playBunny: Thanks for the explanation :-)

Resher: Why would anyone want to re-roll if the first rolls were the same? And what do you mean by "simulated"? I personally never had a vision of Fencer rolling an actual pair of dice every time I click ...

Resher: Thanks for the analysis.

Of course, there's no reason to believe this phenomenon is limited to opening rolls. In general, it seems one should bear in mind the enhanced probability of duplicate or similar rolls in planning strategy.

Has anyone run a test on the distribution of single die rolls? One way that these observed deviations from the norm could arise would be if, say, the chance of rolling a 4 on a single die was significantly higher than it should be. Depending on the pseudo RNG that is used, this might be a simpler explanation than any theory involving pairs of dice.

playBunny: I think we all know the answer to that.

Just out of curiosity I looked at the 55 games in matches I have completed in 2010. There are 8 in which the first two rolls were the same (same two dice, order not considered), versus the predicted 3 and change. Both dice different, predicted 24, actual 19.

Orlandu: There is even a link to the perl script that is used, on the site's Help page:

http://www.dailygammon.com/help/#dice


Now THAT is transparency!

Orlandu: Yes. Dailygammon.com uses random numbers from random.com

Resher: Too bad, as it would probably be more meaningful to measure only the same order case. Still, based on your analysis, there does seem to be something odd going on here!

PS maybe I don't understand what you are tracking here. Can you describe exactly what you are looking for? As I understand it, you are comparing the two dice of the first roll of the game, i.e. of the first player to move, with the two dice on the next roll, i.e. the first roll of the second player to move.

Are you counting situations in which the same dice occur, but in a different order, as a match or non-match?

The probability of the same two dice occurring in the same order on the second roll is 1/36. However, the probability of the same two dice occurring in any order is 2/6 x 1/6 = 1/18, as you observe.

wetware: Good work. There certainly is a suspicious pattern. Your sample size is still quite small, however. What is needed now is a statistical analysis of the probability that this distribution could occur randomly. I.e., is it within a couple of standard deviations of the norm, or is it a one in a billion chance?

moistfinger: Your credibility is already suspect when you say you never whined before -- all real backgammon players whine about the dice ;-)

Thad: It does if he has a mathematical chance to win, and it is a very good reason to double. I was speaking of situations where the opponent has no chance to win, but for one reason or another chooses not to resign.

Nothingness: The entire purpose of the doubling cube is to force the opponent to up the stakes or lose. In a face-to-face game, players will not usually play a game to an end when the outcome is a foregone conclusion. Online, someone has to double or resign to make that happen. Given the pace of play here, some folks like to move things along as quickly as possible.

WASSAIL

Wassail started just before Christmas in 2006 with 109 players in 22 sections. There are still 6 unfinished sections in round 1. With a minimum of 26 players advancing to round 2 and a max section size of 5, we are guaranteed at least six sections, meaning that there will be at least 2 sections in round 3 -- with luck round 4 will be the final. I estimate this will finish somewhere around 2020.

The tournaments of the fathers shall be visited upon their children, unto the seventh generation!

The difficulty of writing code to deliberately skew the dice rolls is staggering. I cannot imagine it being done deliberately. This leaves open the possibility that there is some unanticipated factor that skews the randomness of the rolls. This also I consider unlikely, although I don't know precisely what random or pseudo-random number generator is used here. The fact is that out of hundreds of players, there will always be a few who are currently experiencing what appear in isolation as purposefully distorted results. This is just the result of the normal operation of the laws of chance. However, because only those few notice and report the apparent discrepancy, the anecdotal evidence always supports conspiracy theories. And backgammon players are always paranoid!

wetware: In my case, it's a matter of winding down my presence here and letting my membership lapse. I'll be back on the list briefly before too long :-)

pgt:That's no way to talk about a fellow BKer!

pgt:I think it's the answer to a riddle my father used to ask:

If a hen and a half lays an egg and a half in a day and a half, how far must a raindrop fall to split a shingle?

gogul:This whole discussion is just pterrible!

Thad:Yes, I believe a tetrahertz is a rented fish. ;-)

Czuch:This is probably also true with physical dice  :-)

CryingLoser:Are you assuming there is a separate incidence of the random number generator for each game?  I think that is very unlikely, and that it is more likely that the same RNG is used for all games on the site.  This would make it impossible for two players to anticipate any cyclical result.

paully: Even so, I think every backgammon player has occasionally felt very badly used by the dice :-)  It doesn't always help to know that even a perfectly random system can (indeed, must occasionally) mimic the behaviour of a malevolent demon!

Anjil:  Also, you did not score a backgammon (3 pts), you scored a gammon (2 pts)

tonyh:There's a lot to be said for single point matches. It's an opportunity to practice pure checker play.  It can be a lot of fun, too, when you can take chances you would not take if gammons and cubes were in play.

In discussions of this subject, I find it useful to point out that cubeless games come up in a majority of matches even when the cube is in play.  For example, there is no cube in the Crawford game, and gammons are significant only against the leader.  Post-Crawford games are almost cubeless as well, since the cube is more or less automatic.  The clearest case is when the players are tied at 1-away:  there you are in a pure cubeless situation.

