When I watch or read about backgammon, often there are statements like 'player x is y% to win' or or 'a resilient anker has about 15% to win' but I don't quite understand how these percentages are calculated. Are pro backgammonplayers actually capable of calculating those numbers on the spot (a bit like pot odds in poker) or are these numbers memorized by having them calculated once and then remembering that a specific position has about x% winning chances? Or is it remebered from seeing the percentages calculated by the bots so often (which is pretty much the case with me)?
Same with gammon and backgammon chances, how is that calculated? (if it's advanced calculus don't go too far into it, I study literature, not mathematics)

For races (e.g. no more contact) it is possible to do an exact calculation. You start with the simplest cases and work backwards. With the help of computers, there are now quite extensive databases that cover race situations, and make perfect play possible in those situations.

For certain specialized positions, e.g. one player has a shot that will either (almost always) win or (definitely) lose, it's possible to get quite close by doing the math.

Some numbers are simply heuristic estimates. This might be a human or a computer program that studies the features of the position and produces its best estimate for each number. Sometimes this is based on an actual formula, but usually it's educated (or not-so-educated) intuition.

Other numbers are based on rollouts (almost always done by computer these days), where the position is played out hundreds or thousands of times, and various statistical methods are then used to zoom in on the "correct" numbers.

There are also "reference positions" that come up frequently and have been extensively analyzed. A player or computer can tweak a real-world position that is close to a reference position, and provide a good estimate of the winning chances, gammon chances, etc.

Usually, the odds don't matter. No one knows what they are, no one can figure them out, and if someone could it wouldn't make a difference to the play at hand.

On occasion, especially for cube decisions, it might be easier to estimate the odds.

Yes.

Let's say you are in position X and have a checker off and are off the gammon. You know that Y position is worth 10% wins and Z position is worth 50% wins (let's say because Y & Z are two reference positions you know & winning pct is known due to rollouts). Your opponent cubes you. If X results in something close to Y on 18 of your opponent's rolls and results in something close to Z on the other 18, then you win about 30%. So, you have an easy take.

I rarely do anything this complex. Usually I just look at the board and make a decision. I know others who take a much more mathematical approach to the game.

Well, you can argue that you might know one play is better than another, in the sense that it gives you higher expectation than the other candidate, without having to know precisely what those winning chances are.

But when it comes to the doubling cube, the ability to nail down these numbers as closely as possible is actually a very large advantage IMO, and the primary reason why the bots are unbeatable long-term, especially in match play where the doubling window is changing constantly based on match score, gammons vs. single wins, etc.

The bots simply don't make cube mistakes. It's actually pretty frustrating to play against.

Not really. The numbers are pretty much known anyway.

Again, this is pretty much known or can be guessed. It takes a bit of practice but then you get a feel for it. It's also not that hard to memorize an MET if you really want to, but it's not really necessary.

Bots are better than humans primarily because of their checker play, not cube play. They don't get tired and they don't make oversights or other dumb mistakes. If you look at human ERs the checker ER is almost always higher than the cube ER.

This is definitely not true. Bots very often make large cube errors/blunders. And frequently it is at lopsided match scores. Snowie frequently makes big mistakes in match play; GNU is much better but still makes cube errors as often as any other bot.

LOL. Evidence, please.

Even Jellyfish 15 years ago absolutely crushed humans when it came to match play cube decisions.

In any case, I'd stake my net worth on GNU or Snowie's cube decisions in match play vs. any human, in non-contrived positions.

http://www.bgonline.org/forums/webbb...mes;read=46533

This came up two days ago. I thought it was ND/T, so did GNU. It rolls out to D/P.

http://img12.imageshack.us/img12/9583/racecube.jpg

This came up a day or two before. I thought Stick missed a cube. GNU thinks it's ND/T by .114. Snowie thinks it's ND/T by .057. It rolls out to D/T.

Or just plug in a lot of 2-away or 3-away positions that GNU thinks are close and then roll them out and you will be surprised at how far off it is. I could come up with a plethora more were I so motivated.

15 years ago, people hadn't had time to learn from the bots, and their match play was significantly worse than it is now. Many players haven't evolved since 1994 but top players have.

I'm not claiming that people are better than the bots. But to say the "bots just don't make mistakes" simply is not true and esp. match cubes is a gross misrepresentation. Bots tend to be better largely because of their checker play (relative equities), not because they are particularly great at calculating absolute equities (cube decisions).

I am not sure whether a human could make better match cube decisions or not than Snowie, using a GNU rollout for the comparison. It's certainly possible IMO.

fwiw mr snowie hater, snowie has the first position as double/pass on 2ply and 3ply

Blah blah...I could come up with an infinitum of positions where Snowie is wrong at 3-away. I really don't care to.

Unless you would care to bet on it

The statement "bots don't make mistakes" is certainly false. Very unusual positions for which the neural nets have little experience can lead to extremely odd plays. But your claim about bots being better because of checker play as opposed to cube play seem tenuous at best. To be even remotely believable you need something stronger than this claim.

You also need to define "bots" as a specific setting of a particular "bot." Rollouts are given a very high level of confidence in most settings, but 2-ply this or 3-ply that may be questionable in certain types of positions. But even more importantly, before bots it was essentially impossible to accurately quantify the size of most cube errors so it's not as if human players had *that* much of an edge in cube handling, anyway.

In fact, your whole contention:

Needs quantification before it can even be understandable. How often is "very often" or "frequently" and how large is "large"? By what standard are you even going to measure this? Consensus of human sentiment?

OK, look, admittedly I wasn't very precise in my claims.

Of course bots can make mistakes in their evaluation of the absolute equity of a position.

But there are two factors that are hugely in the favor of the bots:

1.) They are generally far closer in their absolute winning/gammon estimates than a human

2.) Given a particular estimate, THEY WILL NOT GET THE CUBE ACTION WRONG. There is simply no human who can make anything close to a similar claim, especially for match play. Of course their estimate can be wrong. But they won't make the very common error IMO of getting the estimate right, and then messing up the cube action anyway.

Someone who has better technical experience with NNs maybe could address this, but I believe bots (at least, GNU) have been trained primarily in relative equities.

EDIT: Or, I think I should say, all of their absolute equity training is done for money, not match play.

Anyway I am beyond my area of expertise at this point.

I am talking about GNU 2-ply/Snowie 3-ply. Rollouts are basically gospel from God.

Agreed.

My original statement was to compare a bot's cube ER at match scores vs. with a bot's checker ER or, especially, cube ER in money play.

There is also a question of what you consider "match" cube ER. I can imagine that it might be doable to beat Snowie solely on cube ER (as determined by GNU or XG rollouts) in a best-of-99 5-point match series. It'd be virtually impossible in a best-of-45 11-point match series.

Even if it turns out that the bot's cube ER at match scores is larger than the bot's cube ER at money play, this does not really show that bots are significantly worse at match play compared to money play. It could be that the "average" cube error at certain match scores is larger than the "average" cube error for money games.

If you're right 99/100 times, but the one time you're wrong it's a big blunder, are you significantly worse than another player that is right 90/100 times, but all the errors were very small?

Definitely true. Though I am not claiming bots are "better" for money than they are at matches. I am simply claiming that saying that the bots are much better especially with the cube in match play because they can calculate absolute equities is a pretty big misrepresentation of what's going on IMHO.

Who had the higher ER?