Hello,

Do computer players play a lot better then human?I`m talking about GNU artificial intelligence at it`s highest does it play better then most high stakes players?

GNU at supremo or higher is like playing the best human in the world.

The short answer is 'yes'. We evaluate players and bots these days by looking at their error rates, which are basically an evaluation of the amount of equity they give away per move, on average, with their mistakes. (Lower numbers are better.) The best humans have error rates in the 2.5 to 3.5 range. Extreme Gammon is currently the best bot out there, and on its second-highest level (XGR+) it probably has an error rate in the 0.2-0.3 range. It's a solid favorite against the best humans.

Isnt it impossible for the computer to not play the best strategy at all times?

We generally trust long rollouts more than simple evaluations. When a rollout produces a result that is different that what an evaluation recommends, we say the evaluation is "wrong."

As far as strategy goes, the bots don't have one. All they do is calculate the respective equities of competing plays using the outputs of their neural nets. The play with the highest equity is the one chosen by the bot.

This is worlds away from how humans play. We often choose our plays within the context of a general strategy or game plan. In a blitz, for instance, we will give added weight to attacking plays that hit loose in our inner board. In a race (where there is still contact) we tend to reject those sorts of hitting plays out of hand.

One of the trickiest parts about using a bot is learning how to interpret the plays it makes within the context of the strategies and game plans that we may think are applicable.

That's the book that needs to be written!! If I had the qualifications to write a book i'd take that idea and run with it. It would be the modern era(Post Bot) Bible of BG.

Bill already wrote a book addressing this question -- "Modern Backgammon." It's one of the most instructive backgammon books.

I liked that book. I didn't completely buy into its four main theories, but I still found a lot to like. It's been so long since I read it that I probably should go back for a second look. I doubt that all of its plays will stand up to modern XG rollouts.

In my analysis of early game play (and all plays, really), I like to "tell a story" to explain why a bot chooses one play over another. The stories I tell can then be used to find the correct plays in related positions. At its worst, this is called "ex post facto" analysis. The stories may sound good, but that does not mean they are right.

If you test your theories enough, however, and compare them with the ideas of others, you will eventually find some "stories" you like.

Let me give an example.

For a very long time, I have been trying to figure out why it is sometimes wrong to make two points when you roll 11 on the second roll. Usually, you just grab the bar point and 5pt, and be done with it. With certain openings, however, that is wrong. In particular, that's the wrong way to play 11 after you opponent opens with 54-split (24/20, 13/8) or 43-split (24/20, 13/10).

White - Pips 158

Black - Pips 167
54S-11: Black to Play 11

The story we are usually told is that you would have to leave a blot on the 8pt if you make the bar point. What a terrible risk! The opponent can hit with an 8 from the bar. That's a whopping 5 shots. You should be scared. (Note that 22 is blocked, so not all 8s will hit).

I'm calling balderdash on that story! Obviously the 5 shots are important, but they can't be the whole story. The bar point is a valuable point. It is worth taking some risks to make it. There must be a million positions where we would risk 5 shots to grab an asset such as that. The 5 shots are certainly part of the story, but we need something else to go with them.

At first, I toyed with the idea of anchoring rolls. So long as you can enter easily, having a checker on the bar is like have your back checkers split. The bar is like a phantom 25pt. When your two rear checkers are split to the 25pt and 24pt, there are more rolls that make an advanced anchor than there are when both checkers are together on the 24pt. So, the second part of my story became this: against an advanced anchor, the 8pt is a better blocking point than the bar point. Since you can't have both of them, keep the 8pt.

I tried this story for a while, but eventually I decided it was not a very good one. For one thing, there are not that many anchoring rolls anyway, just 43, 32, and perhaps 21.

Now I have a better tale. The problem, indeed, is the blot you leave behind when you make the bar point. The problem is not, however, the 5 shots. The problem is that the opponent will almost never voluntarily enter on the 24pt. The checker on the bar is coming in on a higher point, and no matter which point that is, it will be within 6 pips of the blot on your 8pt.

