How to play a massive backgame?

[blitzxz]

I played very interesting backgame against fellow fibster a while ago. I tried to analyze it but got nowhere. What I found out was that gnu 2-ply is propably playing almost half to moves wrong after the massive 3-point backgame is achieved. This was according to very quick 0-ply rollouts. I tried to make 2-ply rollouts but just one rollout will take several days and I wouldn't still trust it.

Here is 5 positions from the game. What is correct way to handle these positions?

Score is also little bit tricky: 4-2 crawford game black leading. So no cube and gammons doesn't matter. But backgammons does.

I also attach the whole game in here.

[blitzxz]

Couple options here. Gnu wants to hit here which I wouldn't do.

Pipcount: White 147 Black 217

[blitzxz]

This is very hard choice at least for me. Should black hit or not? And if hit what with the 4?

Pipcount: White 140 Black 217

[blitzxz]

Again gnu is hitting here.

Pip count: White 156 Black 208

[blitzxz]

This is a little bit awkward roll.

Pip count: White 148 Black 225

[blitzxz]

Hit, hit, hit, says the bot.

Pip count: White 148 Black 213

[PersianLord]

That's true, dear friend, gnubg is often helpless in evaluating massive backgames. A while ago, I played a historical 1-pt with yeti the great and when analyzing it I found that gnubg is totally unable to evaluate it. here is the link:

http://groups.google.com/group/rec.games.backgammon/browse_thread/thread/be1aab7e9bff99da/9ed23c7a02e2ed35#9ed23c7a02e2ed35

[inim]

gnubg is often helpless in evaluating massive backgames

Why do you think that, can you give statistically relevant data? How often exactly is "often"? Can you give concrete examples of positions where gnubg goes wrong? Can you give examples for where it is right, as "often" doesn't mean "always" ...

I found that gnubg is totally unable to evaluate it

How did you find that? What was your method or experiment? If gnu was "wrong", what reference was used as "right"? Is there such a thing as a "right" move at all?

BTW, the sum of the equities of both players is never zero (in the r.b.g. article you assume that), as equities are always >= 0. Dependeing of the type of equity used (normalized or unnormalized) both actually may not even have any upper limit, assuming you play for an unlimited pot in a money game.

[playBunny]

BTW, the sum of the equities of both players is never zero (in the r.b.g. article you assume that), as equities are always >= 0.

1-point match, Opening roll 5-2

    1. Cubeful 3-ply    24/22 13/8                   Eq.:  -0.009
        49.6%  13.3%   0.4% -  50.4%  12.9%   0.4%

Equities are always zero or positive except, of course, when they are negative.

What PersianLord is referring to is that generally, barring big swings, the equity of one player is the opposite sign of the opponent's from one move to the next. One's good fortune is the other's downfall. When analysing certain backgames, however, GnuBg can be seen to report that whoever is on roll is a huge favourite. Both players have positive equity and the highest wins percentage. It seems that all it takes is owning the dice. Or the opposite, that both players are losing very badly from one roll to the next, with minor changes in the position. That suggests more that GnuBg doesn't have a clue than that it knows something that we don't. The example in the newsgroup shows that, +.9 for each player.

What's happening is that Gnubg is trying to map the given position, which it's never seen (or perhaps only a couple of times, very early on in its training when it didn't know how to play), to the nearest reference position - and failing miserably. The more extreme the backgame the more likely it is that there's no reference position in sight.

[PersianLord]

1-point match, Opening roll 5-2

    1. Cubeful 3-ply    24/22 13/8                   Eq.:  -0.009
        49.6%  13.3%   0.4% -  50.4%  12.9%   0.4%

Equities are always zero or positive except, of course, when they are negative.

What PersianLord is referring to is that generally, barring big swings, the equity of one player is the opposite sign of the opponent's from one move to the next. One's good fortune is the other's downfall. When analysing certain backgames, however, GnuBg can be seen to report that whoever is on roll is a huge favourite. Both players have positive equity and the highest wins percentage. It seems that all it takes is owning the dice. Or the opposite, that both players are losing very badly from one roll to the next, with minor changes in the position. That suggests more that GnuBg doesn't have a clue than that it knows something that we don't. The example in the newsgroup shows that, +.9 for each player.

What's happening is that Gnubg is trying to map the given position, which it's never seen (or perhaps only a couple of times, very early on in its training when it didn't know how to play), to the nearest reference position - and failing miserably. The more extreme the backgame the more likely it is that there's no reference position in sight.

