Playing Backgammon against the computer

[socksey]

When I say "struck by" I mean notice. Are you really saying that you've never noticed that winner of each game is almost always the luckiest player?

I haven't paid that much attention to luck in the matter, but I have noticed that when my skill level is rated exceptionally high, I usually lose the match!   

socksey



That's the time of your life when even your birthday suit needs pressing. â€" Bob Hope, on turning 80

[sixty_something]

i have noticed that my best estimated Snowie ratings often seem to come in games where GNUbg says "Good dice, man!", "Go to Las Vegas immediately!", or "Go to bed" .. this isn't always the case, but i conclude i am at my best when the choices are obvious, yet still have a lot to learn when faced with less than obvious choices

[Zorba]

That's true, however anyone who does any amount of GnuBg analysis cannot help but be struck by how few games are won by the player with the least luck.

Yes, I have only a few matches out of thousand where I won despite having less luck overall (never use gnubg's luck per move rate, it's useless and mostly meaningless). These were matches with long games, against much weaker players.

However, it would be wrong to conclude that luck therefore completely decides nearly all matches.

A better player needs less luck to win a match than a bad player. And less luck happens more often.

Using some numbers, both players start out with 50% MatchWinningChances. Lucky and unlucky rolls add and subtract from the percentage. Errors by you subtract, errors by opponent add. The match ends when you reach either 100% or 0% MWC.

So, f.i. a good player near the end of the match might end up getting to 70% MWC, with both sides having (roughly) equal luck until then, because of the errors of opponent costing 20% MWC more than his.

At that point, the skilled player only needs luck of the size of gaining 30% MWC to win and end the match. The less-skilled player would need luck in the size of 70% MWC to win. The latter is much more unlikely to happen.

So, skilled players are lucky more often, yes, but by smaller amounts on average!
Less skilled players are lucky less often, but when they are lucky, it is by bigger amounts!
Overall, therefore, both players get equal shares of luck. And skilled play is useful, because it reduces the amount of luck you need to win. And smaller amounts of luck happen more frequently than bigger amounts of luck, so you increase your winning chances.

Douglas Zare wrote a good article on it, explaining this in more mathematical terms and detail.

[playBunny]

However, it would be wrong to conclude that luck therefore completely decides nearly all matches.

I quite agree. My conclusion, and the issue that I'm interested in (here and in the thread with the poll) is that the mathematical, bot-calculated definition of luck doen't seem to do that useful a job given how we all (that's a very loose "all", lol) know that skill is a very important factor.

A better player needs less luck to win a match than a bad player. And less luck happens more often.

[...]

So, skilled players are lucky more often, yes, but by smaller amounts on average!
Less skilled players are lucky less often, but when they are lucky, it is by bigger amounts!
Overall, therefore, both players get equal shares of luck. And skilled play is useful, because it reduces the amount of luck you need to win. And smaller amounts of luck happen more frequently than bigger amounts of luck, so you increase your winning chances.

Now these are interesting observations. I haven't looked at anything like thousands of matches yet so this pattern hasn't emerged from the background for me. Certainly these ideas make intuitive sense and I shall watch out for them. Thank you for your thoughtful insight.

Douglas Zare wrote a good article on it, explaining this in more mathematical terms and detail.

I might have read it but then again I may be thinking of a different article. Would you have a link by any chance?

[dorbel]

As far as I remember, that Doug Zare article is on Gammon Village and you need a subscription to view it.

There is indeed more to luck than the bot definition, but it is a good guide. I haven't collected any stats, but my impression is that the player who plays better is slightly more likely to get the luck. After that, it is certainly true that the match result goes with the luck, perhaps as much as 95% of the time.
Some thoughts on this. Matches usually go with the luck overall, but I think that it is the luck in each individual game that is more important. The luck in a single game, in my experience, usually swamps any effect that the checker play has on the outcome. The shorter the game, the more likely this is. The superior player is better placed to take advantage of this phenomenon, because he will use the cube better, winning more points when he gets the luck and losing fewer when he doesn't. His better checker play affects the outcome only insofar as it leads him to positions where his cube skill comes into play. In games where the luck is in his favour and the cube is centred, good checker play leads quickly to a cube turn (or of course to a position where playing on for a gammon is correct for the moment). When the luck is running against him, then good checker play prolongs the game for as long as possible. The longer the game goes on, the more chance there is of the luck evening out and the more chance there is of the weaker player making a cube error.
Quite typically, an expert player who plays with an average Snowie error rate of 5 will see that those errors break down to 4 with the checkers and 1 with the cube, but in my opinion it is that cube error that is vital. You can see practical examples of this in many chouettes, where individuals who make many clear errors with the checkers survive and even prosper week after week, because their cube instincts are good.
This is not a widely held opinion I know, but in practical terms, in an environment such as fibs where a 9 point match is considered a long one, then good cube handlers make hay. You can play the checkers brilliantly, but you won't see much for it in terms of results if you don't use the cube well. Luck does control each game and overall, most short matches, but good cube play will help you to ride the wave.