That means you will lose some of the initiative. It's not the 5 hitting rolls. It's the 23 rolls that neither hit nor dance nor force an entry on the 24pt. Those are the rolls where you will be forced to deal with a blot that is exposed to a direct shot. Instead of playing freely, making the best of what the dice give you, you will be forced to consider whether to save your blot on the 8pt.

In addition to that, I get to toss in a piece of my anchoring story. This time it applies to a blot, however, rather than an anchor. Here goes: Against most splits, the 8pt does a better job of containment than the bar point.

So, that's my new story. I'm still trying it out. I don't know if it's any good. One cool thing is that I invented this story. Unlike the other 99.9% of everything I know about backgammon, this is a theory I came up with by myself.

Hope I don't have to toss it out next week!

Mike,

I like your story and it sounds correct to me, I'm certain it will hold up next week as well.

1-1 as a reply to an opening roll is a really interesting problem. Here's how I think about it.

If you could open with a double, then the best play with 1-1 is 5(2) 7(2). But it's not the monstrously correct play that most players think. XGR++ evaluates it as 0.042 better than 5(2) 22. A clear play, but it's not a blunder to just split your back men.

As a reply to the opening move, we can't just assume that 5(2) 7(2) will be correct. We have to think about how our opponent's play changed the position and whether splitting has gone up or down in value and whether a blot on the 8-point has gone up or down.

In general, if your opponent didn't split, you want to play 5(2) and 7(2). If he didn't split he probably brought down builders, which makes splitting more dangerous. The exception comes when he didn't split because he made his 5-point with 3-1. When your opponent makes his 5-point your desire to split goes way up, so 5(2) and 22 is the play.

If he split with a 6, of course you make the 5 and hit him by making the 7.

That leaves the splits with 1s, 2s, 3s, and 4s.

If he splits with a 1 or a 2, making the 7-point leaves a direct shot, so you play 5(2) and 22.

Splitting with a 3 is a special case, and you point on him with 6/4*(2).

He'll split with a 4 with just two rolls, 4-3 and 5-4. Obviously you now start with 6/5*(2), and now it's either 7(2) or 22 for the last two aces. Splitting in the opening is good, but splitting with tempo is even better. Since your opponent is on the bar, the value of 24/22 has gone up substantially. On the other side of the board, you've traded the 8-point for the 7-point plus a blot.

By itself, the blot's not so bad. It's an asset in that it's both a builder and a slot for the 8-point. It's also a direct liability in that it can be hit with 5 rolls (6-2, 5-3, and 4-4). The problem here is not the number of hits, but the fact that 6-2 and 5-3 are bad shots if you keep the 8-point and play 24/22, but great shots if you play 7(2).

And the last problem with the blot, as Mike points out, is that it's a lingering liability, like an athlete with a sprained knee. Until it's cleared up by either being hit or by making a point, it affects all your future plays because you always need to take into account how likely the blot is to be hit.

The net result for 1-1 after the 4-3 and 5-4 splits is that splitting 24/22 has clearly gone up while 8/7(2) has gone down. Without XG we'd have to make an educated guess at this point, but XG's evaluation lets us say that 24/22 is the better play by a bit.

Nice explanation, Bill! You have added a couple of new layers to my story.

1. Splitting in the opening is good, but splitting with tempo is even better.
2. The swing on 62 and 53 accounts for a big chunk of equity.

Regarding the lingering liability of a blot on the 8pt, it is worth repeating that in the main variation (23 out of 36 rolls), that blot will be exposed to a direct shot as you prepare to roll on the next turn. In those cases, lingering is tending towards immediate.

Of course, you could roll a nice number that solves that problem all at once. There are 15 rolls that give you a 5 to cover from the midpoint (any 5, plus 41 and 32). In addition, you will have some pointing rolls (22, 42, 53, 64) that make use of the blot. Depending where your opponent enters, you may also have additional point-on-head rolls that involve breaking the 7pt (43, 54).

The existence of all these nice possibilities emphasizes that a blot on the 8pt is an asset almost as often as it is a liability.

After an opening 54-split (24/20, 13/8), version 3.7 of the XG Opening Book has making the bar point with a roll of 11 trailing behind the split by a mere 9 millipoints of equity (i.e., by 0.009).