Thank you very much dear bunny for educating and enlightening inim. 

[dorbel]

PersianLord has still not replied to, or even addressed the valid questions raised by inim. let me repeat these questions. Why does PersianLord think that "gnubg is often helpless in evaluating massive backgames"? How did he find "that gnubg was totally unable to evaluate it"?
Further, positions where the advantage lies with the player on roll are quite commonplace and certainly not confined to backgames.

[PersianLord]

PersianLord has still not replied to, or even addressed the valid questions raised by inim. let me repeat these questions. Why does PersianLord think that "gnubg is often helpless in evaluating massive backgames"? How did he find "that gnubg was totally unable to evaluate it"?
Further, positions where the advantage lies with the player on roll are quite commonplace and certainly not confined to backgames.

The question is how many positions are statistically enough to support my claim? I can play yeti and can show you at least 100 positions in which gnubg attributes to both sides ~+1 equities, which is mathematically wrong. If this may be of help, I'm ready to do it.

[inim]

1-point match, Opening roll 5-2

    1. Cubeful 3-ply    24/22 13/8                   Eq.:  -0.009
        49.6%  13.3%   0.4% -  50.4%  12.9%   0.4%

Equities are always zero or positive except, of course, when they are negative.

The -0.009 is just the difference to the equity you had before you rolled 5-2, mulitplied with a scale dependent constant. It basically says that 5-2 is so bad an opening roll that it actually reduces your chances to win.

This becomes more obvious when one transforms gnu's EMG equity into the equivalent (and for many more intuitive) form of MWC, match winning chanches. In this 1pt match, the MWC would have changed from ~50% to ~49.996%. Obviously you can not have a chance less than 0% to win the match -- it means you already lost it.

Depending on the value range you project (normalize) equity into you can epress the MWC %ages an positive or negative values at your liking. You may normalize 0..1, or -1 .. 1, or even π .. 2π.

I stand corrected insofar that in Equivalent-to-Money-Game equity normalization, or EMG as gnubg calls it, indeed normalizes to -1 .. 1, so 0 is the neutral position (before the match starts) and minimum equity is indeed -1. Personally I prefer the normalization 0..1, which more closely resembles the MWC notation.

[playBunny]

The -0.009 is just the difference to the equity you had before you rolled 5-2, mulitplied with a scale dependent constant. It basically says that 5-2 is so bad an opening roll that it actually reduces your chances to win.

My understanding of -0.009 is that if you play out a sufficiently large number of games from that position (your GnuBgesque play against GnubG) and you've got money on every game then you will walk away with less money than you arrived. That's negative equity in real world terms. I've never used MWC much and it's almost meaningless to me.

The -0.009 is just the difference to the equity you had before you rolled 5-2,

We differ in our understanding of this. The -0.009 is the absolute equity of the position after the move, regardless of what went before. If that position had been reached with different dice then it would still have the same equity. Evaluations do not know, nor do they care to know, the history of the position.

[inim]

My understanding of -0.009 is that if you play out a sufficiently large number of games from that position  [...] you will walk away with less money than you arrived. That's negative equity in real world terms. I've never used MWC much and it's almost meaningless to me.

Both EMG and MWC normalizations have their merits, and both are options for display in gnubg.

Your statement is correct, you long term will lose money. But as the amount is scaled over a range of 2, it doesn't of course mean that would be 0.009 monetary units in a real money game. It is more like a % of the amount of money in your average pot after considering cubes, gammons etc. Nevertheless, EMG allows quick assesment for overall win/lose situation.

IMO, the notation of MWC is superior if you e.g. look at cube market windows, which very naturally are expressed as MWC. As I do that more often than playing for money, it's my prefered form.

We differ in our understanding of this. The -0.009 is the absolute equity of the position after the move, regardless of what went before. If that position had been reached with different dice then it would still have the same equity. Evaluations do not know, nor do they care to know, the history of the position.

I'm unsure whether the figure gnubg actually displays in this slot is a delta or an absolute, need to check that. It for sure displays deltas somewhere in the ranked list of moves in some position, may have mixed that up. Several derived values, such as gnubg's definition of of luck, use equity deltas in their formulas as well (as thresholds), because large deltas correspond to large positional swings.

The sweet thing in the special case of the first roll is: the delta to the previous score of 0.000, and the absoulute new EMG equity are the same number, here -0.009. So we are both right for THIS roll, at least

[playBunny]

IMO, the notation of MWC is superior if you e.g. look at cube market windows, which very naturally are expressed as MWC. As I do that more often than playing for money, it's my prefered form.

