grenv: I do not agree that luck usually evens out in the course of a match. It takes much longer, several matches at least. Certainly I have seen many 21 point matches dominated by luck, though hardly a majority of such matches.

Groucho: I've never seen it adopted :) Some people probably like the added luck factor, consider it exciting.

Groucho: Doubles add dramatically to the luck element in hyper as well as in race situations in other backgammon games. I have suggested eliminating doubles in pure races before.

playBunny: The stronger player will win more matches than he loses, but probably not more than he draws, unless the skill difference is great.

The length of a backgammon match is always fixed in terms of a number of points, rather than a fixed number of games (except in the case of a 1 point match which could also be considered a 1 game match). Because there are no draws, BG is almost always played in matches to an odd number of points.

grenv: Talk about putting the rabbit in the hat -- how could you have those point changes if the two players are evenly matched? (You must assume equal ratings to make such an assumption meaningful).

tonyh: I have no objection to the draw option. I have had draws on IYT. However, ithe backgammon world it is an anomaly, and would never be allowed in real-life tournaments.

grenv: There is, of course, such a thing as a draw if the rules permit it as they do here. However, there is no board position that forces a draw (what might be called a "natural" draw) so the ability to agree on a draw is something of an anomaly.

Another anomaly here is the notion of a 2-game match (used in the standard stairs). BG is never played in 2-game matches for the very reason that the predicted outcome in such a case is 1 win apiece, resulting in a drawn match. I don't play standard stairs anymore for that reason: I was losing rating points in the great majority of matches without gaining anything on the stairs.

nabla: Mathematically, it's probably correct for the trailer to double at the first opportunity in all post-Crawford situations. However, BG is more than mathematics and psychological factors lead many to try to game their opponents in situations where the opponent does not have a free drop.

Of course, the biggest psychological factor of all is the risk that you may forget to double altogether, winning 1 point rather than 2 and giving your opponent a free drop in a later game.

On your other point, I don't think there are any first roll/second roll combinations (someone will likely prove me wrong) that create such a gammonish position that the trailer should refrain from doubling on that ground alone. In fact, this is likely to be the situation where an immediate double is called for even by those who tend to hold the cube: if the opponent believes the position is gammonish, he may make a mistake and drop.

Czuch Chuckers: Up 6-0 in a 7 point match, you will be playing the Crawford game where no double is allowed (http://brainking.com/en/GameRules?tp=23). Assuming that the trailer wins the Crawford game, it will be 6-1. Here's where it gets tricky.

Post-Crawford doubling strategy

Leader's strategy:

As the leader, you must assume that the trailer will double at every opportunity. Therefore, the trailer needs only three wins to take the match. When you are leading by an odd number of points, you have one "free drop." This means that if you drop a double at 6-1 making the score 6-2, the trailer must still win three games to win the match.

You should not drop a post-Crawford double when you are leading the current game or when the game is even. You probably should drop the first post-Crawford double that occurs when you are behind in the game (you may not get another opportunity).

You should not drop a post-Crawford double when you are leading by an even number of points, even though you are behind in the game, unless you think you are going to be gammoned. For example, suppose the score is 6-2 and your opponent doubles. You are significantly behind in the pip count but you don't expect to be gammoned. If you drop, the score will be 6-3 and the opponent will need only two more (doubled) wins to win the match. If you take and lose, the score will be 6-4 and the opponent will still need two more wins for the match. In other words, you are no worse off after taking than after dropping, and by taking you have a chance to come back and win the game and match.

Trailer's strategy:

If you are trailing by an odd number of points, you should double as soon as possible. If you wait until after you are ahead in the game, your opponent will use his free drop and you will have wasted a win. If you are trailing by an even number of points, many players will wait until an opportune moment to double. For example, you may double at a time when a good roll will put you in position to win a gammon; the opponent may drop out of fear of losing 4 points, and you will have advanced one win closer to winning the match. Or you may wait to double until you have taken a significant lead in the game, hoping that your opponent will make a mistake and drop.

Because the trailer should double at the first opportunity, he can't -- in the Crawford game only.

pgt: Simplest and least likely solution :)

Most sites that I know of either have an automatic "are you sure" mechanism, or one that can be toggled on and off. It is a convenience that I highly recommend. Blather all you like about reading before you click, if you have a hundred games going here and a life, you are going to make a few mistakes. It would be a thoughtful and useful gesture on Fencer's part to provide the same consideration here as is provided elsewhere.

Hrqls: It is important to distinguish between an average rating and a combined rating. An average rating would be less volatile and separate ratings would be maintained for each sub-type. However, an average rating could be misleading for players with little experience in one or more sub-types. A combined rating would compute the effect of each match on a single overall rating, regardless of which sub-type was played.

WhiteTower: I have discovered that my ratings in the 4 backgammon games mentioned are very close, except for regular backgammon where ratings are higher for some reason -- possibly just because more games have been played, possibly because the makeup of the player pool is different. But when I played backgammon and nackgammon under separate names on a different server, I found the ratings were so close that I decided to give up the idea of separate accounts for different games. I think the 4 games mentioned have essentially the same strategy, and there would be no harm in computing a single rating for all 4. The question, of course, is whether it is meaningful to combine the ratings (you probably wouldn't want to combine backgammon with chess), and I think that it is meaningful to combine those 4 games. With due respect to my carrot-loving and procreative furry friend, I think that Hypergammon and Anti-backgammon are sufficiently different from the 4 I play to make them truly different games, and to make a combined rating less informative than separate ratings.

playBunny: To be honest I forgot all about Hypergammon, while I deliberately excluded anti. It's also true that I only considered the games that I play regularly. If someone else is interested in other games, they are free to investigate them -- but the results won't interest me

Hrqls: I left it out because I don't play it ;-)

No, it wasn't

As of this afternoon there were only 12 players who were in the top 50 in all 4 "positive" gammon games. Here we are:

Name/Avg. Rating/Avg. Rank
arpa/2072/6.50
alanback/2049/5.00
frolind/2018/13.25
jelly/2015/18.75
qusar/2012/12.50
Pedro Martínez/1995/14.75
mrbugs001/1990/18.00
Hrqls/1987/20.00
Brian1971/1962/27.75
cindsman/1961/29.50
Zach/1936/37.50

grenv: This happens on many servers. Usually the dice you are seeing are your opponent's dice from his last roll.

