not simply unmade, but unlikely to be made.

Of the double hitting plays I prefer hitting 12* 9* because it steals all of the opp's remaining timing. What will happen over the next couple turns is we'll hit the opp's other blot on our bar point, we will make our bar point and the opponent have 7, yes 7, checkers behind our at least ever extending four prime. His front position is very inflexible and he'll have nowhere good to play his larger numbers. (fives and sixes)

Nothing wrong with the double hit of 9*, 7* as it does a lot of the same things. It slots the bar point directly and puts two up but we aren't assured of getting that third checker. If we don't get that third checker it leaves the opponent a shade of flexibility and timing, albeit not much but why give him anything when we don't have to? Squeeze the position for everything it's worth.

Stick

[Robert Zimmerman]

On Friday, September 29, 2023 at 10:54:02 AM UTC-4, ah...Clem wrote:

I got curious about whether to hit two vs. hit one and complete a 5 prime. Hitting two is still right by a lot. I was surprised, but I think the idea is that your highly favored to make the prime next roll anyway, and in this case, putting more checkers back will leave O with little to avoid a crunch up front.

Bob

XGID=--b-cCCBBaA-aD---d-d------:1:-1:1:41:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O | +---+
| X O | | O | | 2 |
| X O | | O | +---+
| X O | | O |
| | | |
| |BAR| |
| | | |
| | | |

| | | X X O |

| X X | | X X O O |

| O X O X X | | X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 125 O: 194 X-O: 0-0

Cube: 2, O own cube
X to play 41

1. Rollout¹ 13/12* 13/9* eq:+0.506
Player: 64.44% (G:39.06% B:2.62%)
Opponent: 35.56% (G:4.81% B:0.18%)
Confidence: ±0.035 (+0.470..+0.541) - [100.0%]
Duration: 1 minute 22 seconds

2. Rollout² 13/9* 10/9 eq:+0.401 (-0.104)
Player: 62.47% (G:33.98% B:1.76%)
Opponent: 37.53% (G:4.57% B:0.16%)
Confidence: ±0.027 (+0.374..+0.429) - [0.0%]
Duration: 1 minute 19 seconds


¹ 250 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

² 249 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller


eXtreme Gammon Version: 2.10

[ah...Clem]

XGID=--b-bCCaDaA-aD---d-d------:1:-1:1:41:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O | +---+
| X O | | O | | 2 |
| X O | | O | +---+
| X O | | O |
| | | |
| |BAR| |
| | | |
| X | | |
| X | | X X |
| X | | X X O O |
| O X O X O | | X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 127 O: 191 X-O: 0-0
Cube: 2, O own cube
X to play 41

Timing is important criteria in a backgame, and O has barely enough at
64. Hitting gives her enough and hitting twice gives her more than
enough. I was wary of ceding too much timing to O, but not hitting
seemed too passive so I opted for the goldilocks play of hitting once.

XG strongly prefers the double hit, and doesn't care much which way you
do it.

Tim's observation that the double hit poises X to make a prime is well
received. I'll observe that hitting 0, 1, or 2 times all win about the
same number of games while the more times you hit the more your gammon
rate goes up. That's an important factor in backgames too.



1. Rollout¹ 13/9* 8/7* eq:+0.389
Player: 61.43% (G:35.74% B:2.43%)
Opponent: 38.57% (G:5.32% B:0.22%)
Confidence: ±0.014 (+0.374..+0.403) - [70.0%]
Duration: 9 minutes 20 seconds

2. Rollout¹ 13/12* 13/9* eq:+0.382 (-0.007)
Player: 61.00% (G:37.35% B:2.74%)
Opponent: 39.00% (G:5.68% B:0.37%)
Confidence: ±0.019 (+0.363..+0.402) - [30.0%]
Duration: 10 minutes 16 seconds

3. Rollout¹ 13/9* 10/9 eq:+0.321 (-0.067)
Player: 60.65% (G:31.42% B:1.79%)
Opponent: 39.35% (G:5.36% B:0.21%)
Confidence: ±0.012 (+0.309..+0.334) - [0.0%]
Duration: 9 minutes 39 seconds

4. Rollout¹ 10/5 eq:+0.229 (-0.159)
Player: 60.17% (G:24.60% B:1.25%)
Opponent: 39.83% (G:6.36% B:0.23%)
Confidence: ±0.012 (+0.217..+0.241) - [0.0%]
Duration: 8 minutes 43 seconds


¹ 1296 Games rolled with Variance Reduction.