Happy 4th all

Just some fodder for the boards and my own edification....if someone can post an image please do so.

Go with Magriel's 11/4 or 8/2 8/7?

Gnu says Magriel plays the best move (0-ply cubeless rollout, 648 trials). I also agree but I find these types of decisions agonizing. Is Magriel's logic sound in theory for this class of positions? anyone have any advice or developed theory counter to this line of logic?

Wrong decision from Magriel. 8/7 8/2 is superior.

XG rollouts - 3 ply with variant reeduction, 1296 trials:

8/7 8/2: +0.147
11/4: +0.111 (-0.036)

You made me curious, I would like to see a picture of this problem. Í own the book myself, but I have lend it out to a good friend. When you want to post a picture this is what you can do:

Enter the position in gnu or another BG program.
Make a printscreen
Paste it in a Paint program
Save it as a jpeg
upload it to photobucket.com (after you made a free account)
Then post a reply on this forum and choose insert image (sse the icons above)
Type the photobucket URL
This should work
Then my curiosity will be satisfied.

Greetings k.

here's the position in question. Black to play 61

My goal with posting this was to gain a better understanding and create a rule of thumb for these class of positions. 8/7 8/2 leaves only 11 shots while 11/4 leaves 16. Magriel acknowledges this in the book and goes on to contend that you will most likely have to leave another direct shot unless you're lucky which is why he recommends 11/4.

With this lookahead in place is he right? Even if he's wrong in this particular case is his theory sound? Does anyone have an rule they developed for this class of positions?

When i saw this position i thought it should be possible to calculate the risk myself, without a rollout, thus hoping to get some more understanding about the position.

The direct risks of both plays is clear, but what about the further clearing risks,

a. 8/2 7/2

When the 7-blot is not hit the checkers on the 11-point have 2 landing points, so 2^2 = 4 + 3 doubles =7/36 will land safe,
after that the landing point on 7 will be gone so then 5/36 will land safe.
The chance of not being safe in 2 moves = 29/36x31/36= 69%, the chance of being hit = (lets give it a medium shot of 14/36)
14/36 x 69% = 27%

b. 11/4

When the 11 blot is not hit, the first following move it will be moved to safety. He will succeed in 32/36 of the time,
so the first hit risk = 14/36 x 4/36 = 4%, the move after that we come to the essential part of it all: the 8-point has 4 landing points
instead of the sole 2 of the 11-point. So here all 2456 combinations = 4^2 = 16+ D1 = 17/36 will work. Lets say we also get 2 moves for this, the chance it will not work is
19/36 ^2 = 28%, and then the hits are 13/36*28%=4%

So lets recapitulate:
a: direct risk = 31% later risk =27% total 58%
b: direct risk = 39% later risk = 8% total 47%

So the principle of Magriel seems clear: clearing from the back is good because/when the remaining point has more landing points.

But why do the rollouts give another picture, that is because there is something else going on here as well.
Besides the fact you soon will clear the 11 point, it also serves a purpose, it is a blocking point.
When red throws D2, 31,32,41,21,42 (a total of 11/36) he has the tough choice between putting a blot in front of the 11-point
(thus making it far more easy to come home for black with certain numbers, you can see the blot hitting number as an extra
landing point) or breaking the 6-prime, but this will have the consequence that the red hits are not certain winners anymore but almost
certain winners. So now the 58% hits may be 90% winners (making 52,2%) or even 80% winners(making 46%).

So i think this is the reason that the sound principle doesn't work in this particular case.

I’m with Paul on this one, and here’s how I would analyze the position over the board.

First, the race is 69-126 in Black’s favor after he plays. So White has to hit a shot to win. The cube is centered, so it’s a constant threat.

If Black plays 11/4 (Paul’s play), White hits 16/36 and misses 20/36. If he hits, he wins by doubling next turn. If White misses, Black doubles and White passes. So in a cross-section of 36 games, Black wins 20 and loses 16 after Paul’s play.

Now let’s look at 36 games after the other play, 8/2 8/7. Here White hits and wins right away in 11 games, leaving 25 games where White misses and the game continues.

If Black is going to do better than after 11/4, he’s going to have to win at least 20 of these 25 games. That means that Black has to be better than an 80% favorite on roll after White misses the 2-shot. That means the position has to already be a double and a pass. But the position with an 11-point against the 5-point, with no intervening outfield points, is no double and take in every rollout I’ve ever seen.

So I conclude that Black can’t be 80% to win after White misses the 2-shot, and I play 11/4.