[PersianLord]

Well, I agree with Zorba. But there are some points which I would like to mention:

1- The fact is that the more skilled players distributes their men in such a way that a more portion of the all possible rolls will be considered to be contructive/lucky for them, while the weaker players, who are usually more conservative, often fail to diversify their position by playing too safely and therefore a much less portion of the 36 rolls would be of good value to them. I hardly can label this as a difference in luck.

2- The more skilled players take advantage of their share of luck (be it small or large) in a much more efficient way, especially regarding the cube handling. For example, suppose that after an opening roll of 3-2 by your opponent which have been played as 15/10-24/22, you roll a lucky 5-5, pointing on both. If he fails to roll a double 2s, 4s, or 5s, then you will have a double and he will have a pass in many occasions. A skilled player would double, a non-skilled one might well not. By doubling, the skilled player gains equity and either prevents his opponent from rolling lucky rolls (in case of a right pass) or even might milk him even more equity by going to gammon him on a 2-cube (in case of a wrong take). A less skilled player, by not doubling, doesn't take advantage of the God's blessing (lucky rolls). Again, I don't think this might have anything to do with luck alone.

Regards

[dorbel]

If he fails to roll a double 2s, 4s, or 5s, then you will have a double and he will have a pass in many occasions.

Actually, this isn't true. If he dances with both (25%) you have a cash, although it is a common mistake to play on for a gammon here. If he enters with one (50%) you have a double and it is an easy take. If he enters with both (25%), doubling is a blunder.

Also worth pointing out that playing 24/22, 13/10 is the third best play with an opening 3-2.

This post makes my point rather nicely. The strong player will extract the maximum benefit from his "lucky" 5-5, the weak player won't, even though both have been equally "lucky".

[Zorba]

I quite agree. My conclusion, and the issue that I'm interested in (here and in the thread with the poll) is that the mathematical, bot-calculated definition of luck doen't seem to do that useful a job given how we all (that's a very loose "all", lol) know that skill is a very important factor.

The intuitive idea of luck many people have, is usually pretty messy and even inconsistent, self-contradictory. Like with many subjects in statistics and probabilities, we're just not very good at it, without using mathematics.

If you measure the luck in terms of equity ("average value" of a bg position), then the total luck over all 36 possible rolls should be zero. If not, you get an unworkable situation where the equity before rolling on average will go up (or down) after rolling, begging the question if the equity just shouldn't be higher (lower) in the first place.

Another thing to consider is that luck has two components: frequency, and size (positive and negative). Only by multiplying it all, do you need to get to zero.

For instance if you're playing a succesful backgame and get a quintiple shot, for 35 shot numbers. Suppose any hit would give you a cash next turn, and the one missing roll would obviously be very bad for you (say you get (back-)gammoned nearly always after that).

Is it lucky to roll a hitting number? Many will say no, because 35 out of 36 rolls hit, so you are "supposed" to hit. But since the one missing roll is clearly very unlucky, it must mean by definition that all hitting numbers are lucky, even if only slightly. The "luck" in this case, is the luck of NOT rolling that one missing number.

Another example is when in an almost equal medium-short race. Suppose I roll 66 three times in a row, and my opponent rolls something average every time. Some might feel that the third 66 was the luckiest, since I already got two in a row, a third one is "unbelievable luck"! But the fact is, that the first 66 was by far the luckiest one, and the third 66 was not really all that lucky.

Why not? Because the first 66 moved my winning chances from 50% to say, 80% which can be considered very lucky (0.6 equity jump). The second 6-6 might have brought me from 80% to 92%, which is a much smaller gain. The last 6-6 got me from 92% to 98%, still lucky, but just a 0.12 equity gain.