WhiteTower: I used the term "single game" to distinguish it from a gammon or a backgammon. The value of a single game is equal to the current value of the cube.

Luke Skywalker: A drop in response to a double only gives up a single game, regardless of board position.

grenv: BUT be careful about resiging before bearing off -- the value of the resignation is based on the current board position, so if you resign before bearing off you will be resigning a gammon (double game), or backgammon (triple game), depending upon where your checkers sit.

pgt: True . . . but not satisfying every whim of every customer, but allocating resources optimally to attract the average customer ;-)

Walter Montego: Oh, indeed I would. I just think Fencer's time is better spent on other features. I suspect it isn't as easy to progam as one might think.

pgt: What blissful lives y'all must lead, if this is such a big problem for you!

Walter Montego: I think you just don't want to play backgammon, Walt :-) It's hard to believe such a small thing would be enough to make you quit!

playBunny: Small pleasures . . .

playBunny: Pure randomness cannot guarantee a certain percentage of outcomes in a finite number of trials.

http://money.howstuffworks.com/slot-machine.htm

Walter Montego: I agree in general that slot machines aren't programmed to pay off within a certain time, and the special advertising ploy I described is a very limited exception if it is an exception at all.

Walter Montego: The casinos here are pretty heavily regulated, and I don't think they would get away with advertising "Must hit by $200,000" or the like if what they meant was that they were going to freeze the jackpot when it reaches $199,999.99!

Here's a news story:

http://www.allvegasguide.com/press_release_headlines/2005/jumbo_jackpot.html

Walter Montego: There are some casinos here in Las Vegas, however, that advertise a guarantee that certain progressive jackpot machines will pay off by the time the jackpot reaches a particular total.

skipinnz: Absolutely, one of the crucial differences between money play and match play. Of course, in the situation you described in a money game, you very well might like to continue and play for gammon.

playBunny: Vikings specified 4-0, and at 4-0 in a 5 pt match it can only be the Crawford game!

skipinnz: Skip, I don't think you would want to offer the cube as a way of suggesting to your opponent that they resign. They can accept and recube! If you want to make that suggestion, you can do it in the chat box. Doubling when you are 1 point away from the match win is not allowed by the system because no rational player would make that offer ;-)

grenv: IMHO those who feel compelled to recite gg and gl automatically will do so whether they get a message at the end of each game or not! It would be nice if the email included the match score, though . . .

Vikings: I don't know about metal bats, I was thinking of major leaguers :-)

ajtgirl's comments remind me of baseball players who believe that a bat only has a certain number of hits in it . . . folks who will keep pouring money into a slot machine because "it has to hit soon" . . . and my own sense that life is totally unfair when I dance for the fourth straight roll against a two-point board!

playBunny: I never meant to imply that psychological factors are irrelevant :o)

grenv: In any case, we all have "perfect information" about the game of backgammon, we're just discussing labels

Walter Montego: See also http://www.thegamesjournal.com/articles/DefiningtheAbstract.shtml (backgammon is a perfect information game, but not an "abstract strategy" game due to the random element); http://www.boardgamegeek.com/geeklist.php3?action=view&listid=9930 (confusion between perfect information and complete information)

Walter Montego: Arguably backgammon is not a game of "complete information" as defined at http://en.wikipedia.org/wiki/Complete_information; however, that definition may be broad enough to include games where all the possibilities are known, even though the outcome depends upon a random element.

Walter Montego: Backgammon appears to satisfy the definition of a "perfect informatio n game" at http://www.gametheory.net/dictionary/PerfectInformation.html. Of course, your point is valid that there are unknowns in the future, but the definition focuses on information about moves that have already been made.

Marfitalu: Yes, and there's no bluffing in backgammon (it's a "perfect information" game). My point was that the mechanics of doubling can be compared to a raise in poker: The other player must agree to play the game at the higher stakes, or drop and forfeit the current stakes.

BIG BAD WOLF: In a way it's like poker, but every raise doubles the stakes.

Vikings: I don't understand your point. They can postpone making their play, but the opponent will not use any vacation time while waiting for the player to move. The same would be true in the other match.

grenv: Your original post certainly gave the impression that you DID need a lesson in statistics ;-)

playBunny: Of course :)

grenv: Ratings are an approximation and are no better than the data on which they are based. In backgammon, random factors dominate the early ratings, so a player's rating is really reliable until they have a few hundred games behind them. The ratings aren't bogus, but unquestioning reliance upon them is. They are only an indication of ability, not proof. As you have observed, playing style is the ultimate proof of ability; not even won-loss record is better in that regard.

With all this talk about the cube, I have not given enough attention to another important feature, which is the ability to earn multiple points with gammons and backgammons. (Some folks have discovered this painfully by resigning too early.) The possibility of gammon adds another strategic dimension to the game.

It's not necessary to use the cube in order to allow gammons; in multiple point matches, it would be possible to award multiple wins for gammon and backgammon. Then we could also have separate rankings for gammonish and nongammonish checker play!