So you could say that you don't need to play one-pointers in order to have the opportunity to play cubeless; or you could say that one-pointers give you a chance to practice pure checker play, which will come in handy in those 1-away, 1-away situations.

As is so often the case, it's a matter of personal preference.

playBunny:And yours, dear friend

playBunny:Lucky for me that even at my advanced age I am still able to learn and grow :-)

playBunny:I play mostly for the enjoyment of testing my skills against other players and to some extent for social interaction.  There is an egoic rush associated with a high rating, but in my saner moments I don't value that.  Of course other people do value it, but that doesn't make it important.  Importance is not purely subjective; it is an absolute truth that games and their outcomes are not important.  The most they can do is feed the ego, which is like blowing up a balloon - a biodegradable balloon!

Now, if a site is going to have a rating system, there is a certain internal logic to protecting the integrity of that system.  However, it has been demonstrated so many times that the BKR system has no integrity for reasons that have nothing to do with cheating, that it's hard to get worked up about the latter even from the standpoint of ego.

lukulus:The main reason it's not so important is, well ... that it's about backgammon.  Not even money backgammon!  A game is a game is a game ...

Constellation36:I don't think I've ever seen this phenomenon, so it must be rare, albeit not unprecedented :-)

I agree that tournaments should not be arbitrarily shortened.  I have no particular problem with tournaments that last years; I have gotten myself into tourneys with 7 day timing and regretted it, that's for sure.  There are some players on this site who will always use every available minute, that's the main reason these things are as drawn out as they are.  The only way to avoid it (if you want to) is to play tournaments with short timing and relatively few points per match; it helps if you know who the sluggards are and can avoid playing with them.

Just finished a tournament that started in December, 2005!

7 Points BackGammon > 2100 1/4

Pedro Martínez:Children, children, ... play nice.

playBunny:You might add that backgammon without the cube is an integral part of backgammon with the cube, since most matches include a Crawford game and other cube-dead situations.

aaru:I have no idea what all that means.  Give me plain old backgammon with a cube :-)

2">http://brainking.com/en/Tournaments?trg=29952&trnst=0&u=2741

2 x 7 point matches with cube, 2-day time limit, autopass

Thad:It would only be "fair" if both players were aware of the substitution, and were equally experienced in playing with the altered dice.

Thad:Someone was caught using altered dice in a European tournament.

nabla:  Not worth the effort IMHO.  The contact issue should not be too hard to resolve, but the rest would be difficult and likely error-prone.  Not to mention hard to explain to newcomers.

Except in Triple Gammon, which I don't think should be played here except with long timeout periods, the differences among backgammon, gammon and single game adversely affect only the losing player.  A player can avoid losing too many points by delaying his resignation.  A player who times out doesn't deserve too much sympathy.

nabla:  Indubitably, although this would require some more sophisticated software -- is the contact situation the only one that needs to be dealt with?

nabla:  Good point.  So, resignations in contact situations should always result in a backgammon.

Triple gammon is a special case, and I don't know what to do about that.

saeco:  I apologize if I misunderstood.  However, IMHO contact has nothing to do with the way points are awarded for a resignation.  Nor should it.  Points are properly awarded based only on the position of the resigning player's pieces.  A different rule would permit manipulation.  For example, suppose a player has not borne off and has one checker on his opponent's ace point.  The opponent has borne off all but one checker, and it sits on the opponent's two point.  The trailing player rolls the dice and gets 3-2.  If he plays the roll and his opponent moves, he is guaranteed to lose a backgammon.  He should not be able to resign (or time out) and lose a single game or a gammon.

If a player wants to avoid losing a gammon in a contact situation -- or even in the absence of contact -- he has to play until he has borne off a piece.

There are sites where a player can offer to resign a single, a gammon, or a backgammon.  This turns out not to work very well, because players may offer to resign for fewer points than the opponent is entitled to, inadvertently or intentionally.  If the opponent isn't watching carefully, he may accept and then feel (perhaps rightfully) that he was cheated.

Gordon Shumway:  You certainly should not have lost a backgammon.  Now that you mention it, I think all timeouts in Triple Gammon are awarded 5 points.  But I don't think the backgammon would be awarded outside Triple Gammon, and saeco's post is an example of that.

saeco:  Because you are correct that he lost a gammon (2 pts).  The score was 4-1 before the game started and 6-1 afterwards.  He cited it as an example of a backgammon (3 pts).  He also said that the result was impossible if the game were played out, which is incorrect; gammon was not only possible, but likely.

nabla:  I hadn't thought about the contact part -- though one would rarely resign in such a case.  Otherwise, nabla and pB have got it right.  

paully:   Actually, "Get over it" pretty much summarizes my approach to most problems :-)

Thad:  I think the relevant quantities in context would be ten or more doubles and five or more boxcars.  As far as your calcs go, I think the 10 doubles figure has to be multiplied by the combinations of 10 items chosen from 45, which I think is 45!/(10!*35!).  A comparable adjustment needs to be made to the second calc, but I don't have time to work it out :-)

Kili:  The probability is greater than zero.  Get over it.

Carl:  LOL!  Let me know when Monte Carlo switches over!