I might have read it but then again I may be thinking of a different article. Would you have a link by any chance?

Here it is: http://www.bkgm.com/articles/Zare/AMeasureOfLuck.html

[PersianLord]

Actually, this isn't true. If he dances with both (25%) you have a cash, although it is a common mistake to play on for a gammon here. If he enters with one (50%) you have a double and it is an easy take. If he enters with both (25%), doubling is a blunder.

Also worth pointing out that playing 24/22, 13/10 is the third best play with an opening 3-2.

This post makes my point rather nicely. The strong player will extract the maximum benefit from his "lucky" 5-5, the weak player won't, even though both have been equally "lucky".

True.

[diane]

I haven't paid that much attention to luck in the matter, but I have noticed that when my skill level is rated exceptionally high, I usually lose the match!   

That can come down to just being unlucky.  If you make a perfect opening move, but get hit and blitzed, you wont have any opportunity to make any mistakes.  You will lose and on analysis your skill ranking will be very high - nay almost perfect and your luck rating low, because you didn't get a chance to get any luck either!

I too have observed that if I am unlucky I lose, pretty much consistently [with a handful of notable exceptions in thousands of matches], and that really was causing me to lose interest in the game.  Because if no matter how much better I get, I can be beaten by a lucky opponent, what is the point?

I am playing around at the moment with the concept that has been explained here, and I am sure there is something to it - that better players create luck, otherwise someone up there just hates me 

[dorbel]

The easiest way to be rated highly for a game is to get hit early on, dancing or playing forced moves from then on and getting closed out. Thus you can get a terrific rating when being buried. Winning a long complex game on the other hand, often involves getting a poor rating because the play is so hard. Rating in one game or one match or even ten matches can be misleading. Your average rating over a hundred or more matches is a better guide.

[blitzxz]

I quite agree. My conclusion, and the issue that I'm interested in (here and in the thread with the poll) is that the mathematical, bot-calculated definition of luck doen't seem to do that useful a job given how we all (that's a very loose "all", lol) know that skill is a very important factor.

My conclusion here is that backgammon is _all_ about luck. Any single game or match is decided by luck and you will need hundreds or even thousands of games for skill differences starting to show and luck even up.

And I somewhat agree with dorbel that double error can be more harmful. But this is only if the errors are mainly wrong passes and missed doubles. These errors will cut down the variance and will make the skill show more quickly. However if the errors are too early doubles and wrong takes it will maximaze the variance and with good streak you can win for a long time against better player. And this is based on my experience how maniac cube handler ends up winning quickly 50 points or more against me in money game.

[ah_clem]

A lot of the disagreement here stems from the definition of "luck".  Those of us who are prone to mathematical analysis tend to use the strict mathematical  definition, which is the same as what is used by gnu, snowie, et. al. to define the amount of "luck" in the match.   The problem is that this definition doesn't gibe very well with most layman's notion of the term.  Let's look at two examples:

Suppose we're playing a match to 21 and in the first game I roll high doubles three times in a row to take a commanding lead in the race and then coast home to win the first game.  Is this lucky?  Most people would say yes, but the gnu analysis wouldn't mark these rolls as lucky - at the start of the game my MWC was 50% and after going ahead 20-away to 21-away my MWC is still only about 50%.  Since the dice didn't change my equity by very much, it's neither lucky nor unlucky.

Now, suppose we've played the match almost to the end: the match score is 20-20 and I'm on roll with checkers on my  5 and 2 points and you have a single checker on your one.  Either I bear in both checkers and win the match, or I don't and you win the match.  I've got a 19 out of 36 chance of winning, or just a biscuit over 50% MWC.  No matter what I roll, my chances will change to either 0% or 100%.  So every roll will be either lucky or unlucky.

In this situation, most people wouldn't consider a roll of  6-3 particularly lucky or a roll of 4-2 as particularly unlucky.  But the mathematical definition would mark them as very lucky or very unlucky.  Does this definition make sense, even though it's somewhat counter-intuitive?  Well, The game came down to a single roll of the dice, with probabilities similar to that of a coin-flip.  IOW, the match was decided by luck, so of course it makes sense.  To me anyway.