Today I would like to share a few key positions that were recorded and/or from memory.

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First, I am on roll leading 5 away 6 away and holding a 2 cube. Cube action?

is Ed score: 3 pip: 29 | ||||||||||||||||

9 point match | ||||||||||||||||

pip: 27 score: 4 is Bill | ||||||||||||||||

XGID=---ABBA------------bbaa---:1:1:1:00:4:3:0:9:10 | ||||||||||||||||

on roll, cube action? |

Analyzed in Rollout | No redouble | Redouble/Take |

Player Winning Chances: | 72.31% (G:0.00% B:0.00%) | 72.29% (G:0.00% B:0.00%) |

Opponent Winning Chances: | 27.69% (G:0.00% B:0.00%) | 27.71% (G:0.00% B:0.00%) |

Cubeless Equities | +0.446 | +1.009 |

Cubeful Equities | ||

No redouble: | +0.702 (-0.111) | ±0.000 (+0.702..+0.703) |

Redouble/Take: | +0.814 | ±0.001 (+0.813..+0.814) |

Redouble/Pass: | +1.000 (+0.186) | |

Best Cube action: Redouble / Take | ||

Rollout details | ||

20736 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller | ||

Double Decision confidence: | 100.0% | |

Take Decision confidence: | 100.0% | |

Duration: 14.3 seconds |

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I redoubled and Ed took.

My thought process. Use EPC. I have 27 pips + 6 for wastage or 33 EPC.

33/7 is 4 - 3 is 1. Therefore Ed's point of last take for money is 34.

I did not make any adjustment for match score - I just assumed his 4 cube takepoint was similar to money.

Ed has 29 pips + 6 for wastage or 35 EPC. Therefore the position is Redouble / Pass.

So by my calculation at the table the position was Redouble / Pass. This is obviously wrong. That said, I am not sure where I ade my mistake(s). Comments welcome.

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Later in the same game. Ed trails 5 away 6 away and is on roll. Cube action?

is Ed score: 3 pip: 11 | ||||||||||||||||

9 point match | ||||||||||||||||

pip: 9 score: 4 is Bill | ||||||||||||||||

XGID=----AA--------------aa-a--:2:-1:-1:00:4:3:0:9:10 | ||||||||||||||||

on roll, cube action? |

Analyzed in XG Roller++ | No redouble | Redouble/Take |

Player Winning Chances: | 63.29% (G:0.00% B:0.00%) | 63.29% (G:0.00% B:0.00%) |

Opponent Winning Chances: | 36.71% (G:0.00% B:0.00%) | 36.71% (G:0.00% B:0.00%) |

Cubeless Equities | +0.266 | +0.649 |

Cubeful Equities | ||

No redouble: | +0.389 (-0.260) | |

Redouble/Take: | +0.649 | |

Redouble/Pass: | +1.000 (+0.351) | |

Best Cube action: Redouble / Take |

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

Ed redoubled to 8 and I took.

My thought process. I can drop or play for the match. If I drop my match equity is 2 away 5 away or about 25%. So I need >25% winning chances to take, else I should drop.

My rough winning chances are (Ed misses) x (I win). I can also win a few odd times when Ed fails to bear off in two rolls, but let's ignore those.

Ed wins immediately with double 4 ro better, or he fails to win immediately with 33 rolls.

I then win on my turn with 10 numbers (any combo of 654 plus double 3's).

So out of a crosssection of 1296 games, I win 32 x 10 or 320. This is about 25% by itself so once you add-on the extra wins I have a take.

++++

Still, I feel like I must be doing something wrong here. The computer says my win chances are in fact close to 37%, much higher than 25%. What gives?

Perhaps there are actually many many more variations where Ed fails to bear off in two rolls than I appreciated at the time.

Well any ace kinda sucks for Ed and 32 and 43 aren't the best either. So about 15 rolls and Ed is hardly a lock to get off next time. Let's say he gets off 70% of the time on the second roll after he misses..

So I get 15/36 * 30% or ~12.5% extra wins...

except that ~30% of the time when he misses I win anyway so I really only capture 70% of that 12.5% or just under 9%.

Adding 9% to my baseline of 25% gets me to 34%, fairly close to the 36.7% XG gives me. Still confused as to the math on this, but at least I am closer.

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The next position is approximate from memory. I trail 6 away 8 away and Prince is on roll. Cube action?

is Prince score: 3 pip: 79 | ||||||||||||||||

9 point match | ||||||||||||||||

pip: 113 score: 1 is Bill | ||||||||||||||||

XGID=---aBBCDC--------aabbbbbbA:1:-1:-1:00:1:3:0:9:10 | ||||||||||||||||

on roll, cube action? |

Analyzed in XG Roller++ | No redouble | Redouble/Take |

Player Winning Chances: | 75.27% (G:25.18% B:0.04%) | 75.94% (G:23.24% B:0.03%) |

Opponent Winning Chances: | 24.73% (G:1.58% B:0.03%) | 24.06% (G:1.63% B:0.03%) |

Cubeless Equities | +0.753 | +1.228 |

Cubeful Equities | ||

No redouble: | +0.783 | |

Redouble/Take: | +0.771 (-0.012) | |

Redouble/Pass: | +1.000 (+0.217) | |

Best Cube action: No redouble / Take | ||

Percentage of wrong pass needed to make the double decision right: 5.1% |

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

Prince redoubled and I took.

My thinking at the table. This is mostly a score based take as for money I think this is a drop. Prince has overage on his gammons since a gammon win takes him to 11 points. I don't know my takepoint but assume it is close to money, perhaps a bit lower due to being behind.