As the cube is where I'm weakest and I've only recently started exploring the market window dialogue, without that much comprehension, unfortunately, I'll have to give that a go. Thanks for the tip.

I'm unsure whether the figure gnubg actually displays in this slot is a delta or an absolute, need to check that. It for sure displays deltas somewhere in the ranked list of moves in some position, may have mixed that up.

Yes, the first move is absolute and subsequent moves show their absolute equity plus the delta.

The sweet thing in the special case of the first roll is: the delta to the previous score of 0.000, and the absoulute new EMG equity are the same number, here -0.009. So we are both right for THIS roll, at least

Yep!

[blitzxz]

No one has commented the positions yet.....

[playBunny]

Further, positions where the advantage lies with the player on roll are quite commonplace and certainly not confined to backgames

I agree with you that there are positions in other phases of the game where the equity is positive for whoever's one roll but how frequent is "commonplace"? Of those positions how many are situations, ie. not confined to just a move or two but for a whole period? And how often, too, is the change on the order of +90% to -90%. Wuold you seriously suggest that the player attempting to contain a checker has 90% chances just because they're on roll but on the next roll those chances drop to 10%, or some other such massive swing?

I think the best answer comes from GnuBg itself. You'll see some totally daft moves in some backgames. I had one against it a while back where it made a stacke of 5 or 6 checkers. It looked like a beginner playing "No blots, please". There's no way that I could explain that in terms of it attempting to contain my loose blot but it did make a kind of sense if it was misrecognising the position and getting its neurals in a twist.

[inim]

I think the best answer comes from GnuBg itself. [...] It looked like a beginner playing "No blots, please". There's no way that I could explain that in terms of it attempting to contain my loose blot but it did make a kind of sense if it was misrecognising the position and getting its neurals in a twist.

The best answer comes from Joseph, who trained the initial gnubg net, and it hasn't changed a lot since:  http://pages.quicksilver.net.nz/pepe/ngb/index.html. He was completely aware of the issue with containment, and he experiented with a dedicated NN for such positions (see chapter "The Crashed Net"). However, he found that when containment improved other positions degraded in the net. The crashed net is still in the gnubg sources, but not activated.

So this is really an open research issue, and the the gnubg team would surely be happy to hear about any approach to solve this problem. You can contribute even if you are not a pro coder, the tools to train and verify nets are useable with slightly advanced PC skills already. Some math skills required, however.

[playBunny]

I actually would like to learn how to train the net and have already studied the code but logical I am, mathematical I'm not. Time is also an issue. There are plenty of neural network texts that delight in explaining the maths but I've not come across any that give the idiot's guide to impementing them. I wouldn't even know where to start. I'd love to create a neural net to play other games. Ludo would be a nice small project, for instance. If I knew enough about it then extending GnuBg to play other gammon variants would be an interesting future project.

[dorbel]

OK, lets actually discuss the positions! Position 1.
The first thing to say about this position is that it is not yet a backgame. Granted Black has six men back and can certainly enter a backgame here if he wants to, but as he owns the 20pt and can make his own 5pt here, then surely this is still a positional struggle. Black is in quite good shape for that and should aim to recycle checkers through his high anchor so that he can make points in his own outfield. I don’t think that the massive backgame option is necessarily a non starter, in fact it may do as well as the simpler game plans, but I don’t see how you could know that over the table. 24/20, 8/5 for me, the play of snowie and gnu, although they both think that 24/20, 13/10 is close.
Here’s what Bill Robertie has to say about back games. “Well-timed back games can give you a chance to save a bad game, but that’s all. Don’t seek them out.” Again, “Remember that the back game is the last resort when all other plans have failed, so look for opportunities to break out of the backgame by hitting shots”. Who is Bill Robertie? The first two-time world champion and one of the truly great theorists and teachers. His books are of somewhat variable quality, but I strongly recommend, if you can find them “Reno ‘86”, “Dwek v. Genud” and “Modern Backgammon”. His Advanced Backgammon Vols 1 and 2 will also provide you with a terrific grounding in checker and cube play.
Some points to note. Losing a gammon here doesn’t cost much, but how much is not much? Losing your free drop costs you about 1.5% of match equity, i.e. you are 51.5% to win the match at 1-away, 2-away post Crawford. Losing a backgammon is of course a disaster and it will cramp your style more than somewhat if you get down to the hard end of a backgame.  You will have to run to save the bg in positions that are a big stay normally.
So here we have a choice of two game plans. Make the 5pt and try to play a nice solid positional game that should be fairly straightforward, or go for a big back game which will undoubtedly be hard to play. At this score it seems to me to be an easy choice.