After an opening 43-split (24/20, 13/10), split beats point by a much larger 32 millipoints. The existence of a builder/target in the opponent's outer board jacks up the value of the split by 23 millipoints. The two obvious reasons are:

1. As a builder, the blot increases the opponent's chance to make a key blocking point. Splitting now, before that happens, is the best way for you to advance your anchor or escape.

2. As a target, splitting makes it more likely you can hit the outside blot.

A more subtle advantage is the issue of initiative. Splitting threatens the outside blot in such a way that the opponent loses some of his freedom. When your runners are firmly anchored back on the 24pt, he can usually play freely, leaving the outside blot, if he sees fit. After a split, however, some of that freedom is reigned in. The outside blot becomes one of those lingering liabilities that sometimes must be dealt with before the opponent can take a risk somewhere else.

Anybody care to guess how to play 33 after the opponent opens with 63-run?

White - Pips 158

Black - Pips 167
Black to Play 3-3

The hit 13/10* is automatic, that takes care of the first 3.
Now you could make the bar point with the remaining 3s, but somehow I'm not in love with it, since White won't enter willingly on the 24-pt (unless 61 or 11) and will already threaten to make an anchor.

Based on that, I would probably unstack the 6-pt and make the 3-pt. As much as I would like to make the 5-pt, I'm not too sure about leaving a blot on the 8-pt (and possibly one on the 10-pt if we decide to split).

With the last 3, we could either make the 10-pt or split to the 21-pt. The split seems natural since White doesn't have any builder yet and also is on the bar. Plus, the builder on the 10-pt is not in immediate danger.

So, to summarize:

- 24/21 13/10* 6/3(2) would be my top pick at the moment
- 13/10*(2) 6/3(2) would probably be my 2nd pick
- Close call for 3rd between 13/10*(2) 8/5(2) and 13/10*/7 13/7
- 24/21 13/10* 8/5(2) would round it
- I discarded 8/5(2) 6/3(2) because of the apparent mandatory hit

That being said, I wouldn't be surprised to be all wrong. I hope the best play is at least in the 5 plays I listed.

The discussion on 11 inspired me to repost some old notes on reply rolls.

http://bigmoneybill.blogspot.com/201...ited-aces.html

Thanks for the notes. I've been checking them out.

Thanks, Uber, for taking a stab at 63R-33. It looks like you and me are the only ones who want to play.

Of all the doublets, a second-roll 33 is the hardest to master. That's because it presents more options than the other doublets. The good news is that it is a very strong reply even when misplayed! Nevertheless, it is worth taking the time to investigate the XG Opening Book to see what the best plays are.

In match play, it is sometimes correct to leave a blot when you play 33. At gammon-go, for instance, it may be correct to hit outside by playing 24/15*. In money play, however, it is always correct to move in pairs. That makes sense, because making new points is bound to be a good thing.

Unless you can hit, it is always correct to play 33 on the second roll by making two new points. This also makes sense, because two points are usually better than one. When you can hit on your bar point, for instance, after the opponent opens with a 6-split such as 64-split = 24/18 13/9, then it is correct to make only one point.

White - Pips 158

Black - Pips 167
Black to Play 3-3

I offered up 63-run (24/15) as the opening move because a reply with 33 shares some similarities with the plays of 11 that are discussed above. As with those positions, this one offers an option hit and make your 5pt. If you do, however, you must leave a blot behind on the 8pt.

As above, if you make your 5pt, the opponent will usually elect to enter anywhere he can, except on his 24pt. Remaking his 24pt is usually a very weak play. That means that any blot you leave on the 8pt will be exposed to a direct shot on most of his entering rolls, unless, of course, you get hit!

No doubt, that has an impact on the position. More important, I think, is the poor structure that results from making the 5pt. The correct play is to make your 3pt. Doing that leaves a balanced structure that is frequently easy to improve.

Here are the resulting positions after each candidate.


AFTER MAKING THE 5 POINT

White - Pips 168

Black - Pips 155
13/10*(2), 8/5(2) leaves an awkward structure.



AFTER MAKING THE 3 POINT

White - Pips 168

Black - Pips 155
13/10*(2), 6/3(2) leaves a more balanced position.

Post count: 1.

Spammer, eh?