The main thing I was looking at was the possibility of recubing to 8. I can perfetly use all 8 points to win the match right here and now. So I figured it is a take, as long as I recube aggressively if given the chance.

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Memo. Same position for money. Prince holds 2 cube and is on roll. Cube action?

is Prince score: 0 pip: 79 | ||||||||||||||||

Unlimited Game Jacoby Beaver | ||||||||||||||||

pip: 113 score: 0 is Bill | ||||||||||||||||

XGID=---aBBCDC--------aabbbbbbA:1:-1:-1:00:0:0:3:0:10 | ||||||||||||||||

on roll, cube action? |

Analyzed in XG Roller++ | No redouble | Redouble/Take |

Player Winning Chances: | 75.38% (G:25.25% B:0.04%) | 75.61% (G:24.92% B:0.04%) |

Opponent Winning Chances: | 24.62% (G:1.56% B:0.03%) | 24.39% (G:1.63% B:0.04%) |

Cubeless Equities | +0.744 | +1.490 |

Cubeful Equities | ||

No redouble: | +0.943 (-0.057) | |

Redouble/Take: | +1.325 (+0.325) | |

Redouble/Pass: | +1.000 | |

Best Cube action: Redouble / Pass |

eXtreme Gammon Version: 2.02

Redouble and big pass for money as the above shows.

************

Later in the same game. I trail 6 away 8 away and am on roll holding a 4 cube. Cube action?

is Prince score: 3 pip: 69 | ||||||||||||||||

9 point match | ||||||||||||||||

pip: 113 score: 1 is Bill | ||||||||||||||||

XGID=---aBBCDC-----------dccbbA:2:1:1:00:1:3:0:9:10 | ||||||||||||||||

on roll, cube action? |

Analyzed in XG Roller++ | No redouble | Redouble/Take |

Player Winning Chances: | 46.07% (G:2.31% B:0.06%) | 46.20% (G:2.67% B:0.09%) |

Opponent Winning Chances: | 53.93% (G:10.57% B:0.03%) | 53.80% (G:9.81% B:0.02%) |

Cubeless Equities | -0.098 | +0.302 |

Cubeful Equities | ||

No redouble: | +0.222 (-0.080) | |

Redouble/Take: | +0.302 | |

Redouble/Pass: | +1.000 (+0.698) | |

Best Cube action: Redouble / Take |

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I rolled.

I knew in my gut this was a redouble and was in fact part of the reason I took on 4 in the first place. But when it came to crunch time I wimped out.

This is one of those weird score based cubes where you can redouble as an underdog.

**********

This is the first game of a 9 point match. (Position approximate from memory) I hold a 2 cube and am on roll. Cube action?

is Mary score: 0 pip: 158 | ||||||||||||||||

9 point match | ||||||||||||||||

pip: 82 score: 0 is Bill | ||||||||||||||||

XGID=cCBBCC----------bbccbB----:1:1:1:00:0:0:0:9:10 | ||||||||||||||||

on roll, cube action? |

Analyzed in Rollout | No redouble | Redouble/Take |

Player Winning Chances: | 58.07% (G:44.73% B:0.50%) | 57.64% (G:44.81% B:0.50%) |

Opponent Winning Chances: | 41.93% (G:8.38% B:0.32%) | 42.36% (G:7.14% B:0.32%) |

Cubeless Equities | +0.555 | +1.077 |

Cubeful Equities | ||

No redouble: | +0.610 | ±0.012 (+0.598..+0.622) |

Redouble/Take: | +0.593 (-0.017) | ±0.016 (+0.577..+0.609) |

Redouble/Pass: | +1.000 (+0.390) | |

Best Cube action: No redouble / Take | ||

Percentage of wrong pass needed to make the double decision right: 4.0% | ||

Rollout details | ||

1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller | ||

Double Decision confidence: | 95.5% | |

Take Decision confidence: | 100.0% | |

Duration: 8 minutes 17 seconds |

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

My prior roll was a superjoker from hell. I rolled double 3 which hit two checkers, closed a 5 point board, and advanced my back guy from the 24 point to the 21 point.

To be honest I had no idea what is going on here so I just doubled. Mary dropped. Hard to blame her really - my wins are mostly gammons, vaulting me to 8-0 Crawford. Pretty scary indeed yet apparently her position is so strong that it isn't even a recube.

**********

Finally I have a 63 to play at DMP.

is Carol score: 0 pip: 128 | ||||||||||||||||

2 point match | ||||||||||||||||

pip: 133 score: 0 is Bill | ||||||||||||||||

XGID=aa-C-BCAB----Ab--bBbcbb-A-:1:1:1:63:0:0:0:2:10 | ||||||||||||||||

to play 63 |

1. | Rollout^{1} | 24/18 13/10 | eq: +0.143 | |||

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2. | Rollout^{2} | 13/7 8/5 | eq: +0.104 (-0.039) | |||

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3. | Rollout^{3} | 18/15 13/7 | eq: +0.089 (-0.054) | |||

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^{1} 611 Games rolled with Variance Reduction.Moves: 3-ply, cube decisions: XG Roller ^{2} 612 Games rolled with Variance Reduction.Moves: 3-ply, cube decisions: XG Roller ^{3} 613 Games rolled with Variance Reduction.Moves: 3-ply, cube decisions: XG Roller |

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I went for broke with 18/15, 13/7. I figured I had to make the bar to contain her back checkers and then 18/15 was the most logical 3. Gammons don't matter so put'em where you want em. This sort of puts the game on the line.

A better BIG PLAY was simply escaping the back checker with 24/18, 13/10. This puts tremendous pressure on Carol to roll well from the bar else the game is almost over. With my play, I still have to clean up some blots and escape my back man. With the computer's play I simply have to come home safe if missed - easier.

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