By the way, this method of looking at a cross-section of 36 games and estimating how many games each play can win is a great approach to analyzing these sorts of positions over the board. It’s an exact analogy to poker tournament problems where your opponent moves all-in and you need to decide whether to call or not. You know the pot odds so you can figure out what percentage you need to win, and then you estimate the chances of your hand against the different hand groups in his range, and add them up.

Given all this (which I agree with intuitively), how do you reconcile with the fact that 8/2 8/7 does better in rollouts?

No explanation yet, and I'm puzzled because I wouldn't expect a rollout error in such a clear-cut position. Also, the rollout result quoted for the 11/4 play (EV of +0.111 for Black) exactly agrees with the 20-16 win ratio in my explanation. So the question is -- what's going on in the sequence 8/7 8/2 followed by a miss? How can Black be winning more than 20/25 of these games?

I'm travelling right now, but I'll do some rollouts of my own when I get home and see if I can shed any more light on this. I also try to give Paul a call and see if he has any ideas.

I used hint in Gnu and it picked 11/4 as top play

XG uses live cube rollouts.

XGID=-BBBBcC-B--B-----bbbbbb---:0:0:1:61:0:0:3:0:10



1. Rollout¹ 8/7 8/2 eq:+0.147
Player : 50.52% (G:2.47% B:0.03%)
Opponent: 49.48% (G:6.88% B:0.27%)
Confidence: &plusmn; 0.009 (+0.138<E<+0.156)
Duration: 6 minutes 59 seconds

2. Rollout¹ 11/4 eq:+0.111 (-0.036)
Player : 49.71% (G:3.90% B:0.02%)
Opponent: 50.29% (G:4.99% B:0.13%)
Confidence: &plusmn; 0.000 (+0.111<E<+0.111)
Duration: 6.4 seconds


¹ 1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply


eXtreme Gammon Version: 1.21

There are no intervening outfield points but the blot on the 7 point provides a playable 6 and makes 5-4 a clearing roll.

I did a short GNUBG rollout with 1-ply checker play and 2-ply doubling decisions. (All you XG and Snowie folks need to add 1 to each of these plies to get a comparable rollout.)

1. Rollout 8/7 8/2 Eq.: +0.171
0.504 0.030 0.001 - 0.496 0.049 0.001 CL -0.011 CF +0.171
[0.002 0.001 0.000 - 0.002 0.001 0.000 CL 0.003 CF 0.009]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 882958699 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

2. Rollout 11/4 Eq.: +0.111 ( -0.060)
0.485 0.029 0.000 - 0.515 0.036 0.000 CL -0.036 CF +0.111
[0.000 0.000 0.000 - 0.000 0.001 0.000 CL 0.001 CF 0.001]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 882958699 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

This is simple. After 8/7 8/2 it is a cube, double/take, as it was before this roll which nobody addressed. You can't encompass the entire problem like the cube is on one when 25/36 of the games after clearing the 8 point result in D/T. You don't need to do more rollouts, you need to understand the problem.

You're right about all this but the chapter was dedicated to checker play problems (bear off against contact) and not cube action. I think it's reasonable to assume that the cube would have already been turned prior to this position.

One of the criticisms of Magriel's famous tome is that there is no cube shown in most diagrams. That problem is demonstrated here. The rollouts with a centered cube show 8/2, 8/7 as best. When Black doubles before rolling, however, then the rollouts show 11/4 to be superior.



1. Rollout 11/4 Eq.: -0.086
0.506 0.026 0.000 - 0.494 0.051 0.001 CL -0.015 CF -0.086
[0.002 0.001 0.000 - 0.002 0.002 0.000 CL 0.004 CF 0.004]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883909741 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

2. Rollout 8/7 8/2 Eq.: -0.104 ( -0.018)
0.511 0.029 0.000 - 0.489 0.065 0.002 CL -0.015 CF -0.104
[0.002 0.001 0.000 - 0.002 0.002 0.001 CL 0.004 CF 0.005]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883909741 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

At double match point, 8/7, 8/2 is GNUBG's recommendation. (Although, the joint standard deviation bewteen the two plays is 2.092, my short, 648-trial rollouts are probably not long enough to produce definitive equities.)



1. Rollout 8/7 8/2 MWC: 50.21%
0.502 0.167 0.001 - 0.498 0.120 0.013 CL 50.21% CF 50.21%
[0.002 0.012 0.001 - 0.002 0.011 0.003 CL 0.20% CF 0.20%]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883909741 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

2. Rollout 11/4 MWC: 49.65% ( -0.56%)
0.496 0.187 0.002 - 0.504 0.106 0.005 CL 49.65% CF 49.65%
[0.002 0.013 0.002 - 0.002 0.010 0.001 CL 0.17% CF 0.17%]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883909741 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]