In position 2 we can see what can happen down the back game road. This isn’t a bad roll, it’s just very tough to play but you may like to ask yourself how would you have played any other rolls. This is a rocky road from here to the end! 24/20, 13/11(Snowie’s play) looks reasonable and 24/22*, 13/9 also has its merits. Hitting the blot isn’t an attempt to go forward. The idea is to make the 22pt if possible which will work quite well with any of the other available anchors. 24 and 23 is a poor game at best and neither of those points works well with the 20pt.
Other plans are probably quite reasonable too, but avoid playing 5/3 or 8/6 with the 2. You must keep all your checkers in play and as flexible as possible. Thus 13/7, or 13/9, 13/11 or even 24/20, 24/22* are not too far from the right idea.

Now we move on to position 3 and look at a White play for a change. Oh dear, how has Black got a checker onto his ace point? Now he will have to play with 14 men and the dead checker can’t be part of a winning prime. In some variations it will get recycled, but the move that took it there just had to be wrong. Anyway, should White hit Bar/17* or try Bar/23, 21/15? The other two sixes aren’t worth considering, as the midpoint still has a function connecting with White’s back checkers and burying the spare from the bar point can’t be right. Spares mean choices and flexibility, very important. Snowie will hit here, but the rollout clearly shows that this is wrong. The quiet play wins 60%, the hit 55%, a huge difference. Although White will take a gammon if she can get it and will benefit hugely from a bg, her prime aim is just to win the game and this play is clearly best for that.
Now we move on to position 4. The over-riding concern here is to keep the 23 and 22pts. Black is just about committed to his back game and these are probably the best combination that he can get, only 24 and 22 come close as an effective force. With this in mind the threes have to come from the midpoint. The rollout comes down in favour of Bar/22, 13/10(3), but Bar/22, 13/10, 13/7 is close. Snowie will play Bar/22, 23/20, 13/10(2), trying to avoid committing to the true deep backgame, but that play doesn’t do well in the rollout. We hear a lot about how “Bots don’t know how to play backgames”, but the fact of the matter is that they are extremely tough to play, from both sides and that however badly the bots do or don’t play them, humans are worse!
Finally position 5. Black picked out bar/22, 13/10(3), nice play and once again White has to choose between hitting or not. Sometimes, it doesn’t matter much either way and this is one of those times. The rollout barely distinguishes among half a dozen different plays.
You could try 21/16, 21/17 and 17/12*, 13/9 tries to make another blocking point. Take your pick.
I hope that I have demonstrated that back games are to be avoided if possible. Their outcomes are uncertain, the play extremely difficult. In position one, the computer assigns almost equal equity to the straightforward play that makes the 5pt and the more complex 24/20, 13/10, inviting a backgame. However, you must bear in mind that as humans our chances of attaining the theoretical equity in any difficult position are next to none. I believe that only a true World Class player, of whom there are probably only a hundred or so in the world, will get near to the theoretical equity of position 1 when choosing a back game, whereas an ordinarily strong player should do quite well with 24/20, 8/5. However, any play that hits on the 4pt is clearly a blunder and should be avoided at all costs! I note that one correspondent suggests that gnu hits in this position, but I don’t know why, mine doesn’t!
Enjoy the game!

[blitzxz]

I hope that I have demonstrated that back games are to be avoided if possible. Their outcomes are uncertain, the play extremely difficult. In position one, the computer assigns almost equal equity to the straightforward play that makes the 5pt and the more complex 24/20, 13/10, inviting a backgame. However, you must bear in mind that as humans our chances of attaining the theoretical equity in any difficult position are next to none.

Thanks for the analyzes, dorpel.  I have to say that because backgames are so hard to play that means that the opponent, another human, will make errors too.

There is some mix up in the position 1 also. It is white's turn, white on bar, it is not possible to hit to 4 point or play 24/20 8/5??

[dorbel]

I see. if I could read a diagram correctly I'd be a great analyst! With white on roll it's pretty clear to hit from the bar, mostly to try and stop the opponent from making his 5pt.
There is a tendency to think that hitting a man with  six checkers back must be wrong. it can be, but it isn't always.